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UBC Theses and Dissertations

Effectiveness of educational computer software with hearing impaired students Bell, Charles William 1985

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EFFECTIVENESS OF EDUCATIONAL COMPUTER SOFTWARE WITH HEARING IMPAIRED STUDENTS By Charles William B e l l B.Sc, The University of B r i t i s h Columbia, 1976 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS in THE FACULTY OF GRADUATE STUDIES Department of Educational Psychology and Special Education We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1985 0 Charles William B e l l , 1985 In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbia, I agree that the Library s h a l l make i t f r e e l y available for reference and study. I further agree that permission for extensive copying of t h i s thesis for scholarly purposes may be granted by the head of my department or by h i s or her representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. The University of B r i t i s h Columbia 1956 Main Mall Vancouver, Canada V6T 1Y3 Date Syfcgjttflg DE-6 (A/M1 i i A b s t r a c t T h i s s t u d y a d d r e s s e s the e f f e c t i v e n e s s of e d u c a t i o n a l m i c r o c o m p u t e r s o f t w a r e w i t h h e a r i n g i m p a i r e d s t u d e n t s . A r e v i e w of the l i t e r a t u r e r e v e a l e d a l a r g e v o i d i n the e m p i r i c a l r e s e a r c h on t h i s t o p i c and a l s o i n d i c a t e d t h a t a l a c k of s u i t a b l e and a p p r o p r i a t e s o f t w a r e , was a major h u r d l e to the s u c c e s s f u l use of CAI w i t h h e a r i n g i m p a i r e d s t u d e n t s . T h i s s t u d y i n v e s t i g a t e d the e f f e c t i v e n e s s of a s p e c i f i c e d u c a t i o n a l m i c r o c o m p u t e r program (MECC : T r a p e z o i d s and T r i a n g l e s A r e a s ) w i t h a group of h e a r i n g i m p a i r e d s t u d e n t s . The 18 s t u d e n t s were randomly d i v i d e d i n t o two g r o u p s . One g r o u p viewed the t u t o r i a l p o r t i o n of the s o f t w a r e and t h e n worked w i t h the p r a c t i s e s e c t i o n . W h i l e the o t h e r group worked o n l y w i t h the p r a c t i s e s e c t i o n of the s o f t w a r e . T h i s was done to measure and compare the e f f e c t i v e n e s s of both p o r t i o n s of the program. The s t u d e n t s were c a r e f u l l y o b s e r v e d as t h e y i n t e r a c t e d w i t h the computer. P r o b l e m s t h e y e n c o u n t e r e d w i t h the s o f t w a r e , t h e i r a c h i e v e m e n t d u r i n g e x p o s u r e to the s o f t w a r e and on pre and p o s t t e s t s , were a l l r e c o r d e d by the e x p e r i m e n t e r . These d a t a were used to measure the changes t h a t took p l a c e due to m i c r o c o m p u t e r a p p l i c a t i o n , to e v a l u a t e the e f f e c t i v e n e s s of t h i s s o f t w a r e , t o make recommendations r e g a r d i n g the c h a r a c t e r i s t i c s r e q u i r e d to improve t h i s s o f t w a r e , and to s e t " g u i d e l i n e s " f o r the d e v e l o p m e n t of f u t u r e e d u c a t i o n a l l y e f f e c t i v e s o f t w a r e f o r the h e a r i n g i m p a i r e d . i i i The r e s u l t s r e v e a l e d t h e need f o r s o f t w a r e t h a t c o n t a i n s a m e asured and c o n t r o l l e d l e v e l of s y n t a x , more a d v a n c e d d i a g n o s t i c and r e m e d i a l c a p a b i l i t i e s , and a s i m p l i f i e d more t h o r o u g h p r e s e n t a t i o n of t h e i n f o r m a t i o n . T h i s s t u d y d e m o n s t r a t e d t he need f o r more r e s e a r c h r e l a t e d t o i d e n t i f i c a t i o n o f the i m p o r t a n t f a c t o r s and t e a c h i n g s t r a t e g i e s w h i c h make s o f t w a r e more e d u c a t i o n a l l y e f f e c t i v e f o r use w i t h h e a r i n g i m p a i r e d s t u d e n t s . i v T a b l e of C o n t e n t s Ab s t r a c t . i f L i s t of T a b l e s v i Aknowledgement v i i C h a p t e r 1: I n t r o d u c t i o n 1 C h a p t e r 2: A Condensed H i s t o r y of the use of M i c r o c o m p u t e r s and CAI w i t h the Deaf 10 C u r r e n t D e v e l o p m e n t s 13 Computer M i s u s e 19 C h a p t e r 3: A Review of the L i t e r a t u r e 21 C h a p t e r 4: R e s e a r c h D e s i g n and M e t h o d o l o g y 25 S t a t e m e n t of the P r o b l e m 25 D e f i n i t i o n of Terms 26 S u b j e c t s 26 M a t e r i a l s 28 D e s i g n 32 H y p o t h e s e s . . 35 C h a p t e r 5: R e s u l t s and D i s c u s s i o n 39 MECC M a t h e m a t i c s Volume 3 : T r a p e z o i d and T r i a n g l e A r e a s • 39 T u t o r i a l S e c t i o n 39 P r a c t i s e S e c t i o n 42 T u t o r i a l Group Case S t u d i e s 44 N o n - t u t o r i a l Group Case S t u d i e s 94 Q u a n t a t a t i v e D a t a f o r T u t o r i a l and N o n - t u t o r i a l Groups 125 C h a p t e r 6: Summary and C o n c l u s i o n s 132 T u t o r i a l S o f t w a r e : S u g g e s t e d I m p r o v e m e n t s 132 P r a c t i s e S o f t w a r e : S u g g e s t e d I m p r o v e m e n t s 138 T u t o r i a l vs N o n - t u t o r i a l A c h i e v e m e n t 142 I m p l i c a t i o n s and S u g g e s t i o n s f o r F u t u r e R e s e a r c h 143 R e f e r e n c e s 1 45 A p p e n d i x A , 148 v i L i s t of T a b l e s 1. D i s t r i b u t i o n of R e s e a r c h A r t i c l e s 22 2. R e s u l t s from the T u t o r i a l Group 126 3. R e s u l t s from the N o n - t u t o r i a l Group 126 4. R e s u l t s from the T u t o r i a l Group ....129 5. R e s u l t s from the N o n - t u t o r i a l G r o u p . . . . . 129 v i i Acknowledgement I would l i k e to e x p r e s s my thanks and a p p r e c i a t i o n to a l l t h o s e who h e l p e d me w i t h t h i s t h e s i s . T h e i r encouragement and p o s i t i v e t h o u g h t s e n a b l e d me to comp l e t e t h i s work. I w i s h to e x t e n d s p e c i a l thanks to D r . Br y a n C l a r k e , my a d v i s o r , f o r the c o u n t l e s s hours of g u i d a n c e and c o n s t r u c t i v e comments d u r i n g the w r i t i n g of t h i s t h e s i s . H i s d e d i c a t i o n and work e t h i c have made me a b e t t e r s t u d e n t and t e a c h e r . I would a l s o l i k e to thank the o t h e r member of my co m m i t t e e , Dr. D a v i d K e n d a l l . Many thanks to my c o l l e a g u e s a t K i t s i l a n o ( J e r i c h o H i l l o f f - c a m p u s ) who a s s i s t e d as d a t a c o l l e c t o r s and morale b o o s t e r s . And v e r y s p e c i a l thanks to my w i f e Susan. W i t h o u t her h e l p and encouragement o v e r the p a s t f o u r y e a r s , none of t h i s would have been p o s s i b l e . I d e d i c a t e the many l o n g h o u r s i n v o l v e d i n t h i s t h e s i s to PKB and any who f o l l o w i n h i s f o o t s t e p s . C .W.Bell 1985 1 Chapter 1 : I n t r o d u c t i o n We are only at the dawn of the e d u c a t i o n a l use of the microcomputer. I t i s much too e a r l y to see c l e a r l y what the p o t e n t i a l and a p p r o p r i a t e a p p l i c a t i o n s of the microcomputer are f o r enhancing the education of our hearing impaired students. None the l e s s , almost every a r t i c l e which d i s c u s s e s hearing impaired students and the use of microcomputers suggests that the microcomputer could be a very valuable a d d i t i o n to a teacher's armamentarium, i f i t i s a p p l i e d a p p r o p r i a t e l y . Despite the general p r e v a i l i n g a t t i t u d e that the microcomputer w i l l be a powerful and v e r s a t i l e t o o l , there are those who c r i t i c i z e and m i s t r u s t the emergence of t h i s r e l a t i v e l y new e d u c a t i o n a l a i d . They f e e l that the microcomputer i s simply a machine to e n t e r t a i n and on which to play games, and consider that i t has l i t t l e of the e d u c a t i o n a l value that others have suggested. Wright (1980), i n her paper, d i s c u s s e d the s u s p i c i o n s of both parents and educators brought about by e a r l y attempts with computer i n s t r u c t i o n . With older main frame computers, there were many breakdowns, responses were slow, the a p p l i c a t i o n s were l i m i t e d and the cost was e x o r b i t a n t . Wright s t a t e s that " i n s h o r t , there i s an inherent d i s b e l i e f that technology can do anything to r e a l l y promote e d u c a t i o n a l goals of the school" (p.16) and b e l i e v e s that "technology i s not a s o l u t i o n i t i s a resource, which must be manipulated by the teacher for the student's b e n e f i t . " ( p . 1 7 ) 2 O r i g i n a l l y a key c r i t i c i s m of Computer A s s i s t e d I n s t r u c t i o n ( C A I ) and c omputer use was t h e i n i t i a l h i g h c o s t o f t h e h a r d w a r e , but now w i t h t h e d e v e l o p m e n t of t h e m i c r o p r o c e s s o r , much c h e a p e r m i c r o c o m p u t e r s can be m a n u f a c t u r e d . I n d e e d , compared w i t h t h e o v e r a l l c o s t s of e d u c a t i n g a h e a r i n g i m p a i r e d c h i l d , t h e c o s t of a m i c r o c o m p u t e r i s n e g l i g i b l e . One of the b i g m i s t a k e s made by p e o p l e i s e q u a t i n g the m i c r o c o m p u t e r w i t h v i s u a l a i d s ( W r i g h t , 1981, p . 1 0 ) . The m i c r o c o m p u t e r r e q u i r e s a g r e a t d e a l of i n t e r a c t i o n between i t s e l f and the s t u d e n t . I t i s n o t a p a s s i v e medium of e d u c a t i o n b e c a u s e the s t u d e n t i s c o n t i n u o u s l y r e q u i r e d t o i n t e r a c t w i t h i t , s u p p l y i n g a n s w e r s and i n f o r m a t i o n . The m i c r o c o m p u t e r may of c o u r s e be u s e d s o l e l y as a v i s u a l a i d , b u t i t a l s o has the p o t e n t i a l of g o i n g f a r beyond any v i s u a l a i d s of the p a s t . Now t h a t t h e low c o s t of m i c r o c o m p u t e r s has f a c i l i t a t e d t h e i r use i n a v e r y l a r g e number of s c h o o l s , many p o s i t i v e a t t r i b u t e s have been a s s o c i a t e d w i t h t h e i r u s e . B e c a u s e s o u n d i s n o t g e n e r a l l y an i m p o r t a n t component, t h e y a r e good m a c h i n e s t o use w i t h d e a f s t u d e n t s . I n e d u c a t i o n of the h e a r i n g i m p a i r e d , t e a c h e r s g e n e r a l l y p r e s e n t i n f o r m a t i o n t o t h e s t u d e n t s , c h e c k f o r u n d e r s t a n d i n g of t h e p r e s e n t a t i o n , and r e w a r d them f o r c o r r e c t c o m p r e h e n s i o n . The m i c r o c o m p u t e r c a n p e r f o r m a l l of t h e s e f u n c t i o n s . A l l t e a c h e r s of the h e a r i n g i m p a i r e d know a b o u t t h e need f o r r e d u n d a n c y when p r e s e n t i n g new c o n c e p t s ( S m a l d i n o , 1983, p.644) and the 3 m i c r o c o m p u t e r can be u s e d v e r y e f f e c t i v e l y t o g i v e r e p e a t e d e x p o s u r e t o new t o p i c s w i t h o u t the s t u d e n t s b e c o m i n g b o r e d w i t h t h e r o u t i n e . T e a c h e r s of t h e h e a r i n g i m p a i r e d who a r e u s i n g c o m p u t e r a s s i s t e d i n s t r u c t i o n w i t h m i c r o c o m p u t e r s a r e now f i n d i n g t h a t t h e s t u d e n t s r e a l l y e n j o y l e a r n i n g i n t h i s f a s h i o n . S t u d e n t s f i n d t h e c o m p u t e r e x c i t i n g and s e l d o m t i r e o f t h e i r t a s k . Many t e a c h e r s a l s o see a g r o w t h i n t h e s t u d e n t s ' c o n f i d e n c e and s e l f - e s t e e m due t o s u c c e s s f u l i n t e r a c t i o n s w i t h the c o m p u t e r . F u r t h e r m o r e , t h e p r o g r a m s now a v a i l a b l e f o r use on m i c r o c o m p u t e r s can be u s e d not o n l y f o r t e a c h i n g new c o n c e p t s , but a l s o f o r r e m e d i a l work and r e i n f o r c e m e n t of b a s i c s k i l l s . N i c o l a y ( 1 9 8 3 ) i n h i s a r t i c l e on g r o u p l e a r n i n g and the c o m p u t e r , d i s c u s s e d what many t e a c h e r s have a l r e a d y d i s c o v e r e d . T h a t i s , t h a t t i m e s p e n t i n t e r a c t i n g a c a d e m i c a l l y w i t h the s t u d e n t s , g i v i n g them new e x p e r i e n c e s and i n f o r m a t i o n i s most r e w a r d i n g . He a l s o s u g g e s t e d t h a t s t u d e n t s do b e t t e r when t h e y a r e i n v o l v e d i n more a c a d e m i c i n t e r a c t i o n w i t h t h e i n s t r u c t o r , and showed t h a t t e a c h e r l e d g r o u p i n s t r u c t i o n i s b e t t e r t h a n i n d i v i d u a l s e a t w o r k. He p r o p o s e d t h a t t h e c a r e f u l l y managed use of m i c r o c o m p u t e r as a t e a c h e r ' s a i d i n t h e c l a s s r o o m w o u l d i n f a c t a f f o r d t h e t e a c h e r more t i m e to i n t e r a c t w i t h s t u d e n t s b e c a u s e l e s s t i m e was r e q u i r e d t o m o n i t o r t h e i r p r o g r e s s . C u r r e n t l y t h e r e i s a g r e a t d e a l of o p t i m i s m and e x c i t e m e n t a b o u t t h e o p p o r t u n i t i e s t h e m i c r o c o m p u t e r and CAI w i l l a f f o r d our h e a r i n g i m p a i r e d s t u d e n t s . The c o m p u t e r as 4 an e x t e n s i o n of t h e t e a c h e r ' s c r e a t i v i t y c a n become one of h i s / h e r b e s t m o t i v a t i o n a l t o o l s . The com p u t e r i s not i n c o m p e t i t i o n w i t h t h e t e a c h e r n o r w i l l i t r e p l a c e the t e a c h e r , b u t i t does r e p l a c e o v e r h e a d s , f l a s h c a r d s , and c h a l k . P e r h a p s t h e f i n e s t a s p e c t of t h e c o m p u t e r i s t h a t i t can be u s e d t o t e a c h a v a r i e t y of s k i l l s . I n b r i e f , modern t e c h n o l o g y has g i v e n us a v e r y p o w e r f u l e d u c a t i o n a l t o o l and i t i s now our t a s k t o l e a r n to use i t t o i t s f u l l e s t p o t e n t i a l . When a n e o p h y t e s t a r t s t o work w i t h and r e a d about c o m p u t e r s , t h e new t e r m i n o l o g y can a t t i m e s seem q u i t e e x t e n s i v e and f o r m i d a b l e , but i n r e a l i t y o n l y a few b a s i c t e r m s a r e needed t o c o n v e r s e i n " c o m p u t e r e s e " . Some of the more common t e r m s a r e h a r d w a r e , s o f t w a r e , f l o p p y d i s k , d i s k d r i v e s , memory, i n p u t and o u t p u t d e v i c e s , p r i n t e r s , modems, i n t e r f a c e , t e r m i n a l , m i c r o c o m p u t e r s , m a i n f r a m e c o m p u t e r s and g r a p h i c s . C o mputer h a r d w a r e i s s i m p l y t h e com p u t e r and i t s components s u c h as t h e p r i n t e r , t . v . m o n i t o r , d i s k d r i v e , c o m p u t e r and any o t h e r d e v i c e w h i c h can be h o o k e d i n t o the c o m p u t e r . On t h e o t h e r hand when p e o p l e d i s c u s s s o f t w a r e t h e y a r e t a l k i n g a b o u t p r o g r a m s t h a t a r e u s e d w i t h t h e c o m p u t e r . S o f t w a r e can t a k e v a r i o u s f o r m s , f r o m computer games t o m a t h e m a t i c d r i l l s . The s o f t w a r e o r p r o g r a m c o n t r o l s t h e a c t i o n s of the com p u t e r and i s s t o r e d on f l o p p y d i s k s , w h i c h a r e r o u n d v i n y l d i s k s c o v e r e d by a p r o t e c t i v e 5 1/4 i n c h s q u a r e of h a r d p l a s t i c . T h i s f l o p p y d i s k goes i n t o the 5 d i s k d r i v e w h i c h i s r e s p o n s i b l e f o r w r i t i n g ( s a v i n g ) i n f o r m a t i o n o n t o t h e d i s k and r e a d i n g i n f o r m a t i o n ( p r o g r a m s ) f r o m t h e d i s k and p l a c i n g i t i n t o t h e c o m p u t e r ' s memory where a l l d a t a p u t i n t o t h e c o m p u t e r a r e s t o r e d . I n p u t and o u t p u t d e v i c e s a r e c o m p u t e r components w h i c h make i t p o s s i b l e t o put d a t a i n t o t h e c o m p u t e r ( i n p u t ) , and g e t d a t a out of t h e c o m p u t e r ( o u t p u t ) . K e y b o a r d s , l a s e r beam p e n s , g r a p h i c s p a d s , and t h e human v o i c e a r e e x a m p l e s o f i n p u t d e v i c e s . O u t p u t d e v i c e s a r e components l i k e m o n i t o r s ( T . V . ) , p r i n t e r s (many d i f f e r e n t v a r i e t i e s ) , c o l o u r e d p l o t t e r s ( g r a p h s ) , and sound s y n t h e s i z e r s ( c o m p u t e r v o i c e s ) . T e l e p h o n e modems a r e a l s o c o n s i d e r e d i n p u t - o u t p u t d e v i c e s b e c a u s e t h e y a l l o w one m i c r o c o m p u t e r t o commmunicate w i t h o t h e r m i c r o c o m p u t e r s or w i t h l a r g e r m a i n f r a m e c o m p u t e r s u s i n g t h e t e l e p h o n e s y s t e m . A l l of t h i s e x t e r n a l h a r d w a r e ( d i s k d r i v e , i n p u t - o u t p u t d e v i c e s e t c . ) i s c o n n e c t e d t o or i n t e r f a c e d w i t h t h e c o m p u t e r . E a c h component has an i n t e r f a c e c a r d w h i c h a l l o w s i t t o be c o n n e c t e d t o the c o m p u t e r . Once t h e s e components a r e c o n n e c t e d to t h e c o m p u t e r , i t has t o t a l c o n t r o l o v e r t h e a c t i o n s of e a c h component. M a i n f r a m e c o m p u t e r s a r e l a r g e r c o m p u t e r s w h i c h many p e o p l e can use a t t h e same t i m e . The t e r m i n a l i s a n o t h e r i n p u t - o u t p u t d e v i c e w h i c h a l l o w s a c c e s s t o the m a i n f r a m e c o m p u t e r t h r o u g h a s p e c i a l t e l e p h o n e l i n e . The m i c r o c o m p u t e r , as t h e name s u g g e s t s , i s a s m a l l computer w h i c h i s t o t a l l y s e l f c o n t a i n e d . The whole c o m p u t e r f i t s on 6 t h e t o p of a desk i n t h e c l a s s r o o m and t h e r e a r e no t e l e p h o n e l i n e s o r i n d e e d any e x t r a c o s t s i n v o l v e d . G r a p h i c s a r e t h e p i c t u r e s t h a t can be p r o d u c e d on the c o m p u t e r ' s T.V. m o n i t o r . T h e s e s t i l l o r m o v i n g d r a w i n g s can be h e l p f u l b o t h i n e x p l a i n i n g c o n c e p t s on t h e c o m p u t e r and i n m a k i n g d r i l l work more e n t e r t a i n i n g f o r t h e l e a r n e r . The a c t i v i t i e s of t h e c o m p u t e r a r e c o n t r o l l e d by an e x p l i c i t s e r i e s of i n s t r u c t i o n s . T h i s s e r i e s of i n s t r u c t i o n s ( p r o g r a m ) can be w r i t t e n i n a v a r i e t y of l a n g u a g e s d e p e n d i n g on the r e q u i r e d a p p l i c a t i o n . M o st c o m p u t e r s a r e c a p a b l e of u s i n g s e v e r a l of t h e s e l a n g u a g e s . Computer l a n g u a g e s a r e b r o k e n down i n t o two g r o u p s , low l e v e l and h i g h l e v e l . H i g h l e v e l l a n g u a g e s a r e t h o s e t h a t c l o s e l y r e s e m b l e human l a n g u a g e ( B a s i c , L o g o , F o r t r a n , C o b o l , and P a s c a l e ) ( M c R i t c h i e , 1 9 8 2 ) . Low l e v e l l a n g u a g e s a r e c l o s e r to t h e i n t e r n a l l a n g u a g e of t h e com p u t e r ( m a c h i n e l a n g u a g e ) . B a s i c i s t h e l a n g u a g e t h a t most s t u d e n t s l e a r n i n s c h o o l b e c a u s e i t has a v a r i e t y of a p p l i c a t i o n s and i s e a s i e r f o r a b e g i n n e r to l e a r n . The o t h e r h i g h l e v e l l a n g u a g e s g e n e r a l l y used i n s p e c i f i c a p p l i c a t i o n s a r e L o g o f o r t h e p r o d u c t i o n of g r a p h i c s , F o r t r a n f o r m a t h e m a t i c s and s c i e n c e , C o b o l f o r b u s i n e s s and P a s c a l f o r t h e a c q u i s i t i o n of p r o g r a m m i n g s k i l l s . An example o f a low l e v e l l a n g u a g e and i t s a p p l i c a t i o n i s m a c h i n e o r a s s e m b l y l a n g u a g e u s e d i n v i d e o games and o t h e r s i t u a t i o n s where s p e e d i s i m p o r t a n t . CAI i s an a c r o n y m f o r c o m p u t e r a s s i s t e d i n s t r u c t i o n . The c o m p u t e r i s u s e d t o p r e s e n t d r i l l s , p r a c t i s e e x e r c i s e s 7 and t u t o r i a l s e q u e n c e s t o the s t u d e n t , f o r t h e p u r p o s e of t e a c h i n g f a c t s , s k i l l s and c o n c e p t s . I n most c a s e s t h e CAI m a t e r i a l i s d i v i d e d i n t o a l a r g e number of s m a l l s t e p s i n t e r s p e r s e d w i t h p e r i o d i c t e s t s d e s i g n e d t o t e s t t h e s t u d e n t ' s u n d e r s t a n d i n g . I f t h e s t u d e n t meets a c e r t a i n c r i t e r i o n i n h i s p e r f o r m a n c e t h e n he may c o n t i n u e t o t h e n e x t s t e p i n t h e l e s s o n . U s i n g CAI t h e s t u d e n t ' s work and p r o g r e s s a r e m o n i t o r e d and c o n t r o l l e d by t h e c o m p u t e r . Computer h a r d w a r e p l a y s an i m p o r t a n t p a r t i n C A I , but a more c r i t i c a l r o l e i s p l a y e d by t h e a v a i l a b l e and a p p r o p r i a t e s o f t w a r e . T h e r e a r e many d i f f e r e n t k i n d s of s o f t w a r e a v a i l a b l e f o r e d u c a t i o n a l u s e . A l i s t o f e i g h t d i f f e r e n t k i n d s ( S t a c y , 1982, p . 6 1 8 - 2 3 ) . w i t h a b r i e f e x p l a n a t i o n of e a c h i s p r e s e n t e d b e l o w . ( i ) T u t o r i a l : T h i s t y p e of s o f t w a r e i s d e s i g n e d t o t e a c h s t u d e n t s a l l o r p a r t of a new c o n c e p t . I t s t a r t s by g i v i n g t h e s t u d e n t an i n t r o d u c t i o n t o t h e c o n c e p t and t h e n a s k s q u e s t i o n s . B a s e d on t h e s t u d e n t ' s r e s p o n s e s , t h e p r o g r a m w i l l l e a d t h e s t u d e n t t h r o u g h a s e r i e s o f l e s s o n s t o b r i n g a b o u t a b e t t e r u n d e r s t a n d i n g o f t h e c o n c e p t , ( i i ) D r i l l and p r a c t i c e : T h i s t y p e of s o f t w a r e i s d e s i g n e d t o r e i n f o r c e p r e v i o u s l y a c q u i r e d c o n c e p t s . I t can be f o r m a t t e d i n many d i f f e r e n t ways : t r u e o r f a l s e ; f i l l t h e b l a n k ; m u l t i p l e c h o i c e ; o r e n t e r i n g c o r r e c t n u m b e r / l e t t e r ( m a t c h i n g ) . G r a p h i c s can a l s o be 8 u s e d t o enhance i n t e r e s t and to r e i n f o r c e a c o r r e c t r e s p o n s e . ( i i i ) S p e c i a l p u r p o s e s o f t w a r e : T h i s t y p e of s o f t w a r e i s d e v e l o p e d and i n most c a s e s w r i t t e n by t h e t e a c h e r , t o h e l p s t u d e n t s b e t t e r u n d e r s t a n d a c o n c e p t . T h i s s o f t w a r e i s t h e h a r d e s t t o o b t a i n , but i s u s u a l l y the most a p p r o p r i a t e b e c a u s e , g e n e r a l l y , t h e t e a c h e r knows t h e p r e c i s e c o n c e p t and t h e b e s t way t o t e a c h i t to p a r t i c u l a r s t u d e n t s . T h i s " t a i l o r made" s o f t w a r e i s g e n e r a l l y p r e f e r a b l e t o t h o s e p r o d u c e d c o m m e r c i a l l y , ( i v ) Games : T h i s s o f t w a r e i s g e n e r a l l y u s e d f o r f u n and e n j o y m e n t , but at the same t i m e a s s i s t s i n t h e d e v e l o p m e n t of motor s k i l l s , eye hand c o o r d i n a t i o n , r e a d i n g and o t h e r t h i n k i n g s k i l l s . Games a r e a l s o used t o e n t i c e s t u d e n t s t o work h a r d e r and l o n g e r on t u t o r i a l , d r i l l and p r a c t i c e t y p e s of s o f t w a r e , ( v ) S i m u l a t i o n : T h i s t y p e of s o f t w a r e i s u s e d t o t e a c h h i g h e r l e v e l s k i l l s w h i c h c o u l d be d i f f i c u l t i n a n o r m a l c l a s s r o o m s e t t i n g . U s i n g g r a p h i c s and d i f f e r e n t s i m u l a t e d s i t u a t i o n s , s t u d e n t s a r e f o r c e d t o t h i n k a b o u t an a p p r o p r i a t e r e s p o n s e . C o n c e p t s s u c h as a f o o d web i n a l a k e e c o s y s t e m can be t a u g h t u s i n g a s i m u l a t i o n p r o g r a m . C o m p u t e r s have been u s e d f r e q u e n t l y by e n g i n e e r s and s c i e n t i s t s t o s i m u l a t e t h e r e a l w o r l d ; and t h e s e same t e c h n i q u e s can now be used i n t h e c l a s s r o o m t o h e l p t e a c h d i f f i c u l t c o n c e p t s , ( v i ) T e a c h e r u t i l i t i e s : These a r e pr o g r a m s t h a t h e l p 9 t e a c h e r s c r e a t e a i d s f o r c l a s s r o o m u s e . P o s t e r s , c r o s s w o r d p u z z l e s , and match games a r e but a few e x a m p l e s of a i d s t h a t can r e a d i l y be c r e a t e d by the t e a c h e r w i t h t h e h e l p of t h e m i c r o c o m p u t e r , ( v i i ) A d m i n i s t r a t i o n u t i l i t i e s : T h i s t y p e of s o f t w a r e i s u s e d to h e l p i n t h e a d m i n i s t r a t i o n of a s c h o o l . C l a s s s c h e d u l i n g , r e p o r t s and a t t e n d a n c e f o r example can a l l be d e a l t w i t h u s i n g t h e s e p r o g r a m s , ( v i i i ) P rogrammer u t i l i t i e s : These a r e p r o g r a m s t h a t h e l p t h e programmer a d a p t s o f t w a r e t o s u i t h i s n e e d s . E x i s t i n g s o f t w a r e can be a l t e r e d so t h a t i t i s more a p p r o p r i a t e to b o t h t h e t e a c h e r ' s e d u c a t i o n a l g o a l s and t h e s t u d e n t ' s i n d i v i d u a l a b i l i t i e s . 10 Chapter 2 : A Condensed H i s t o r y of the use of Microcomputers and CAI with the Deaf. To obtain a c l e a r understanding of the f u t u r e p o t e n t i a l of the microcomputer as an e d u c a t i o n a l t o o l , i t i s important to review i t s development from the beginning. The h i s t o r y of the e d u c a t i o n a l use of computers with hearing impaired students p a r a l l e l s that of computer use with hearing students. In many smaller schools f o r the deaf, the computer i s a r e l a t i v e l y new e d u c a t i o n a l a i d . The high costs involved with older computer systems made i t economically d i f f i c u l t to have one i n every s c h o o l . For those schools that were large enough to i n v e s t i n computers during the "pioneer days", a t y p i c a l s c e nario f o l l o w s . In the e a r l y seventies a school would have one or two t e r m i n a l s which were connected to a large mainframe computer by telephone l i n e s . The mainframe computer was l o c a t e d i n a c e n t r a l part of the c i t y and the schools would share time on t h i s computer. At that time the software used c o n s i s t e d almost s o l e l y of language and math programs. During these i n i t i a l stages teachers n o t i c e d that students were making c o n s i d e r a b l e gains i n t h e i r computational a b i l i t i e s (Arcanin, 1979, p. 574). The computer also gave the teacher more time to give i n d i v i d u a l help. A d m i n i s t r a t o r s found that computers were reducing the cost of i n d i v i d u a l i z e d i n s t r u c t i o n , hence, when a school could a f f o r d i t and the need arose, more ter m i n a l s would be added. Indeed some p r o g r e s s i v e schools 11 went on t o h i r e c o m p u t e r l i t e r a t e p e o p l e t o h e l p d e s i g n and c r e a t e a p p r o p r i a t e s o f t w a r e . A l t h o u g h t e a c h e r s a t t h e s e s c h o o l s c o u l d see t h e enormous b e n e f i t s of t h e c o m p u t e r i n t h e i r c l a s s r o o m s , t h e r e w ere a few p r o b l e m s i n v o l v e d w i t h m a i n f r a m e c o m p u t e r s . The c o s t of i m p l e m e n t i n g t i m e - s h a r e d c o m p u t e r s e r v i c e was s u b s t a n t i a l . The i n i t i a l p u r c h a s e of h a r d w a r e s u c h as c o m p u t e r t e r m i n a l s and t e l e p h o n e modems, r e g u l a r m o n t h l y payments f o r t e l e p h o n e s e r v i c e and r o u t i n e m a i n t e n a n c e on the t e r m i n a l s and m a i n f r a m e c o m p u t e r p r o v e d to be e x p e n s i v e . L i m i t a t i o n s a l s o e x i s t e d . The s o f t w a r e c o u l d o n l y be used i n a m a i n f r a m e c o m p u t e r and due t o t h e h i g h c o s t s of t i m e s h a r i n g the s o f t w a r e c o u l d n o t be s h a r e d w i t h o t h e r s c h o o l s . T h e r e was a l s o t h e p r o b l e m of l a g t i m e between e n t e r i n g and r e c e i v i n g i n f o r m a t i o n , g r a p h i c s were v e r y l i m i t e d , and f i n a l l y a m a j o r p r o b l e m o c c u r r e d e a c h t i m e t h e m a i n f r a m e c o m p u t e r c r a s h e d and no one c o u l d a c c e s s the s y s t e m . I t became o b v i o u s t h a t a l e s s e x p e n s i v e d e l i v e r y s y s t e m was n e c e s s a r y ( A r c a n i n , 1979, p.575) i f CAI was t o have more g e n e r a l a p p l i c a t i o n . I n 1978/79 a t e c h n o l o g i c a l b r e a k t h r o u g h came w i t h the d e v e l o p m e n t of t h e s i l i c o n c h i p and t h e m i c r o p r o c e s s o r ( e s s e n t i a l l y a c o m p l e t e c o m p u t e r b u i l t i n t o a c h i p t h e s i z e o f a f i n g e r ) . T h i s advancement made p o s s i b l e t h e p r o d u c t i o n o f m i c r o c o m p u t e r s , w h i c h have many a d v a n t a g e s f o r t h e c l a s s r o o m o v e r t h e o l d e r m a i n f r a m e s y s t e m . The m i c r o c o m p u t e r has a much l o w e r i n i t i a l c o s t and t h i s i s a one t i m e c o s t (no 12 more t i m e s h a r i n g o r c o m m u n i c a t i o n l i n e r e n t a l s ) . C o n s e q u e n t l y , t h e s c h o o l s c o u l d a f f o r d more m i c r o c o m p u t e r s and e x p o s e more s t u d e n t s and t e a c h e r s t o t h e i r u s e . These m i c r o c o m p u t e r s were p o r t a b l e and had much t o o f f e r i n t h e a r e a s of c o l o u r and g r a p h i c s . R e g i o n a l s u p p o r t c e n t r e s were now e s t a b l i s h e d t o h e l p w i t h d i s t r i b u t i n g k n o w l e d g e and s o f t w a r e ( A r c a n i n , 1979, p . 5 7 6 ) . T h e r e were no c r a s h e s and no downtime t o f r u s t r a t e t e a c h e r s and s t u d e n t s a l i k e . I f one m i c r o c o m p u t e r went down, t h e o t h e r s r e m a i n e d w o r k i n g . Now t e a c h e r s were not l i m i t e d by t h e s o f t w a r e a v a i l a b l e t h r o u g h t h e t i m e s h a r i n g s y s t e m and t h e y c o u l d c u s t o m i z e s o f t w a r e by t a i l o r i n g i t t o t h e i r own n e e d s . W i t h t h e b i r t h of t h e m i c r o c o m p u t e r more s c h o o l s c o u l d now a f f o r d t o g e t i n t o CAI and c o m p u t e r s c i e n c e s t u d i e s . T h i s has spawned an i n c r e d i b l e g r o w t h i n the v a r i e t y and vo l u m e of e d u c a t i o n a l s o f t w a r e a v a i l a b l e t o t o d a y ' s e d u c a t o r s . New s o f t w a r e i s d e v e l o p e d e v e r y day and anyone i n v o l v e d i n t h e f i e l d of c o m p u t e r s c i e n c e i s aware t h a t a g r e a t d e a l of r e a d i n g i s n e c e s s a r y to keep up w i t h t h e t e c h n o l o g i c a l a d v a n c e s i n t h e c o m p u t e r i n d u s t r y . Now w i t h t h e m i c r o c o m p u t e r f i r m l y e s t a b l i s h e d i n our s o c i e t y and i n e d u c a t i o n a l s y s t e m s , i t i s i n t e r e s t i n g to a s s e s s i t s i m p a c t . What t y p e s o f s o f t w a r e a r e b e i n g used w i t h h e a r i n g i m p a i r e d s t u d e n t s ? How u s e f u l i s t h i s s o f t w a r e ? How a r e c o m p u t e r s b e i n g e d u c a t i o n a l l y m i s u s e d ? What a r e some o f t h e new e x c i t i n g a d v a n c e s i n t h e c o m p u t e r f i e l d t h a t c o u l d be s i g n i f i c a n t f o r h e a r i n g i m p a i r e d s t u d e n t s and t h e i r 13 t e a c h e r s ? A n s w e r s t o t h e s e and o t h e r p e r t i n e n t q u e s t i o n s a r e f o u n d i n the r e c e n t l i t e r a t u r e . 2.2 C u r r e n t D e v e l o p m e n t s P r o g r a m s t h a t h e l p t o t e a c h r e a d i n g , l a n g u a g e , m a t h e m a t i c s , s p e l l i n g , s c i e n c e , s o c i a l s t u d i e s , and o t h e r c o n t e n t a r e a s a r e now a v a i l a b l e and some s o f t w a r e p r o g r a m s have been d e v e l o p e d e s p e c i a l l y f o r use w i t h h e a r i n g i m p a i r e d s t u d e n t s . One s u c h p r o g r a m t e a c h e s l i p r e a d i n g s k i l l s ( H i g h t , 1 9 8 2 ) . The word b e i n g p r o n o u n c e d i s shown at the b o t t o m of t h e m o n i t o r and the l i p shape and a r t i c u l a t i o n i s shown i n t h e s p a c e a b o v e . O t h e r s o f t w a r e p a c k a g e s have been d e v e l o p e d to t e a c h s i g n l a n g u a g e ( J o h n s t o n , 1 9 8 2 ) . U s i n g m i c r o c o m p u t e r g r a p h i c s and a n i m a t i o n , t h i s p r o g r a m h e l p s to t e a c h t h e s t u d e n t new s i g n s and i m p r o v e r e a d i n g s k i l l s . A f u r t h e r p r o g r a m has been d e v e l o p e d t o h e l p t h e t e a c h e r of the d e a f t e a c h s p e e c h and has d i a g n o s t i c and p r e s c r i p t i v e c o m ponents b a s e d on t h e LING m o d e l ( S t o k e r , 1 9 8 3 a ) . The p r o g r a m p r o m p t s i n f o r m a t i o n f r o m t h e t e a c h e r and t h e n s p e c i f i e s what i s t o be t a u g h t as a n e x t s t e p . I t a l s o p r o v i d e s s t r a t e g i e s f o r a c h i e v i n g t h e g o a l s and k e e p s a p e r m a n e n t r e c o r d of t h e s t u d e n t ' s p r o g r e s s . Q u i g l e y ' s T e s t o f S y n t a c t i c A b i l i t i e s i s a l s o now a v a i l a b l e f o r A p p l e I I c o m p u t e r s ( J o n e s , 1 9 8 2 ) . B e c a u s e math i s a s u b j e c t w h i c h i n v o l v e s a g r e a t d e a l of d r i l l and p r a c t i c e , i t i s n o t u n e x p e c t e d t h a t t h e most common f o r m s of s o f t w a r e a r e f o u n d i n t h i s c u r r i c u l u m a r e a . C a s t l e ( 1 9 8 2 ) has f o u n d t h a t t h e s o f t w a r e o r i e n t a t e d f o r h e a r i n g s t u d e n t s i s " s o metimes j u s t as good o r b e t t e r t h a n m a t h e m a t i c s s o f t w a r e g e a r e d f o r t h e h e a r i n g i m p a i r e d " ( p . 4 9 5 ) . T h e r e a r e math p r o g r a m s t h a t a l l o w t h e s t u d e n t to p r a c t i s e by h i m s e l f o r compete a g a i n s t the c o m p u t e r or a n o t h e r s t u d e n t . The c o m p u t e r not o n l y c o n t r o l s t h e pace and a d v a n c e m e n t of t h e m a t e r i a l , but a l s o k e e p s a r e c o r d of the s t u d e n t ' s work and p r o g r e s s . Most of t h e s o f t w a r e u t i l i z e s i m m e d i a t e f e e d b a c k and e x c i t i n g g r a p h i c s to h e i g h t e n i n t e r e s t . One p r o g r a m ( M e l b o r p ) a l l o w s t h e s t u d e n t t o p l a y a s h o r t game i f he o b t a i n s enough c o r r e c t a n s w e r s ( B a r d e n s t e i n , 1 9 8 2 ) . A l t h o u g h some e x c e l l e n t p r o g r a m s a r e a v a i l a b l e , t h e b i g g e s t p r o b l e m i n u s i n g CAI w i t h h e a r i n g i m p a i r e d s t u d e n t s i s t h e u n f o r t u n a t e l a c k of a p p r o p r i a t e s o f t w a r e . M o st of t h e c o m m e r c i a l l y a v a i l a b l e s o f t w a r e i s l a n g u a g e bound and not a l w a y s a p p r o p r i a t e f o r h e a r i n g i m p a i r e d s t u d e n t s . T h i s l a c k o f s o f t w a r e has f o r c e d t e a c h e r s of t h e d e a f t o become more r e s o u r c e f u l . They must e v a l u a t e and c r i t i c a l l y a s s e s s a v a i l a b l e s o f t w a r e and use o n l y t h o s e p r o g r a m s w h i c h a r e a t an a p p r o p r i a t e c o m p r e h e n s i o n l e v e l f o r t h e i r s t u d e n t s and t h e y must make a d a p t a t i o n s t o c o m m e r c i a l l y a v a i l a b l e s o f t w a r e , s u c h as r e v i s i n g t h e d i r e c t i o n s and s i m p l i f y i n g the v o c a b u l a r y , t o make i t meet s p e c i f i c l e a r n i n g o b j e c t i v e s . An even b e t t e r s o l u t i o n t o t h i s p r o b l e m i s f o r t e a c h e r s t o p r o d u c e the s o f t w a r e . Teacher-made s o f t w a r e i s o b v i o u s l y g o i n g t o be more a p p r o p r i a t e b o t h f o r t h e l e v e l of the s t u d e n t s and f o r s p e c i f i c l e a r n i n g o b j e c t i v e s . The p r o b l e m s 15 w i t h m a k i n g a d a p t a t i o n s t o c o m m e r c i a l s o f t w a r e o r c r e a t i n g o n e's own s o f t w a r e a r e t h a t i t t a k e s a l o n g t i m e and demands a g r e a t d e a l of e x p e r t i s e . M o st t e a c h e r s have l i t t l e of one, o t h e r , o r b o t h . A t t h e C a l i f o r n i a S c h o o l f o r t h e Deaf a t F r e m o n t , t h e y e x p e r i e n c e d many f r u s t r a t i o n s t r y i n g to f i t a v a i l a b l e s o f t w a r e f o r t h e i r s t u d e n t s ' n e e d s , u n t i l t h e y d e v e l o p e d a new c o n c e p t i n CAI c a l l e d " a u t h o r i n g " ( S l o v i c k , 1 9 8 2 ) . T h e s e a u t h o r i n g p r o g r a m s a l l o w t e a c h e r s w i t h l i t t l e o r no c o m p u t e r e x p e r i e n c e t o c r e a t e and i l l u s t r a t e c o m p u t e r i z e d l e s s o n m a t e r i a l s w h i c h a r e s p e c i f i c t o t h e i r s t u d e n t s ' i n s t r u c t i o n a l n e e d s . O t h e r s c h o o l s a r e u s i n g a team a p p r o a c h . T e a c h e r s d e s i g n t h e c o n t e n t and the g r a p h i c s t h e y want i n a p r o g r a m and a programmer t a k e s on the l o n g and d i f f i c u l t t a s k of w r i t i n g t h e p r o g r a m . T h i s a p p r o a c h g e n e r a l l y i s v e r y c o s t l y . One of t h e m a j o r h u r d l e s t o the s u c c e s s f u l use of CAI w i t h h e a r i n g i m p a i r e d s t u d e n t s i s t h e l a c k of s u i t a b l e s o f t w a r e . I t i s up t o b o t h a d m i n i s t r a t o r s and t e a c h e r s to d e v e l o p and a q u i r e s o f t w a r e t h a t can be us e d t o o b t a i n s p e c i f i c l e a r n i n g g o a l s w i t h o u r h e a r i n g i m p a i r e d s t u d e n t s . G a l l a u d e t C o l l e g e i s p r e s e n t l y c o m p i l i n g a c a t a l o g u e of s o f t w a r e u s e d by s c h o o l s f o r t h e d e a f i n N o r t h A m e r i c a and i t w i l l i n c l u d e b o t h c o m m e r c i a l and t e a c h e r made s o f t w a r e . The V o l t a R e v i e w ( D e c . 1 9 8 3 ) , i n r e c o g n i t i o n o f t h e p o t e n t i a l of t h e m i c r o c o m p u t e r and C A I , has s t a r t e d a new s e c t i o n of t h e j o u r n a l c a l l e d , "The V o l t a S o f t w a r e R e v i e w " w h i c h a c c o r d i n g t o S t o k e r ( 1 9 8 3 b ) w i l l " p r o v i d e an i n - d e p t h e v a l u a t i o n of e d u c a t i o n a l c o m p u t e r s o f t w a r e t h a t i s s p e c i f i c a l l y d e s i g n e d f o r h e a r i n g i m p a i r e d l e a r n e r s , as w e l l as o t h e r s o f t w a r e w i t h s i g n i f i c a n t p o t e n t i a l a p p l i c a t i o n t o t h i s p o p u l a t i o n " ( p . 3 5 6 ) . H o p e f u l l y i n i t i a t i v e s s u c h as t h e s e w i l l p r o v e t o be t h e b e g i n n i n g of a c o o p e r a t i v e a p p r o a c h t o w a r d t h e s o l u t i o n o f t h i s p r o b l e m . A l t h o u g h t h e r e have been many s o f t w a r e p r o g r a m s d e v e l o p e d t o h e l p t e a c h s t u d e n t s , t h e r e a r e a l s o o t h e r s i n t e n d e d t o h e l p t e a c h e r s p r e p a r e l e a r n i n g a i d s , r e c o r d s t u d e n t s ' p r o g r e s s , and a s s e s s s t u d e n t s ' a b i l i t i e s . These t e a c h e r u t i l i t y p r o g r a m s a l l o w t e a c h e r s t o c o n s t r u c t c r o s s w o r d p u z z l e s , word f i n d s , c o m p u t e r t e s t s and v a r i o u s o t h e r c o m p u t e r g e n e r a t e d e d u c a t i o n a l a i d s . T hese p r o g r a m s can save t e a c h e r s a g r e a t d e a l of t i m e , and h e l p t o c r e a t e e d u c a t i o n a l a i d s t h a t can be u s e d w i t h o r w i t h o u t t h e c o m p u t e r . The C a l i f o r n i a S c h o o l f o r t h e Deaf a t F r e m o n t ( I r w i n 1982) has d e v e l o p e d a c o m p u t e r i z e d l e s s o n p l a n n e r t h r o u g h w h i c h a t e a c h e r i s a b l e t o i n f l u e n c e t h e c h o i c e of l e s s o n s done by e a c h s t u d e n t on t h e c o m p u t e r . T h i s p r o g r a m a l l o w s a t e a c h e r t o s e l e c t t h e l e s s o n s t h a t a s t u d e n t must work t h r o u g h and f r e e s h e r f r o m t h e need t o d i r e c t t h e s t u d e n t e v e r y few m i n u t e s . Many p r o g r a m s h e l p t e a c h e r s by r e c o r d i n g and s t o r i n g i n f o r m a t i o n a b o u t a s t u d e n t ' s p e r f o r m a n c e on a s e r i e s of l e s s o n s . L a t e r t h e t e a c h e r can c h e c k t h e s t u d e n t ' s s c o r e s and make a d e c i s i o n on advancement or r e m e d i a t i o n . 17 Computer A s s i s t e d E v a l u a t i o n (CAE) i s a l s o b e i n g used i n many s c h o o l s t o a n a l y s e a s t u d e n t ' s l a n g u a g e s k i l l s ( R i l e y , 1 9 8 3 ) and t o a s s e s s c u r r i c u l u m s t r e n g t h s and w e a k n e s s e s . Once t h e s t u d e n t ' s w e a k n e s s e s have been d i s c o v e r e d , t h e n CAI i s p r o v i d e d t o s t r e n g t h e n t h e s e a r e a s . A n o t h e r CAE p r o g r a m i s u s e d t o d e t e r m i n e how a s t u d e n t d i s c r i m i n a t e s — a u d i t o r i a l l y o r v i s u a l l y ( F u l t o n , 1 9 8 3 ) . A number of v i s u a l and a u d i t o r y s t i m u l i a r e g i v e n to the s t u d e n t and the s t u d e n t ' s r e s p o n s e s a r e r e c o r d e d by the c o m p u t e r . T h e r e a r e many s o f t w a r e p a c k a g e s a v a i l a b l e w h i c h h e l p i n c l a s s r o o m management and d e p e n d i n g on t h e p r o g r a m , a v a r i e t y o f d u t i e s can be h a n d l e d by t h e c o m p u t e r . A t t e n d a n c e , g r a d e s , p r o g r e s s r e p o r t s , t e s t e v a l u a t i o n and m o n i t o r i n g t h e p r o g r e s s of i n d i v i d u a l s t u d e n t s a r e j u s t a few of the c h o r e s t h a t the c o m p u t e r can h e l p t h e t e a c h e r a c c o m p l i s h . One of t h e n ewest and most e x c i t i n g t r e n d s i n CAI f o r t h e h e a r i n g i m p a i r e d has o c c u r r e d b e c a u s e of t h e a b i l i t y to i n t e r f a c e a v i d e o t a p e r e c o r d e r w i t h a m i c r o c o m p u t e r . C o m p uter a s s i s t e d v i d e o i n s t r u c t i o n ( C A V I ) c o m b i n e s t h e i n t e r a c t i o n q u a l i t i e s of t h e m i c r o c o m p u t e r w i t h t h e v i s u a l i m p a c t of t h e v i d e o t e r m i n a l ( D i l l i n g h a m , 1 9 8 2 ) . Most of t h e i n s t r u c t i o n comes f r o m t h e v i d e o t e r m i n a l , but t h e p a c i n g , r e i n f o r c e m e n t , r e v i e w , e v a l u a t i o n and n o t e t a k i n g i s c a r r i e d o u t by t h e m i c r o c o m p u t e r . CAVI i s much l i k e CAI b e c a u s e the s t u d e n t i s p r e s e n t e d w i t h i n f o r m a t i o n , g i v e s a r e s p o n s e to q u e s t i o n s and i s n e x t p r o v i d e d w i t h f e e d b a c k d e p e n d i n g on 18 h i s / h e r r e s p o n s e . F o r e xample t h e v i d e o t a p e s t o p s and a q u e s t i o n i s a s k e d . I f an i n c o r r e c t r e s p o n s e o c c u r s the v i d e o t a p e m a c h i n e r e w i n d s and t h e m a t e r i a l i s p r e s e n t e d a g a i n ( N e w e l l , 1 9 8 3 ) . The b i g d i f f e r e n c e between CAI and CAVI i s t h a t CAVI i s n o t l i m i t e d t o c o m p u t e r t e x t o r s i m p l i f i e d g r a p h i c s . W i t h C A V I , o p t i o n s e x i s t t o use c o m p u t e r t e s t s and g r a p h i c s or v i d e o t a p e s c e n e s o r b o t h . When compared w i t h t h e s i m p l e r g r a p h i c s of t h e c o m p u t e r , t h e m o v i e - l i k e q u a l i t y o f t h e v i d e o t a p e may w e l l have b e t t e r a t t e n t i o n k e e p i n g q u a l i t i e s . The one p r e v i o u s p r o b l e m w i t h u s i n g v i d e o t a p e was t h a t i t was a l i n e a r s e q u e n c e and few v i d e o t a p e m a c h i n e s gave t h e random a c c e s s f e a t u r e t h a t i s needed t o r e v i e w o r r e i n f o r c e a c o n c e p t , but by u s i n g a m i c r o c o m p u t e r w i t h t h e v i d e o t a p e , t o t a l f l e x i b i l i t y i s p o s s i b l e on t h e t a p e m a t e r i a l p r e s e n t e d . CAVI t h e n c o m b i n e s t h e b e s t q u a l i t i e s o f b o t h m e d i a . As w i t h C A I , t h e h e a r t of CAVI i s t h e s o f t w a r e . S o f t w a r e f o r CAVI i s d e s i g n e d much l i k e t h e B l o c k s s y s t e m c o n c e p t i n CAI and a l l o w s t h e t e a c h e r t o c r e a t e p r o g r a m s ( a c t i v i t i e s ) f o r t h e s t u d e n t t o u s e . The t e a c h e r i s f r e e t o c h o o s e n o t o n l y t h e s o u r c e and c o n t e n t of t h e i n f o r m a t i o n p r e s e n t e d t o t h e s t u d e n t , but a l s o , t h e q u e s t i o n s t o be a s k e d . The t e a c h e r a l s o p u t s i n t h e answer o p t i o n s and c o n t r o l s t h e m a c h i n e ' s r e s p o n s e t o t h e s t u d e n t ' s a n s w e r s ( D i l l i n g h a m , 1 9 8 2 ) . D u r i n g t h e e n t i r e d e v e l o p m e n t of the s o f t w a r e , t h e t e a c h e r can c h o o s e t o use t h e c o m p u t e r , the v i d e o t a p e , or b o t h t o p r e s e n t m a t e r i a l . 19 Now t h a t our t e c h n o l o g y has g i v e n us t h e m i c r o c o m p u t e r and t h e VCR ( v i d e o c a s s e t t e r e c o r d e r ) , t h e i r m a r r i a g e as an e d u c a t i o n a l t o o l may i n t h e i m m e d i a t e f u t u r e p r o v i d e t h e u l t i m a t e a i d f o r t e a c h e r s o f t h e d e a f . The mind b o g g l e s a t t h e e d u c a t i o n a l v a l u e made a v a i l a b l e t h r o u g h CAVI f o r the i n s t r u c t i o n of h e a r i n g i m p a i r e d s t u d e n t s . Any c o n c e p t t h a t one w i s h e s t o t e a c h can be b r o u g h t i n t o t h e c l a s s r o o m i n l i v i n g c o l o u r . Many h i g h e r l e v e l c o n c e p t s w h i c h e i t h e r f r u s t r a t e d s t u d e n t s o r were n o t a t t e m p t e d , can now be m a s t e r e d by v i s u a l l y o r i e n t e d h e a r i n g i m p a i r e d s t u d e n t s . The a b i l i t y t o show T.V. s e q u e n c e s t o e x p l a i n a c o n c e p t w i l l , w i t h o u t d o u b t , make i t much e a s i e r t o comprehend. Money and s o f t w a r e a r e now needed t o g i v e CAVI an o p p o r t u n i t y t o p r o v e i t s w o r t h . 2.3 Computer M i s u s e As w i t h any m a c h i n e , t h e r e i s t h e p o t e n t i a l f o r a p p r o p r i a t e and i n a p p r o p r i a t e a p p l i c a t i o n s . The a v a i l a b l e l i t e r a t u r e g i v e s v e r y few e x a m p l e s o f c o m p u t e r m i s u s e , h o w e v e r c a s e s do e x i s t . One s u c h e x a m p l e has t h e c o m p u t e r b e i n g u s e d as a r e c o r d e r of i n f o r m a t i o n on an e l a b o r a t e s c o r e s h e e t f o r a s i g n l a n g u a g e t e s t ( G r o s m a n , 1 9 8 3 ) . I t w o u l d h a v e been much s i m p l e r and l e s s t i m e c o n s u m i n g i f t h e i n f o r m a t i o n had been r e c o r d e d on p a p e r and t h e n r e m e d i a t i o n d i s c u s s e d w i t h t h e s t u d e n t a f t e r w a r d s . I n s t e a d , a r e c o r d e r w a t c h e d t h e s t u d e n t ' s p e r f o r m a n c e o n l y to e n t e r t h e d a t a w i t h g r e a t d e t a i l i n t o t h e c o m p u t e r . A t t h e end of t h i s l e n g t h y p r o c e s s t h e c o m p u t e r t e l l s t h e s t u d e n t w h i c h a r e a s needed 20 i m p r o v e m e n t . T h i s w h o l e p r o c e d u r e w o u l d have been more p r o d u c t i v e i f t h e r e had been l e s s t i m e s p e n t e n t e r i n g c o p i o u s q u a n t i t i e s of d a t a i n t o the c o m p u t e r and more t i m e g i v e n to r e m e d i a t i o n i m m e d i a t e l y a f t e r e a c h t r i a l . Many p e o p l e w i l l be c a u g h t up i n t h e e x c i t e m e n t of u s i n g t h e m i c r o c o m p u t e r w i t h t h e i r s t u d e n t s , b u t t h i s e n t h u s i a s m s h o u l d not l e a d down t h e " s o f t w a r e " g a r d e n p a t h . The v a l u e o f s o f t w a r e s h o u l d be e x a m i n e d b e f o r e money i s s p e n t b e c a u s e t h e r e a r e some s o f t w a r e p a c k a g e s t h a t s h o u l d s t a y b e h i n d when p u r c h a s e s a r e made. I t i s i m p o r t a n t to e n s u r e t h a t t h e s o f t w a r e c h o s e n i s m u l t i f u n c t i o n a l and has s e v e r a l l e v e l s of d i f f i c u l t y ( F l e m i n g , 1 9 8 3 ) . I t s h o u l d a l s o a l l o w t e a c h e r s t o change o p t i o n s f o r i n d i v i d u a l s t u d e n t s and p e r m i t s u f f i c i e n t f l e x i b i l i t y t o meet a number of e d u c a t i o n a l n e e d s . 21 C h a p t e r 3 : A R e v i e w of t h e R e s e a r c h I t i s r e v e a l i n g t o r e a d t h e v a r i o u s r e s e a r c h a r t i c l e s t h a t a p p e a r i n t h e j o u r n a l s and p a p e r s c o n c e r n e d w i t h e d u c a t i o n of the d e a f . Of t h e a r t i c l e s u n c o v e r e d ( s e e a t t a c h e d b i b l i o g r a p h y ) , o n l y f i v e d e a l t a t a l l w i t h any k i n d o f measurement of c o l l e c t e d d a t a . Of t h e f i v e e m p i r i c a l s t u d i e s , two were c o m p l e t e d i n 1 9 7 3 , and one e a c h i n 1974, 1 9 7 5 , and 1983. As w o u l d be e x p e c t e d , t h e 1973-1975 s t u d i e s were v e r y g e n e r a l i n s c o p e . One ( S u p p e s , 1973) f o u n d t h a t CAI d i d i n c r e a s e math c o m p u t a t i o n a l s k i l l s . The s e c o n d p r o j e c t ( F l e t c h e r , S u p p e s , 1973) i n i t i a t e d a l a r g e s c a l e use o f CAI f o r s e v e r a l s u b j e c t s ( a l g e b r a , l o g i c , c o m p u t e r p r o g r a m i n g , and b a s i c E n g l i s h ) i n s c h o o l s f o r t h e d e a f and showed t h a t CAI c o u l d be of b e n e f i t f o r h e a r i n g i m p a i r e d s t u d e n t s . The t h i r d s t u d y ( F l e t c h e r , 1974) was s i m i l i a r i n s c o p e and outcome to t h e F l e t c h e r - S u p p e s p r o j e c t . The f o u r t h s t u d y ( M o r g a n , 1975) e v a l u a t e d a m a t h e m a t i c s and r e a d i n g CAI p r o g r a m . M o r g a n , c o n c l u d e d t h a t n o t o n l y was CAI b e n e f i c i a l f o r the d e a f , but a l s o t h a t t e a c h e r s , s t u d e n t s , and p a r e n t s r e a c t e d f a v o r a b l y t o w a r d s i t s u s e . The f i n a l s t u d y ( S m a l d i n o e t a l , 1983) was d e s i g n e d t o c o n t r a s t t h e e f f i c i e n c y of t e a c h e r d i r e c t e d and c o m p u t e r b a s e d i n s t r u c t i o n f o r h e a r i n g i m p a i r e d s t u d e n t s . The r e s u l t s showed t h a t m i c r o c o m p u t e r i n s t r u c t i o n a p p e a r e d t o i n c r e a s e i n s t r u c t i o n a l e f f i c e n c y . The f o u r e a r l i e r s t u d i e s were s i m p l e i n s c o p e , d e s i g n , and f i n d i n g s but t h e l a t e r s t u d y i s a s t a r t t o w a r d s a f o c u s on some of t h e i m p o r t a n t p r o b l e m s a s s o c i a t e d w i t h t h e use of 22 C A I . O v e r a l l t h e r e were few a t t e m p t s t o p r o v i d e e v i d e n c e of s p e c i f i c c h anges t h a t had o c c u r r e d w i t h h e a r i n g i m p a i r e d l e a r n e r s as a r e s u l t o f m i c r o c o m p u t e r u s e . The 79 a r t i c l e s / b o o k s f o u n d i n t h e b i b l i o g r a p h y d a t e b a c k t o 1969, b u t t h e m a j o r i t y were w r i t t e n b e t ween 1979 and 1983 ( s e e T a b l e 1 ) . Of the few n o n e m p i r i c a l a r t i c l e s t h a t d i d t r y t o make some k i n d of j u d g e m e n t on m i c r o c o m p u t e r u s e , a l l f o u n d a g a i n i n s t u d e n t a b i l i t y and were v e r y p o s i t i v e t o w a r d m i c r o c o m p u t e r a p p l i c a t i o n s . T a b l e 1 ( 1 ) D i s t r i b u t i o n of r e s e a r c h a r t i c l e s C a t e g o r y Number ( 1 ) D e s c r i p t i o n o f CAI use i n a p r o g r a m f o r 13 t h e h e a r i n g i m p a i r e d . [ 13, 2 3 , 26, 3 1 , 3 8 , 4 1 , 4 2 , 44, 4 5 , 4 9 , 52, 5 3 , 62 ] ( 2 ) CAI i n g e n e r a l ( w i t h h e a r i n g i m p a i r e d s t u d e n t s ) . 22 f 15, 18, 2 1 , 24, 2 5 , 3 5 , 36, 46, 4 7 , 4 8 , 5 0 , 54, 63 , 6 5 , 6 8 , 6 9 , 7 2 , 7 3 , 7 5 , 7 6 , 7 7 , 78 ] ( 3 ) S o f t w a r e 32 [ 1, 2, 7, 8, 1 1 , 12, 13, 17, 19, 20, 24, 2 5 , 27, 30, 3 1 , 3 2 , 3 3 , 34, 3 9 , 4 9 , 50, 52, 55, 56, 5 9 , 60, 6 1 , 6 3 , 6 6 , 6 7 , 74, 78 ] ( 4 ) H a r d w a r e 10 [ 1, 4, 13, 17, 2 1 , 2 8 , 4 7 , 52, 67, 78 ] ( 5 ) E m p i r i c a l r e s e a r c h 5 [ 14, 16, 3 7 , 5 7 , 64 ] ( 6 ) Computer a s s i s t e d v i d e o i n s t r u c t i o n ( C A V I ) 7 [ 5, 10, 2 2 , 4 0 , 4 3 , 5 5 , 79 ] ( 7 ) C o m p u t e r s i n g e n e r a l 9 [ 1, 3, 6, 9, 2 9 , 5 1 , 58, 7 1 , 78 ] [ ( 1 ) see a r t i c l e s l i s t e d i n A p p e n d i x A ] 23 The a r t i c l e s d i s c u s s e d a v a r i e t y of t o p i c s , but the most common was an e x p l a n a t i o n of how p e o p l e were u s i n g c o m p u t e r s and the a c c u r i n g b e n e f i t s . O t h e r s d i s c u s s e d a v a i l a b l e s o f t w a r e , e x p l a i n e d how the s o f t w a r e w o r k e d and o u t l i n e d the k i n d of h a r d w a r e needed t o r u n t h e s o f t w a r e and a few a d i s c u s s e d the e s t a b l i s h m e n t of a c omputer l a b i n a s c h o o l . A l t h o u g h most of t h e a r t i c l e s a r e h e l p f u l and i n f o r m a t i v e , v e r y few r e s e a r c h e r s have as y e t t a k e n up t h e c h a l l e n g e of m e a s u r i n g t h e c h a n g e s t h a t t a k e p l a c e t h r o u g h t h e use of m i c r o c o m p u t e r s , o r of l o o k i n g a t how s t u d e n t s l e a r n u s i n g m i c r o c o m p u t e r s . W i t h o u t a n s w e r s t o t h e s e and o t h e r q u e s t i o n s , t h e t r u e p o t e n t i a l of t h e m i c r o c o m p u t e r may not be f u l l y r e a l i z e d . The p o t e n t i a l f o r c o m p u t e r use i n c l a s s r o o m s f o r the h e a r i n g i m p a i r e d i s i n d e e d g r e a t . T h e r e i s no q u e s t i o n but c o m p u t e r s w i l l be u s e d b o t h as t e a c h i n g a i d s ( c o m p u t e r a s s i s t e d i n s t r u c t i o n ) and f o r e d u c a t i n g our s t u d e n t s i n p r o g r a m m i n g s k i l l s and c o m p u t e r , l i t e r a c y . One needs o n l y to p i c k up t h e n e w s p a p e r t o l e a r n of t h e e x c i t i n g d e v e l o p m e n t s i n t he c o m p u t e r i n d u s t r y . I t i 6 w i d e l y h e l d t h a t o v e r the n e x t decade c o m p u t e r s w i l l d r a s t i c a l l y change a l l of our l i v e s , e s p e c i a l l y now t h a t c o m p u t e r s a r e b e c o m i n g more u s e r f r i e n d l y , w i t h t h e r e s u l t t h a t b o t h s t a f f and s t u d e n t s can become c o m p e t e n t programmers ( S t u c k l e s s , 1 9 8 3 ) . P r o gramming i s a v a l u a b l e s k i l l t o l e a r n b e c a u s e i t e n a b l e s s t u d e n t s t o b r e a k down p r o b l e m s i n t o p a r t s and a n a l y s e and r e c o n s t r u c t 24 t h a t i n f o r m a t i o n i n a m e a n i n g f u l way. Computer a s s i s t e d i n s t r u c t i o n can and has been u s e d s u c c e s s f u l l y by d e a f s t u d e n t s ( F l e t c h e r , 1973) and many c o m p u t e r s y s t e m s a r e now b e i n g d e v e l o p e d s p e c i f i c a l l y t o a i d t h e d e a f . G e n e r a l l y i m p r o v e d a c a d e m i c p r o g r e s s has been s e e n i n s t u d e n t s who g e t i n c r e a s e d p r a c t i s e t i m e on t h e computer t h e p o t e n t i a l f o r ^ t h e f u t u r e i s v e r y e x c i t i n g and i s o n l y l i m i t e d by t h e q u a l i t y and q u a n t i t y of a p p r o p r i a t e s o f t w a r e t h a t i s made a v a i l a b l e . O ver t h e n e x t few y e a r s of t r i a l and e r r o r we w i l l h o p e f u l l y d e t e r m i n e t h e c h a r a c t e r i s t i c s of s o f t w a r e w h i c h b e s t meet our r e q u i r e m e n t s . T h r o u g h t h i s l e a r n i n g p r o c e s s we w i l l become more s k i l l e d a t d e s i g n i n g s o f t w a r e to meet our n e e d s . C o m p u t e r s w i l l s t i l l be h e r e c h a n g i n g and i m p r o v i n g , but t h e t e a c h e r w i l l be t h e one to d e c i d e when and how t o use t h e t e c h n o l o g y . I n t h e f u t u r e , c o m p l e m e n t i n g c o n v e n t i o n a l e d u c a t i o n a l p r a c t i c e s w i t h m i c r o c o m p u t e r s u p p o r t w i l l p r o b a b l y be the t e a c h e r ' s main r e s p o n s i b i l i t y . S o f t w a r e i s t h e c r u x of t h e w h o l e s y s t e m . Once s o f t w a r e i s d e v e l o p e d t h a t meets t h e e d u c a t i o n a l needs of h e a r i n g i m p a i r e d s t u d e n t s , many b e n e f i t s w i l l u n d o u b t e d l y r e s u l t . 2 5 C h a p t e r 4 : R e s e a r c h D e s i g n and M e t h o d o l o g y 4.1 S t a t e m e n t of t h e P r o b l e m T h i s s t u d y a d d r e s s e s a s m a l l p a r t of t h e r e s e a r c h i s s u e o f t h e e f f e c t i v e n e s s of e d u c a t i o n a l m i c r o c o m p u t e r s o f t w a r e w i t h h e a r i n g i m p a i r e d s t u d e n t s . I t a t t e m p t s t o measure t h e c h a n g e s t h a t t a k e p l a c e t h r o u g h s o f t w a r e a p p l i c a t i o n and to u n c o v e r c h a r a c t e r i s t i c s w h i c h c o u l d make s o f t w a r e more s u i t a b l e f o r use by h e a r i n g i m p a i r e d s t u d e n t s . I t i s a d e s c r i p t i v e and e m p i r i c a l e x p l o r a t o r y s t u d y t o r e v e a l f u r t h e r i n s i g h t s a b o u t t h e use of e d u c a t i o n a l s o f t w a r e i n h e a r i n g i m p a i r e d c l a s s r o o m s . The r a t i o n a l e and r e a s o n i n g f o r t h i s s t u d y a r e based on t h e f i n d i n g s i n t h e l i t e r a t u r e . From a c r i t i c a l r e v i e w of a v a i l a b l e l i t e r a t u r e d e a l i n g w i t h CAI and i t s use w i t h h e a r i n g i m p a i r e d s t u d e n t s , a l a r g e v o i d i n the a r e a of e m p i r i c a l r e s e a r c h i s a p p a r e n t . Few s t u d i e s have a c c e p t e d t h e c h a l l e n g e of m e a s u r i n g t h e ch a n g e s t h a t t a k e p l a c e t h r o u g h m i c r o c o m p u t e r a p p l i c a t i o n s . The l i t e r a t u r e a l s o p o i n t s t o a m a j o r h u r d l e i n t h e s u c c e s s f u l use of C A I , namely t h e l a c k of s u i t a b l e and a p p r o p r i a t e s o f t w a r e . Most c o m m e r c i a l l y a v a i l a b l e ( h e a r i n g ) p r o g r a m s a r e l a n g u a g e bound e i t h e r i n t h e t e x t o r i n s t r u c t i o n s w h i c h may p r e c l u d e t h e i r u s e by h e a r i n g i m p a i r e d s t u d e n t s w i t h o u t t h e d i r e c t i n t e r v e n t i o n of a t e a c h e r . S o f t w a r e s h o u l d be p r o d u c e d t h a t a l l o w s t h e s t u d e n t t o i n t e r a c t f r e e l y , one on one w i t h the c o m p u t e r , a l l o w i n g t h e t e a c h e r t o a t t e n d t o o t h e r t a s k s . What c h a r a c t e r i s t i c s s h o u l d t h i s s o f t w a r e f o r t h e h e a r i n g 26 i m p a i r e d e x h i b i t to a l l o w t h i s " u t o p i a " t o become a r e a l i t y ? 4.2 D e f i n i t i o n of Terms H e a r i n g i m p a i r e d i s a t e r m u s e d to d e s c r i b e a p e r s o n who has any d e g r e e of h e a r i n g l o s s . I t i s a g e n e r i c t e r m w h i c h i n c l u d e s b o t h d e a f and h a r d - o f - h e a r i n g p e r s o n s . Deaf p e r s o n i s one whose h e a r i n g d i s a b i l i t y p r e c l u d e s s u c c e s s f u l p r o c e s s i n g of l i n g u i s t i c i n f o r m a t i o n t h r o u g h a u d i t i o n w i t h o r w i t h o u t a h e a r i n g a i d ( F r i s i n a , 1 9 7 5 ) . S i g n l a n g u a g e i s t h e v i s u a l l a n g u a g e of s i g n s , f a c i a l e x p r e s s i o n , and body l a n g u a g e used by d e a f p e o p l e to c o m m u n i c a t e . T u t o r i a l s o f t w a r e i s a c o m p u t e r " p r o g r a m i n w h i c h t h e c o m p u t e r a c t s as a t e a c h e r : i n t r o d u c i n g riew c o n c e p t s , e v a l u a t i n g s t u d e n t s r e p o n s e s , p r o v i d i n g e x e r c i s e s and t e s t s , and b r a n c h i n g t o r e m e d i a t i o n and e n r i c h m e n t b a s e d on t h e s t u d e n t ' s s u c c e s s " (PEMC, 1 9 8 4 ) . D r i l l and p r a c t i c e a r e "programs w h i c h e n a b l e s t u d e n t s t o d r i l l and p r a c t i c e c o n c e p t s p r e v i o u s l y t a u g h t , u n t i l t h e y a c h i e v e m a s t e r y " (PEMC, 1 9 8 4 ) . 4.3 Subj e c t s T h i s s t u d y i n v o l v e d a l l of t h e h e a r i n g i m p a i r e d s t u d e n t s ( 1 8 ) a t t e n d i n g a s e c o n d a r y o f f - c a m p u s p r o g r a m of t h e p r o v i n c i a l s c h o o l f o r t h e d e a f . T h i s o f f - c a m p u s p r o g r a m i s l o c a t e d i n a r e g u l a r s e c o n d a r y s c h o o l w h i c h o f f e r s g r a d e s 8 t o 12 f o r a p o p u l a t i o n of a p p r o x i m a t e l y 900 s t u d e n t s . The m a j o r i t y o f t h e d e a f s t u d e n t s t a k e t h e i r a c a d e m i c c o u r s e s i n s e l f - c o n t a i n e d c l a s s e s w i t h a t e a c h e r of t h e h e a r i n g 27 i m p a i r e d , and i n t e g r a t e i n t o r e g u l a r c l a s s e s o r n o n - a c a d e m i c c l a s s e s w i t h t h e a s s i s t a n c e of a t e a c h e r of t h e h e a r i n g i m p a i r e d who a c t s as i n t e r p r e t e r - t u t o r . S i x of t h e s e s t u d e n t s a r e g r a d u a t i n g t h i s y e a r . F o u r have been a c c e p t e d i n t o t he f r e s h m a n c l a s s a t G a l l a u d e t C o l l e g e and the o t h e r two a c c e p t e d i n t o t h e L o n d o n , O n t a r i o p r o g r a m ( e q u i v a l e n t t o p r e p y e a r a t G a l l a u d e t C o l l e g e ) . The s e l e c t i o n of t h e 18 s u b j e c t s f o r t h i s s t u d y was b a s e d on c o n v e n i e n c e and a c c e s s i b i l i t y of t h e s u b j e c t s and t h e e x p e r i m e n t e r , who i s one of t h e t e a c h e r s of t h e h e a r i n g i m p a i r e d a t t h i s l o c a t i o n . F o r t h i s s t u d y t h e e x p e r i m e n t e r i d e a l l y w a n t e d two g r o u p s w h i c h were matched on r e a d i n g a b i l i t y , m a t h e m a t i c a b i l i t y , and e x p e r i e n c e w i t h e d u c a t i o n a l s o f t w a r e . T h i s p o p u l a t i o n had no e x p e r i e n c e w i t h e d u c a t i o n a l s o f t w a r e , but v a r i e d g r e a t l y i n the o t h e r two c a t e g o r i e s . To o b t a i n s u b j e c t s f o r t h i s s t u d y t h e e x p e r i m e n t e r t o l d the s t u d e n t s t h a t t h e i r s e r v i c e s were r e q u i r e d t o h e l p i n a p r o j e c t , i n o r d e r f o r the w r i t t e r t o c o m p l e t e h i s M.A. d e g r e e . He a l s o t o l d t he s t u d e n t s t h a t i t w o u l d i n v o l v e l e a r n i n g some new c o n c e p t s f r o m t h e c o m p u t e r and w o u l d o n l y t a k e up a b o u t 30 m i n u t e s o v e r a one week p e r i o d . The e x p e r i m e n t e r gave a l l s t u d e n t s c o n s e n t f o r m s f o r p a r e n t a l a p p r o v a l . Of t h e 18 f o r m s , a l l 18 w e r e r e t u r n e d w i t h c o n s e n t and a l l t h e s t u d e n t s became i n v o l v e d i n t h e s t u d y . To accommodate f o r t h e v a r i a b i l i t y i n r e a d i n g and m a t h e m a t i c a b i l i t y w i t h i n t h e e x p e r i m e n t a l g r o u p t h e 18 s t u d e n t s were r a n d o m l y p l a c e d i n t o two g r o u p s of 9 e a c h . 4.4 M a t e r i a l s The d e s i g n r e q u i r e d t h a t t h e r e be two e x p e r i m e n t a l g r o u p s . One of t h e g r o u p s w o u l d work t h r o u g h a t u t o r i a l p r o g r a m (TUTORIAL o r T r e a t m e n t g r o u p : TG ) , w h i l e t h e o t h e r had no e x p o s u r e t o i t (non-TUTORIAL o r C o n t r o l g r o u p : NTG). The t u t o r i a l s o f t w a r e was p i c k e d a f t e r t h e e x p e r i m e n t e r had v i e w e d o v e r 40 d i f f e r e n t t y p e s of t u t o r i a l s o f t w a r e . The s o f t w a r e v a r i e d g r e a t l y on f o r m a t , c u r r i c u l u m a r e a or c o n c e p t , and s t y l e of p r e s e n t a t i o n . T h i s s p e c i f i c s o f t w a r e was c h o s e n b e c a u s e the i n s t r u c t i o n s were t h e most s t r a i g h t f o r w a r d of t h e p r o g r a m s v i e w e d and t h e c o n c e p t w o u l d be n o v e l t o t h e s t u d e n t s w h i l e a t the same t i m e i m p o r t a n t t o t h e i r e d u c a t i o n . The o t h e r c o m m e r c i a l l y a v a i l a b l e programs v i e w e d d i d not s a t i s f y a l l of t h e s e c r i t e r i a . T h i s s o f t w a r e i s p r o d u c e d by M i n n e s o t a E d u c a t i o n a l C o m p u t i n g C o n s o r t i u m , a r e p u t a b l e and t r u s t e d s o u r c e and i s i n wi d e use i n s c h o o l s a c r o s s N o r t h A m e r i c a . The M i n i s t r y of E d u c a t i o n i n B.C. t h i n k s so h i g h l y of t h e s o f t w a r e p r o d u c e d by MECC t h a t , "The B r i t i s h C o l u m b i a g o v e r n m e n t has bought t h e r i g h t s t o a l l MECC s o f t w a r e so t h a t i t can be o b t a i n e d a t a b e t t e r p r i c e and be d i s t r i b u t e d more e a s i l y t o a l l s c h o o l s i n B. C." ( D a n e l i u k , 1 9 8 5 ) . The f l o p p y d i s k i s t i t l e d MECC M a t h e m a t i c s Volume 3. The p o r t i o n o f t h i s s o f t w a r e u s e d i n t h e s t u d y i s " T r a p e z o i d and T r i a n g l e A r e a s " . T r a p e z o i d and T r i a n g l e A r e a s i s a t u t o r i a l p r o g r a m w h i c h a t t e m p t s t o i n t r o d u c e and t e a c h t h e c o n c e p t of m e a s u r i n g a r e a s of t h e s e two g e o m e t r i c c o n f i g u r a t i o n s . T h e r e i s a l s o a 29 p r a c t i s e s e c t i o n i n v o l v e d i n t h e p r o g r a m , where s t u d e n t s may p r a c t i s e t h e n e w l y a c q u i r e d s k i l l s . The t u t o r i a l p o r t i o n of t h e p r o g r a m was b r o k e n down i n t o 25 s e p e r a t e f r a m e s . E a c h f r a m e was a n a l y z e d t o d i s c o v e r what t a s k s were i n v o l v e d f o r t h e l e a r n e r and t o e s t a b l i s h t h e t i m e p e r i o d between t h e c o m p l e t i o n of one f r a m e and t h e e n t i r e p r e s e n t a t i o n of t h e n e x t f r a m e . M ost of t h e f r a m e s r e q u i r e d an answer t o a s p e c i f i c q u e s t i o n p e r t a i n i n g t o t h e c o n t e n t of t h e f r a m e , b e f o r e t h e t u t o r i a l c o n t i n u e d . On a few o c c a s i o n s t h e r e were no q u e s t i o n s t o c h e c k t h e s t u d e n t ' s c o m p e h e n s i o n . E x p e r i e n c e has t a u g h t the e x p e r i m e n t e r t h a t a h e a r i n g i m p a i r e d s t u d e n t p r e s e n t e d w i t h d a t a t h a t s/he does not u n d e r s t a n d , u s u a l l y c o n t i n u e s , i g n o r i n g t h e p o r t i o n s t h a t a r e not u n d e r s t o o d . To p r e v e n t t h i s f r o m o c c u r r i n g i n f r a m e s where no c h e c k s were p r o v i d e d t h e e x p e r i m e n t e r d e v e l o p e d h i s own c o m p r e h e n s i o n c h e c k i n g q u e s t i o n s t o t e s t t h e s t u d e n t s . T h e r e f o r e on t h e s e few f r a m e s a l t e r a t i o n s were made to make t h e s o f t w a r e more i n q u i s i t i v e . T h i s p r o g r a m assumes t h a t s t u d e n t s can a l r e a d y m u l t i p l y by p o i n t f i v e ( . 5 ) , d i v i d e 2 i n t o odd numbers, and c a l c u l a t e t h e a r e a s of r e c t a n g l e s and p a r a l l e l o g r a m s . To a s s u r e t h a t t h e s e p r e r e q u i s i t e s k i l l s were a c h i e v e d t h e e x p e r i m e n t e r a s k e d t h a t a l l math c l a s s e s i n v o l v i n g t h e s e s u b j e c t s g e t i n s t r u c t i o n on t h e s e f o u r c o n c e p t s b e f o r e t h e s t u d y commenced. The t u t o r i a l p r o g r a m draws on t h i s u n d e r s t a n d i n g o f a r e a c a l c u l a t i o n w i t h r e c t a n g l e s and p a r a l l e l o g r a m s t o show how t h e f o r m u l a e f o r c a l c u l a t i n g a r e a i n t r a p e z o i d s and 30 l a t e r t r i a n g l e s were d e r i v e d . T h i s p r o g r a m i s r a t e d by MECC t o be a t a r e a d i n g l e v e l o f g r a d e 5 - 6 ( D a l e - C h a l l a n a l y s i s ) . T h i s l e v e l was not c o n s i d e r e d t o be c r i t i c a l b e c a u s e t h e s t u d e n t s were p e r m i t t e d t o ask q u e s t i o n s i f t h e y d i d n o t u n d e r s t a n d t h e l a n g u a g e ( i n f o r m a t i o n ) p r e s e n t e d i n t h e T u t o r i a l p r o g r a m . I n o t h e r w o r d s any r e a d i n g p r o b l e m s e n c o u n t e r e d , c o u l d be s o l v e d by t h e s t u d e n t a s k i n g f o r an e x p l a n a t i o n . S t u d e n t s w o r k i n g on t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e w o u l d n o t be e x p o s e d t o t h e w r i t t e n t e x t . I t i s g e n e r a l l y a c k n o w l e d g e d t h a t t h e m a j o r i t y o f h e a r i n g i m p a i r e d s t u d e n t s a c h i e v e a t a h i g h e r g r a d e l e v e l i n m a t h e m a t i c s t h a n i n r e a d i n g . So any c o m m e r c i a l l y a v a i l a b l e " h e a r i n g " s o f t w a r e t h a t i s a t an a p p r o p r i a t e g r a d e l e v e l i n m a t h e m a t i c a l d e v e l o p e m e n t f o r h e a r i n g i m p a i r e d s t u d e n t s , w i l l p r o b a b l y be a t a h i g h e r r e a d i n g l e v e l t h a n t h e s t u d e n t s a r e p r e s e n t l y a c h i e v i n g . T h i s i s one of t h e main p o i n t s of i n t e r e s t f o r t h i s i n v e s t i g a t i o n . What t y p e of p r o b l e m s o c c u r when h e a r i n g i m p a i r e d s t u d e n t s use " h e a r i n g " s o f t w a r e t h a t i s a t an a p p r o p r i a t e l e v e l of raathematic s o p h i s t i c a t i o n ? T e a c h e r s o f t h e h e a r i n g i m p a i r e d a c q u i r i n g c o m p u t e r s o f t w a r e t o h e l p w i t h t h e i n s t r u c t i o n of t h e i r s t u d e n t s have been and w i l l be l i m i t e d t o u s i n g t h i s " h e a r i n g " c u r r i c u l u m b a s e d s o f t w a r e due t o t h e l a c k o f o t h e r c o m m e r c i a l m a t e r i a l s on t h e m a r k e t . The more i m p o r t a n t a s p e c t o f t h i s p r o g r a m was i t s r a t e d g r a d e l e v e l , 6 - 8 . The s t u d e n t s i n t h i s sample w e r e , a t t h e t i m e of t e s t i n g , w o r k i n g i n math c l a s s e s a t h a l f way t h r o u g h 31 t h e g r a d e 7 l e v e l o r h i g h e r (7 1 / 2 - 1 2 ) . However some s t u d e n t s had S a t - H i ( 1 9 8 3 ) s c o r e s w h i c h i n d i c a t e d t h a t t h e y w e r e a c h i e v i n g a t l o w e r l e v e l s t h a n g r a d e 6-8. The t u t o r i a l p r o g r a m a f f o r d s t h e s t u d e n t o n l y two o p p o r t u n i t i e s t o p r a c t i s e t h e s e n e w l y " l e a r n e d " c o n c e p t s . E a c h p r a c t i c e t a k e s t h e s t u d e n t t h r o u g h t h e s t e p by s t e p method needed t o c a l c u l a t e t h e d e s i r e d a r e a . The c a l c u l a t i o n o f a r e a i s b r o k e n down i n t o i t s i n d i v i d u a l components t o s i m p l i f y t h e t a s k . I f a m i s t a k e i s made d u r i n g any p a r t of t h e p r o c e s s t h e s t u d e n t i s t o l d what t h e c o r r e c t r e s p o n s e s h o u l d have been and the c o r r e c t d i g i t a p p e a r s i n t h e a p p r o p r i a t e s p a c e . The p r a c t i s e p o r t i o n of t h e p r o g r a m i s a l m o s t i d e n t i c a l t o t h e p r a c t i c e i n v o l v e d i n t h e t u t o r i a l . The o n l y d i f f e r e n c e i s t h a t i n t h e p r a c t i s e p o r t i o n t h e s t u d e n t i s f i r s t r e q u i r e d t o g i v e t h e a r e a of t h e g e o m e t r i c shape ( i n i t i a l a r e a q u e s t i o n ) . I f t h i s r e p o n s e i s i n c o r r e c t t h e n t h e same s t e p by s t e p method i s e m p h a s i z e d a g a i n u n t i l t h e a r e a c a l c u l a t i o n i s c o m p l e t e d . The h a r d w a r e u s e d t o r u n t h i s p r o g r a m c o n s i s t e d of an A p p l e l i e c o m p u t e r , b l a c k and g r e e n A p p l e m o n i t o r I I I , and an A p p l e d i s k I I d r i v e u n i t . The p r o g r a m was t r a n s f e r e d f r o m a 5 i n c h f l o p p y d i s k . F u l l d o c u m e n t a t i o n i s a v a i l a b l e i n c l u d i n g h a n d o u t s (#4) u s e d d u r i n g i n s t r u c t i o n f r o m MECC. MECC's d e s c r i p t i o n o f t h e p r o g r a m I s as f o l l o w s : " B u i l d i n g u p o n t he c a l c u l a t i o n s of t h e a r e a o f p a r a l l e l o g r a m s , t h i s p r o g r a m d e v e l o p s a f o r m u l a f o r TRAPEZOID and TRIANGLE a r e a s . 32 A p r a c t i c e p r o b l e m o p t i o n w h i c h d r i l l s s t u d e n t s on t h e use of t h e s e f o r m u l a s i s i n c l u d e d . " So t h e i n s t r u c t i o n a l s t r a t e g y i m p l e m e n t e d i n t h i s p r o g r a m i s t u t o r i a l b ased l e a r n i n g of a new c o n c e p t f o l l o w e d by d r i l l and p r a c t i c e . A more d e t a i l e d d e s c r i p t i o n o f t h i s s o f t w a r e w i l l be g i v e n a t the b e g i n i n g of C h a p t e r 5 . 4 . 5 D e s i g n The s u b j e c t s i n e a c h g r o u p r e c e i v e a p r e - t e s t c o n s i s t i n g o f 10 m u l t i p l e c h o i c e q u e s t i o n s (8 on a r e a of t r a p e z i o d and 2 on t h e a r e a of t r i a n g l e s ) . The r e a s o n f o r e m p h a s i z i n g t r a p e z o i d s on b o t h p r e and p o s t t e s t s i s b e c a u s e t h e y make up t h e m a j o r p o r t i o n of b o t h t h e t u t o r i a l and p r a c t i s e s e c t i o n s o f t h e s o f t w a r e . T h i s p r e t e s t was a d m i n i s t e r e d one week b e f o r e t h e s t u d y commenced. The a p p l i c a t i o n of t h e t r e a t m e n t s f o r b o t h g r o u p s was e x a c t l y t h e same e x c e p t t h e T u t o r i a l G r oup (TG) was e x p o s e d t o the t u t o r i a l p o r t i o n of t h e p r o g r a m , and t h e N o n - T u t o r i a l G r o u p (NTG) was n o t . S t u d e n t s i n t h e t u t o r i a l g r o u p were g i v e n a p e n c i l , p i e c e of s c r a p p a p e r , and h a n d o u t #4 w h i c h had a d i a g r a m of a t r i a n g l e and t r a p e z o i d . N e a r b o t h d i a g r a m s was a s p e c i f i c p l a c e f o r t h e s t u d e n t s t o w r i t e t h e c o r r e s p o n d i n g f o r m u l a f o r e a c h f i g u r e . T h i s was a r e p l i c a o f t h e h a n d o u t p r o d u c e d by MECC f o r use w i t h t h e t u t o r i a l p r o g r a m . The TG were t o l d t h a t t h i s p r o g r a m w o u l d t e a c h them t o c a l c u l a t e t h e a r e a of t r a p e z o i d s and t r i a n g l e s . S t u d e n t s were t o r e a d c a r e f u l l y t h e i n f o r m a t i o n t h a t a p p e a r e d on t h e m o n i t o r ( T . V . ) , and i f t h e y had any p r o b l e m w i t h t h e meaning of a word o r p o r t i o n of 33 t h e t e x t t h e y c o u l d ask t h e e x p r i m e n t e r f o r a s s i s t a n c e . The s c r a p p a p e r was f o r c a l c u l a t i o n s , and the c o m p u t e r w o u l d t e l l them what to do w i t h t h e o t h e r p a p e r ( h a n d o u t //4). The TG s t u d e n t s were a s k e d i f t h e y had any q u e s t i o n s and t h e n the t r e a t m e n t commenced. The e x p e r i e n c e s of t h e TG s t u d e n t s as t h e y w o rked t h r o u g h t h e t u t o r i a l were c a r e f u l l y d ocumented. E a c h q u e s t i o n , r e a c t i o n , and p r o b l e m e n c o u n t e r e d by t h e s t u d e n t s was c a r e f u l l y r e c o r d e d by one a s s i s t a n t w h i l e a n o t h e r a s s i s t a n t n o t e d t h e t i m e s p e n t on e a c h frame of the p r o g r a m , and t h e e x p e r i m e n t e r h e l p e d t o r e s o l v e s t u d e n t p r o b l e m s . Once t h e TG s u b j e c t had w o r k e d t h r o u g h t h e t u t o r i a l p o r t i o n o f t h e s o f t w a r e s/he w o u l d r e c e i v e a s h o r t s i g n e d ( s i g n l a n g u a g e ) t e s t t o c h e c k c o m p r e h e n s i o n of some a s p e c t s p r e s e n t e d i n t h e t u t o r i a l . Then the s u b j e c t c o n t i n u e d o n t o the p r a c t i s e s e c t i o n where s/he had t o r e a c h an e f f i c i e n c y l e v e l of 80% (4/5 q u e s t i o n s c o r r e c t on the f i r s t a t t e m p t ) . Due to t h e r i g i d s e q u e n c e of q u e s t i o n s a p p e a r i n g i n t h e p r a c t i s e p o r t i o n , t h e e x p e r i m e n t e r s e t the f o l l o w i n g r e q u i r e m e n t s ; a t l e a s t 2 o f t h e 4 q u e s t i o n s must be t r a p e z o i d s and a t l e a s t 1 o f t h e q u e s t i o n s must be a t r i a n g l e . I f a s t u d e n t had s u c e s s f u l l y a n s w e r e d 3 t r a p e z o i d s i n a row, t h e e x p e r i m e n t e r w o u l d s t o p t h e t i m e and a d v a n c e t o t h e n e x t t r i a n g l e . Once t h e y had a c c o m p l i s h e d t h i s t h e y were a s k e d t o do two q u e s t i o n s c o r r e c t l y i n a row w i t h o u t t h e a i d o f t h e f o r m u l a e w r i t t e n out b e f o r e them. E a c h t i m e t h e e x p e r i m e n t e r r e c o r d e d t h e e l a p s e d t i m e , t h e number of t r i a l s r e q u i r e d t o r e a c h 80% e f f i c i e n c y , and the number needed t o 34 answer c o r r e c t l y two questions (1 on area of a t r a p e z o i d and 1 on the area of a t r i a n g l e ) without the a i d of formulae. When t h i s was completed the students were dism i s s e d . One week l a t e r the students were r e t e s t e d with a m u l t i p l e choice t e s t balanced with the p r e - t e s t to determine how much of the concept they had r e t a i n e d since the treatment was administered. The p r a c t i s e group was not exposed to the t u t o r i a l s e c t i o n of the program. They learned the concepts through t r i a l and e r r o r with the a s s i s t a n c e of the p r a c t i s e p o r t i o n of the program. The questions i n the p r a c t i s e p o r t i o n were presented i n e x a c t l y the same f a s h i o n as the two p r a c t i s e questions i n the t u t o r i a l p o r t i o n , except the p r a c t i s e questions f i r s t asked the student to give the area of the f i g u r e , then i f t h i s input was wrong the c o r r e c t step by step method was o u t l i n e d as i n the t u t o r i a l . The NTG d i d not r e c e i v e the i n f o r m a t i o n given during the t u t o r i a l or the p r a c t i c e gained from the two t u t o r i a l p r a c t i s e q u e s t i o n s . Otherwise t h e i r experience was e x a c t l y the same as the su b j e c t s i n the TG. Students i n the n o n - t u t o r i a l group were given a p e n c i l and a sheet of scrap paper and a l s o the same handout #4 that the TG r e c e i v e d . However, on t h i s handout the area formulae were already w r i t t e n i n the app r o p r i a t e spots. They were t o l d that t h i s program would teach (show) them how to c a l c u l a t e the area of t r a p e z o i d s and t r i a n g l e s . They did not know how to c a l c u l a t e area y et, so they would need to guess 35 a t t h e f i r s t few q u e s t i o n s . Soon t h e y w o u l d see t h e p a t t e r n ( p l a n ) and d i s c o v e r t h e c o r r e c t method of c a l c u l a t i n g a r e a . The s c r a p p a p e r was f o r c a l c u l a t i o n s and h a n d o u t #4 d i s p l a y e d t h e c o r r e c t f o r m u l a e needed t o c a l c u l a t e t h e a r e a of b o t h f i g u r e s . The NTG w o r k e d w i t h t h e p r a c t i s e p o r t i o n of the p r o g r a m u n t i l t h e y d i s p l a y e d an 80% e f f i c i e n c y l e v e l . Then t h e y were a s k e d t o answer two q u e s t i o n s c o r r e c t l y w i t h o u t h a v i n g t h e f o r m u l a e d i s p l a y e d as i t had been d u r i n g the p r a c t i c e . A g a i n t h e e l a p s e d t i m e and t h e number of t r i a l s r e q u i r e d t o c o m p l e t e b o t h t e s t s were r e c o r d e d by t h e e x p e r i m e n t e r and t h e same b a l a n c e d p o s t - t e s t was g i v e n to e a c h i n d i v i d u a l one week a f t e r t h e t r e a t m e n t was a d m i n i s t e r e d . The e x p e r i m e n t e r s e t a t i m e l i m i t f o r e x p o s u r e to the p r a c t i s e s o f t w a r e of a p p r o x i m a t e l y 20 m i n u t e s f o r the TG and 30 m i n u t e s f o r the NTG. I f a t t h i s t i m e the s t u d e n t a p p e a r e d u n a b l e to r e a c h t h e 80% e f f i c i e n c y l e v e l t h e t r e a t m e n t was s t o p p e d . The TG was l i m i t e d t o a s h o r t e r e x p o s u r e b e c a u s e of t h e a p p r o x i m a t e l y 10 m i n u t e s of CAI t h e y had a l r e a d y r e c e i v e d d u r i n g t h e t u t o r i a l . T h i s was done i n an a t t e m p t to b a l a n c e t h e o v e r a l l c o m p u t e r i n t e r a c t i o n t i m e of b o t h g r o u p s . 4 . 6 H y p o t h e s e s One h y p o t h e s i s was t h a t s t u d e n t s w i l l r e c e i v e l i t t l e b e n e f i t f r o m t h e t u t o r i a l s e c t i o n of t h e s o f t w a r e . S t u d e n t s who v i e w e d b o t h t h e t u t o r i a l and p r a c t i c e segments w o u l d do no b e t t e r t h a n t h o s e who v i e w o n l y t h e p r a c t i c e [ N u l l H y p o t h e s i s : mean of TG > mean of NTG], T h e r e a r e t h r e e 36 s p e c i f i c t i m e s when t h e i m p a c t of the t u t o r i a l was m e a s u r e d . I m m e d i a t e l y a f t e r c o m p l e t i o n of the t u t o r i a l t h e s t u d e n t s w e r e a s k e d a s e t of q u e s t i o n s t o t e s t t h e i r u n d e r s t a n d i n g of i t s c o n t e n t s . S t u d e n t ' s who v i e w t h e t u t o r i a l s h o u l d be f a s t e r t o r e a c h t h e 80% e f f i c i e n c y i n p r a c t i c e . A l s o , due t o e x p o s u r e t o the l o g i c b e h i n d t h e d e r i v a t i o n o f f o r m u l a e n e e d e d t o c a l c u l a t e t h e a r e a of b o t h t r i a n g l e s and t r a p e z o i d s , t h e s e same s t u d e n t s s h o u l d remember t h e c o n c e p t (how t o c a l c u l a t e t h e a r e a s ) b e t t e r on a p o s t - t e s t one week a f t e r e x p o s u r e t o t h e s o f t w a r e , t h a n t h o s e s t u d e n t s who j u s t m e c h a n i c a l l y go t h r o u g h t h e s t e p s i n t h e p r a c t i c e . The t u t o r i a l p o r t i o n of the p r o g r a m t r i e s t o c o n v e y a v e r y d i f f i c u l t and e l a b o r a t e c o n c e p t ( t h e d e r i v a t i o n of the f o r m u l a e f o r a r e a c a l c u l a t i o n i n b o t h t r a p e z o i d s and t r i a n g l e s ) , In a v e r y s h o r t t i m e . I t was f e l t t h a t few s t u d e n t s w o u l d g r a s p t h i s c o n c e p t f r o m e x p o s u r e to t h i s s o f t w a r e . H e a r i n g i m p a i r e d s t u d e n t s m i g h t f i n d t h e l a n g u a g e and m e t h o d o l o g y u s e d i n t h i s segment d i f f i c u l t t o u n d e r s t a n d , t h e r e b y a d d i n g m i s u n d e r s t a n d i n g , c o n f u s i o n and f r u s t r a t i o n to t h e t a s k . I n a d d i t i o n t o t h e s e p r o b l e m s t h e t u t o r i a l i s a l s o v e r y l i m i t e d b e c a u s e i t o n l y a f f o r d s t h e s t u d e n t one p r a c t i s e q u e s t i o n t o t e s t t h e n e w l y l e a r n e d c o n c e p t . I n t h e p r a c t i s e p o r t i o n o f t h e p r o g r a m no l a n g u a g e i s i n v o l v e d , e v e r y m i s t a k e i s p o i n t e d out and c o r r e c t e d , t h e p r o b l e m s a r e b r o k e n down i n t o t h e i r i m p o r t a n t c o m p o n e n t s , and t h e c o r r e c t methods of c a l c u l a t i o n i s r e - e n f o r c e d i n a v e r y m e c h a n i c a l way, as t h e y a r e i n t h e one example d u r i n g t h e 37 t u t o r i a l . As s t a t e d before, t h i s i s a d e s c r i p t i v e and e m p i r i c a l study designed to r e v e a l f u r t h e r i n s i g h t s about the use of e d u c a t i o n a l computer software with hearing impaired students. The study attempts to answer the f o l l o w i n g questions: 1. Can hearing impaired students l e a r n to c a l c u l a t e the area of t r a p e z o i d s and t r i a n g l e s through the use of e d u c a t i o n a l microcomputer software? 2. What types of problems do hearing impaired students have i n working through a t u t o r i a l program that contains r e l a t i v e l y simple language? 3. What types of problems do hearing impaired students have i n working through a d r i l l and p r a c t i c e program which i n v o l v e s no language, when they are introduced to a new concept? 4. Which concepts presented i n the t u t o r i a l program are not understood by the students? 5. Which concepts presented i n the t u t o r i a l program are understood by the students? 6. Which areas of t h i s t u t o r i a l program could be changed or modified to make i t s use by hearing impaired students more e d u c a t i o n a l l y p r o f i t a b l e ? 7. Which areas of the p r a c t i s e program could be changed or modified to make i t s use by hearing impaired students more e d u c a t i o n a l l y p r o f i t a b l e ? 8. Are there any s i g n i f i c a n t d i f f e r e n c e s i n the performances of the two groups with respect to the post 38 t e s t s ? 9. What i n f l u e n c e s does t h e t u t o r i a l p r o g r a m have on s t u d e n t a c h i e v e m e n t ? I t w i l l be e n l i g h t e n i n g to o b s e r v e how e a c h i n d i v i d u a l r e a c t s and l e a r n s f r o m e x p o s u r e t o t h e two d i f f e r e n t t y p e s of c o m p u t e r s o f t w a r e . The p u r p o s e was t o e x p o s e t h e s t r e n g t h s and w e a k n e s s e s of t h i s s o f t w a r e i n r e l a t i o n to i t s use w i t h h e a r i n g i m p a i r e d s t u d e n t s and t h e n g e n e r a l i z e t h e f i n d i n g s t o make r e c o m m e n d a t i o n s r e g a r d i n g t h e c h a r a c t e r i s t i c s of s o f t w a r e w h i c h can be u s e d more e f f e c t i v e l y w i t h h e a r i n g i m p a i r e d s t u d e n t s . 39 C h a p t e r 5 : R e s u l t s and D i s c u s s i o n 5.1 MECC M a t h e m a t i c s Volume 3 : T r a p e z o i d and T r i a n g l e A r e a s B e f o r e p r e s e n t i n g t h e q u a l i t a t i v e d a t a f o r b o t h t h e t u t o r i a l and n o n - t u t o r i a l g r o u p s a b r i e f d e s c r i p t i o n of t h e s o f t w a r e i s r e q u i r e d . T u t o r i a l S e c t i o n The t u t o r i a l p r o g r a m opened w i t h t h e t i t l e and a g r a p h i c o f a t r a p e z o i d a p p e a r i n g on t h e m o n i t o r . I t d i s c u s s e d and a t t e m p t e d to show v i a g r a p h i c s t h a t p a r a l l e l o g r a m s and r e c t a n g l e s have two p a i r o f p a r r a l l e l s i d e s ( " e i t h e r p a i r c o u l d be us e d f o r t h e base l e n g t h " ) w h i l e a t r a p e z o i d has o n l y one p a i r of p a r r a l l e l s i d e s . The g r a p h i c f o r a p a r a l l e l o g r a m ( r e c t a n g l e ) a p p e a r e d f i r s t ( f r a m e #2) and t h e n t h e c o m p a r i s o n w i t h t h e t r a p e z o i d g r a p h i c happened i n frame //3. I n fr a m e #4 t h e t e x t s t a t e d " U n l i k e p a r a l l e l o g r a m s , t h e p a r a l l e l s i d e s of a t r a p e z o i d have d i f f e r e n t l e n g t h s . " I t t h e n u s e d g r a p h i c s t o i l l u s t r a t e t h e t h r e e p a r t s of a t r a p e z o i d : B ase 1 ( B l ) , Base 2 ( B 2 ) , H e i g h t ( H ) . As e a c h p a r t was named and g i v e n a n u m e r i c a l v a l u e ( i e Base 1 ( B l ) = 4) t h e v a l u e w o u l d a p p e a r on t h e g r a p h i c t o show t h e s t u d e n t e x a c t l y where B l , B2, and H were l o c a t e d on t h e t r a p e z o i d b e i n g d i s c u s s e d . I n f r a m e s #5-#8 t h i s t r a p e z o i d ( f r a m e #4) was compared t o two d i f f e r e n t r e c t a n g l e s and t h e s t u d e n t was a s k e d t o d e c i d e w h i c h had t h e l a r g e r a r e a . The f i r s t r e c t a n g l e had s i d e s t h e same l e n g t h as the t r a p e z o i d s l a r g e r b a s e ( 8 c m ) , and i t had a l a r g e r a r e a t h a n t h e t r a p e z o i d . The s e c o n d c o m p a r i s o n was w i t h a r e c t a n g l e t h a t had s i d e s the 40 same l e n g t h as t h e t r a p e z o i d s s h o r t e r base ( 4 c m ) , and i t had a s m a l l e r a r e a t h a n t h e t r a p e z o i d . The s t u d e n t s were r e q u i r e d t o d e c i d e w h i c h was l a r g e r and i n p u t t h e i r r e s p o n s e i n t o t h e c o m p u t e r . Then t h e p r o g r a m u s i n g a n i m a t i o n g r a p h i c s w o u l d move t h e r e c t a n g l e o v e r t o t h e t r a p e z o i d and v i s u a l l y show w h i c h was l a r g e r . I n frame #9 and #9.5 t h e t e x t s t a t e d "The 8cm r e c t a n g l e was t o o l a r g e , t h e 4cm r e c t a n g l e was t o o s m a l l . L e t s t r y a r e c t a n g l e w i t h l e n g t h e x a c t l y b e t w e e n 4cm and 8cm. What i s an a v e r a g e b etween 4cm and 8cm? cm." The s t u d e n t s were p e r m i t t e d two g u e s s e s h e r e and i f t h e y were n o t s u c c e s s f u l t h e c o r r e c t method was shown i n f r a m e #9.5. I n frame #10 t h e t h i r d and l a s t c o m p a r i s o n o c c u r r e d . T h i s t i m e t h e t r a p e z o i d was compared t o a r e c t a n g l e w i t h base l e n g t h s e q u a l to the a v e r a g e l e n g t h of t h e two b a s e s of t h e t r a p e z o i d ( 6 c m ) , as c a l c u l a t e d i n frame 9.5. A n i m a t i o n was a g a i n used t o show t h e s t u d e n t t h a t t h e two f i g u r e s have t h e same a r e a . And the t e x t s t a t e d "The t r a p e z o i d a r e a f o r m u l a i s l i k e t h e p a r a l l e o g r a m f o r m u l a B ( a v e r a g e ) x H = A . " B e l o w t h i s f o r m u l a o u t l i n e d i n a l a r g e r e c t a n g u l a r box a p p e a r e d the f o r m u l a [B1+B2/2xH=A]. T h e r e was no t i t l e above the f o r m u l a o r i n f o r m a t i o n i n t h e f r a m e ' s t e x t , t o c l e a r l y i n d i c a t e i t s a p p r o p r i a t e a p p l i c a t i o n . I n f r a m e #12 t h e p a r a l l e l o g r a m f o r m u l a d i s a p p e a r e d and t h e s t u d e n t was a s k e d t o copy t h e f o r m u l a ( t r a p e z o i d ) o n t o h a n d o u t #4. T h i s method ( f r a m e s # 5 - # l l ) of c o m p a r i n g t h r e e d i f f e r e n t r e c t a n g l e s t o t h e t r a p e z o i d was used by t h e p r o g r a m to i l l u s t r a t e t h e d e r i v a t i o n of t h e t r a p e z o i d f o r m u l a . I n f r a m e s #13-#17 t h e A l u s e r w o r k s t h r o u g h one p r a c t i s e q u e s t i o n . The computer gave t h e v a l u e f o r B l ( B l = 7 ) and a s k e d t h e u s e r t o i d e n t i f y o r compute t h e f o l l o w i n g i n t h i s o r d e r : B2, H, B1+B2/2, A r e a . I f t h e s t u d e n t s gave an i n c o r r e c t a n swer a t B2, H, or B1+B2/2 t h e c o m p u t e r r e p l a c e d t h e i r a n swer w i t h t h e c o r r e c t one. On t h e a r e a q u e s t i o n t h e s t u d e n t was g i v e n two o p p o r t u n i t i e s t o i n p u t t h e c o r r e c t answer and i n fr a m e #17 t h e c o r r e c t method was i l l u s t r a t e d . I n f r a m e #18 t h e t e x t s t a t e d "Here i s one l a s t t r a p e z o i d . L e t s s h r i n k t h e t o p base down." I n fr a m e #19 t h e t o p base s h r a n k and a t r i a n g l e was f o r m e d . The t e x t s t a t e d t h a t we can s t i l l use t h e t r a p e z o i d f o r m u l a where one b a s e e q u a l s z e r o . Frame #20 showed t h e t r i a n g l e f o r m u l a i n s i d e a l a r g e r e c t a n g u l a r b ox, but u n l i k e t h e t r a p e z o i d f o r m u l a i n frame #11 and #12 t h i s f o r m u l a had a t i t l e " t r i a n g l e f o r m u l a " above i t i n t h e box. T h i s gave t h e s t u d e n t a l i t t l e more i n f o r m a t i o n a b o u t t h e a p p l i c a t i o n of t h e f o r m u l a s e e n i n s i d e t h e box. A t r i a n g l e p r a c t i s e q u e s t i o n a p p e a r e d i n f r a m e s #22-#2A, where the u s e r was a s k e d t o i d e n t i f y B, H, and c a l c u l a t e t h e a r e a . T h i s p r a c t i s e q u e s t i o n d i d not ask t h e s t u d e n t t o f i n d B/2. I n t h i s t u t o r i a l p r a c t i c e t h e p r o b l e m was n o t b r o k e n down i n t o a l l of i t s component p a r t s as i t was i n t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e . The s t u d e n t was n o t r e q u i r e d t o compute B/2. He/she was a s k e d t o c a l c u l a t e t h e a r e a w i t h o u t d o i n g t h i s i n t e r m e d i a r y s t e p , w h i c h c o u l d make t h e t a s k more d i f f i c u l t . T h i s was n o t c o n s i s t e n t w i t h t h e method u s e d i n t h e p r a c t i s e p o r t i o n o f t h e s o f t w a r e . 42 I n f r ame #25 t h e c o r r e c t method f o r s o l v i n g t h i s t r i a n g l e a r e a c a l c u l a t i o n was shown and t h e p r o g r a m was t h e n c o m p l e t e d . P r a c t i s e S e c t i o n The method of p r e s e n t a t i o n f o r e a c h q u e s t i o n was i d e n t i c a l . A g r a p h i c of t h e t r a p e z o i d o r t r i a n g l e t o be s o l v e d was p r e s e n t e d on t h e r i g h t s i d e of t h e m o n i t o r ' s s c r e e n . The base ( t r i a n g l e ) o r b a s e s ( t r a p e z o i d ) and t h e h e i g h t were r e p r e s e n t e d by n u m e r i c v a l u e s w h i c h a p p e a r e d b e s i d e t h e c o r r e s p o n d i n g s o l i d base l i n e s o r t h e d o t t e d h e i g h t l i n e . The " i n i t i a l a r e a q u e s t i o n " a p p e a r e d on the l e f t s i d e of t h e s c r e e n , AREA = . The s t u d e n t s s h o u l d h a v e u s e d t h e g i v e n f o r m u l a ( h a n d o u t #4) and n u m e r i c a l d a t a on the g r a p h i c t o s o l v e t h e a r e a and e n t e r e d t h e i r r e s p o n s e . I f t h e c o r r e c t answer was e n t e r e d t h e n t h e s t u d e n t was t o l d " t h a t i s c o r r e c t " and i n s t r u c t e d t o push t h e s p a c e bar t o c o n t i n u e t o t h e n e x t p r a c t i s e q u e s t i o n . I f h e / s h e f a i l e d t o c a l c u l a t e t he c o r r e c t answer f o r t h i s i n i t i a l a r e a q u e s t i o n , " s o r r y t h a t s not i t " a p p e a r e d and t h e s t e p by s t e p r e m e d i a l p o r t i o n o f t h e p r a c t i s e q u e s t i o n was i n i t i a t e d once t h e s t u d e n t pushed t h e s p a c e b a r . F i r s t t h e s t u d e n t was a s k e d t o i d e n t i f y t h e i m p o r t a n t p a r t s of t h e f i g u r e s t a r t i n g w i t h t h e b a s e ( s ) , B = ( t r i a n g l e ) o r B l - , B2 = ( t r a p e z o i d ) , a p p e a r i n g on t h e m o n i t o r . The p e r s o n i n t e r a c t i n g w i t h t h e c o m p u t e r was e x p e c t e d t o e n t e r t h e c o r r e c t v a l u e ( s ) f o r the b a s e ( s ) . Then t h e c o m p u t e r u s e r was A3 r e q u i r e d t o a s s i g n t h e c o r r e c t v a l u e t o t h e h e i g h t . H = a p p e a r e d on t h e m o n i t o r b e l o w t h e B = . I f the e n t e r e d v a l u e was i n c o r r e c t , t h e c o m p u t e r w o u l d t e l l t h e u s e r t h a t t h e i r a nswer was wrong and r e p l a c e t h e i n c o r r e c t number w i t h t h e c o r r e c t d i g i t and t h e p r o c e d u r e w o u l d c o n t i n u e . N e x t t h e s t u d e n t was a s k e d t o use t h e base v a l u e s t o c a l c u l a t e e i t h e r B / 2 o r B 1 + B 2 / 2 . B / 2 = o r B 1 + B 2 / 2 = a p p e a r e d on t h e m o n i t o r . A g a i n i f h i s / h e r r e s p o n s e was i n c o r r e c t t h e c o m p u t e r w o u l d r e p l a c e i t w i t h t h e c o r r e c t a n s w e r . The l a s t p a r t o f t h e p r a c t i c e a s k e d t h e s t u d e n t t o t r y and c a l c u l a t e t h e a r e a f o r t h e s e c o n d t i m e , u s i n g t h e g i v e n f o r m u l a w h i c h a p p e a r e d above t h e g r a p h i c j u s t b e f o r e t h e a r e a q u e s t i o n (AREA = ) a p p e a r e d b e l o w B 1 + B 2 / 2 on t h e m o n i t o r . The s t u d e n t was e x p e c t e d t o use t h e d a t a and t h e f o r m u l a t o o b t a i n t h e c o r r e c t a r e a . I f h i s / h e r answer was wrong t h e n t h e c o m p u t e r s t a t e d " t h e c o r r e c t a n s w e r i s " ( t h e c o r r e c t a n s w e r i s g i v e n ) and t h e s t u d e n t was t o l d t o push t h e s p a c e b a r t o c o n t i n u e . The n e x t q u e s t i o n i s p r e s e n t e d w i t h i t s g r a p h i c and i n i t i a l a r e a q u e s t i o n (AREA = ) and t h e same p a t t e r n was f o l l o w e d . A c o m p l e t e d e s c r i p t i o n o f e a c h s t u d e n t s ' e x p e r i e n c e w i t h t h e s o f t w a r e f o l l o w s . F i r s t t h e t u t o r i a l g r o u p (TG) t h e n t h e n o n - t u t o r i a l g r o u p (NTG) q u a l i t a t i v e d a t a i s p r e s e n t e d . 44 5.2 T u t o r i a l G r oup Case S t u d i e s CASE #1 S t u d e n t #1 w o u l d be p l a c e d a t o r above t h e 7 5 t h p e r c e n t i l e i n a r a n k i n g of o v e r a l l a b i l i t y f o r p a t i c i p a n t s i n v o l v e d i n t h i s s t u d y . T h i s s t u d e n t who was r e c e n t l y a c c e p t e d i n t o t h e f r e s h m a n y e a r a t G a l l a u d e t C o l l e g e i s p r e s e n t l y w o r k i n g midway t h r o u g h t h e g r a d e 11 a l g e b r a c u r r i c u l u m . He r e a d s a t a g r a d e l e v e l of 6.3 ( S a t - H i J u n e 8 4 ) . T h i s s t u d e n t s c o r e d 0/10 on t h e p r e - t e s t g u e s s i n g at t h e a r e a of t h e t r a p e z o i d s and c o n s i s t e n t l y u s i n g BxH f o r t h e a r e a of the t r i a n g l e s . A t t h e c o m p u t e r t h e s t u d e n t h e s i t a t e d a f t e r r e a d i n g the i n i t i a l i n s t r u c t i o n "Push s p a c e b a r t o c o n t i n u e " , t h e n a s k e d t h e e x p e r i m e n t e r i f he s h o u l d p u s h i t . He seemed u n s u r e and d i d not a p p e a r to t r u s t h i m s e l f . He knew t h a t the f i q u r e on t h e s c r e e n i n frame //1 was a t r a p e z o i d and a l s o u n d e r s t o o d t h e t e r m p a r a l l e l i n f r a m e #2. A f t e r r e a d i n g f r a m e //3 he t h o u g h t t h a t he was r e q u i r e d t o answer a q u e s t i o n . I n f a c t he a s k e d t h e e x p e r i m e n t e r i f t h e r e was a q u e s t i o n on t h e s c r e e n . The e x p e r i m e n t e r s a i d , "no." A t t h i s f rame the s t u d e n t showed t h e f i r s t s i g n s of h a v i n g d i f f i c u l t y w i t h t h e l a n g u a g e p r e s e n t e d . The e x p e r i m e n t e r posed the q u e s t i o n , ("What i s t h e d i f f e r e n c e b e t ween a p a r a l e l l o g r a m and a t r a p e z o i d ? " ) t h a t r e l a t e d t o i n f o r m a t i o n c o n t a i n e d i n t h e f i r s t s e n t e n c e of t h e f r a m e . E v e n t h o u g h t h e s t u d e n t had f i n i s h e d " r e a d i n g " and " r e r e a d i n g " i t s e v e r a l t i m e s , he c o u l d n o t answer t h e q u e s t i o n . T h i s was a n o t h e r s i g n t h a t he 45 u n d e r s t o o d l i t t l e of what was b e i n g p r e s e n t e d . I n frame #5 t h e s t u d e n t was a s k e d to d e c i d e w h i c h i s l a r g e r a t r a p e z o i d o r a r e c t a n g l e . He c a r e f u l l y r e a d t h r o u g h t h e t e x t and was u n c e r t a i n a b o u t t h e t a s k . He r e a d t h e l a s t l i n e a g a i n and t h e n a s k e d f o r h e l p , but b e f o r e h e l p was g i v e n e n t e r e d an i n c o r r e c t r e s p o n s e . A f t e r e n t e r i n g h i s answer he w a i t e d f o r a l o n g t i m e w h i l e n o t h i n g h a p p e n e d . Then he a s k e d t h e e x p e r i m e n t e r f o r i n s t r u c t i o n s and was t o l d t o f i n i s h e n t e r i n g h i s r e s p o n s e by p u s h i n g t h e r e t u r n k e y . A n o t h e r c o m p r e h e n s i o n p r o b l e m a r o s e i n f r a m e #7. The t a s k was e x a c t l y t h e same as t h a t i n frame #5. The s t u d e n t a s k e d f o r g u i d a n c e and t h e e x p e r i m e n t e r t o l d him t o c o n t i n u e . He s t u d i e d t h e t e x t and t h e n had no p r o b l e m w i t h t h e m e c h a n i c s o f e n t e r i n g h i s c o r r e c t c h o i c e . He knew how t o c a l c u l a t e t h e a v e r a g e i n fr a m e #9. A t fr a m e #10 t h e same t a s k as t h a t f o u n d i n frame #5 and #7 i s g i v e n t o the s t u d e n t . He was a g a i n u n c e r t a i n and s i g n e d , "Not know what t o do." The e x p e r i m e n t e r e x p l a i n e d t h e t a s k and t h e s t u d e n t s i g n e d , "Now I u n d e r s t a n d " , and p r o c e e d e d to i n c o r r e c t l y p ush t h e s p a c e b a r . The e x p e r i m e n t e r s t o p p e d t h e s t u d e n t and t o l d him to r e a d i t . The s t u d e n t h e s i t a t e d and t h e n i n p u t an i n c o r r e c t a n s w e r and pushed r e t u r n . T h i s was a f u r t h e r i n d i c a t i o n t h a t as t h e s t u d e n t c o n t i n u e d he was n o t c o m p r e h e n d i n g t h e i n f o r m a t i o n p r e s e n t e d . Frame #12 r e q u e s t s t h a t t h e s t u d e n t c o p y t h e f o r m u l a o n t o h a n d o u t #4. The e x p e r i m e n t e r had t o s t o p t h e s t u d e n t f r o m p u s h i n g t h e s p a c e b a r to c o n t i n u e . The s t u d e n t had n o t u n d e r s t o o d t h e s t r a i g h t f o r w a r d i n s t r u c t i o n s 46 t o copy t h e f o r m u l a . The e x p e r i m e n t e r p o i n t e d to the i m p o r t a n t d a t a on t h e s c r e e n . Then t h e s t u d e n t r e a d i t a g a i n and p r o c e e d e d t o copy t h e f o r m u l a o n t o t h e a p p r o p r i a t e p l a c e on h a n d o u t #4. Frame #13 g i v e s t h e s t u d e n t a f i r s t o p p o r t u n i t y t o p r a c t i s e w i t h t h e new f o r m u l a . I t a s k s t h e s t u d e n t t o e n t e r the a p p r o p r i a t e d i g i t f o r b a s e 2 . I t a l r e a d y d i s p l a y s t h e v a l u e f o r b a s e l and t h e c u r s o r f l a s h e s n e x t to t h e s p a c e r e s e r v e d f o r t h e v a l u e f o r b a s e 2 . The s t u d e n t d i d n o t u n d e r s t a n d t h e t a s k and a s k e d the e x p e r i m e n t e r f o r h e l p . The e x p e r i m e n t e r e x p l a i n e d t h a t he needs t o e n t e r a d i g i t t h a t c o r r e p o n d s t o the b a s e 2 . E v e n w i t h t h e c l u e of Bl=4 on t h e m o n i t o r the s t u d e n t c o u l d n o t f i g u r e out the t a s k . The s t u d e n t e n t e r e d the wrong d i g i t and t h e c o r r e c t d i g i t a u t o m a t i c a l l y t a k e s i t s p l a c e . A t frame #14 he had no p r o b l e m e n t e r i n g t h e c o r r e c t d i g i t f o r the h e i g h t . A g a i n at f r a m e #15 t h e s t u d e n t was p u z z l e d and a s k e d f o r an e x p l a n a t i o n of B1+B2/2. The e x p e r i m e n t e r e x p l a i n e d t h a t he must add B l and B2 t h e n d i v i d e t h e t o t a l by 2. The s t u d e n t d i d t h i s and g o t t h e c o r r e c t a n s w e r . Frame #16 p r o v e d to be t o o d i f f i c u l t , i t a s k e d f o r t h e a r e a of t h e f i g u r e . The e x p e r i m e n t e r e x p l a i n e d t h e t a s k t w i c e and b o t h t i m e s t h e s t u d e n t d i d n o t u n d e r s t a n d , b u t he p r o c e e d e d and made two i n c o r r e c t g u e s s e s . On b o t h g u e s s e s the s t u d e n t d i d not use t h e f o r m u l a o r o t h e r i n f o r m a t i o n a b o u t B1+B2/2 o r H. At f r a m e #17 t h e s t u d e n t s l o w l y , c a r e f u l l y , and r e p e a t e d l y e x a m i n e d t h e c o r r e c t method f o r c a l c u l a t i n g t h e a r e a . The s t u d e n t u n d e r s t o o d t h e word " s h r i n k " i n frame #18, and at f r a m e #19 he c o p i e d t h e t r i a n g l e f o r m u l a w i t h o u t d e l a y o n t o t h e a p p r o p r i a t e s p o t on h a n d o u t #4. The s t u d e n t had no p r o b l e m e n t e r i n g t h e c o r r e c t d a t a f o r the t r i a n g l e p r a c t i s e p r o b l e m . D u r i n g f r a m e #24 t h e s t u d e n t s i g n e d , "Dumb math", e x p r e s s i n g h u m o r o u s l y h i s d i f f i c u l t y w i t h math. He c o u l d not c a l c u l a t e t h e a r e a f o r t h e t r i a n g l e u s i n g t h e f o r m u l a o r t h e d a t a r i g h t on t h e s c r e e n . He t r i e d t o use p a p e r and p e n c i l , b u t two a t t e m p t s l e d to two i n c o r r e c t and r i d i c u l o u s a n s w e r s . I n frame #25 t h e s t u d e n t was shown t h e c o r r e c t method and s i g n e d , "Now I see how t o do i t . " A f t e r c o m p l e t i n g t h e t u t o r i a l t h e s t u d e n t was a s k e d a number of q u e s t i o n s t o m e a s u r e h i s u n d e r s t a n d i n g of t h e t u t o r i a l s e c t i o n . He u n d e r s t o o d most of t h e v o c a b u l a r y ( i s o l a t e d w o r d s ) p r e s e n t e d i n the t u t o r i a l . He d i d not u n d e r s t a n d the r e a s o n i n g b e h i n d t h e c o m p a r i s o n of t h e t h r e e d i f f e r e n t s i z e d r e c t a n g l e s w i t h t h e t r a p e z o i d w h i c h a t t e m p t e d t o show how the t r a p e z o i d f o r m u l a i s d e r i v e d . He d i d not u n d e r s t a n d the t e r m b a s e , but he d i d know f r o m p r e v i o u s math e x p e r i e n c e how to c a l c u l a t e an a v e r a g e . He s t a t e d t h a t he u n d e r s t o o d some of t h e i n f o r m a t i o n t h a t t h e c o m p u t e r t a u g h t him and i n d e e d t h o u g h t t h a t some of i t was e a s y t o u n d e r s t a n d . He e n j o y e d w o r k i n g w i t h t h e c o m p u t e r and w o u l d l i k e t o do i t a g a i n . Then t h i s s t u d e n t c o n t i n u e d o n t o t h e p r a c t i s e s e c t i o n of t h e s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : Wrong on h i s i n i t i a l g u e s s . Then he c o r r e c t l y a n s w e r e d B l , B2, B1+B2/2, and t h e a r e a . Q u e s t i o n #2 ( t r i a n g l e ) : Wrong on h i s i n i t i a l g u e s s . Then 48 he c o r r e c t l y a n s w e r e d B, H, B/2, and t h e a r e a . Q u e s t i o n s #3 , #4 , #5 , #6 , #7 , #8 , #9 ( t r a p e z o i d s ) : The s t u d e n t i n c o r r e c t l y a n s w e r e d e a c h of t h e i n i t i a l a r e a q u e s t i o n s . And t h e n as i n #1 a f t e r t h e p r o b l e m s were b r o k e n down i n t o t h e i r c omponent p a r t 6 he was a b l e t o c o r r e c t l y c a l c u l a t e e ach a n s w e r . He d i d not work out t h e answer on p a p e r . He q u i c k l y g u e s s e d a t the i n i t i a l a r e a q u e s t i o n t h e n c a r e f u l l y worked t h r o u g h t h e p a r t s . He became a n n o y e d a t h i s i n a b i l i t y t o a n s w e r t he i n i t i a l q u e s t i o n c o r r e c t l y . He knew how t o do t h e q u e s t i o n s but seemed s a t i s f i e d t o q u i c k l y g u e s s and g e t t h e i n i t i a l a r e a q u e s t i o n w r o n g , t h e n work t h r o u g h t h e p r o b l e m p a r t by p a r t . Q u e s t i o n #10 (2nd t r i a n g l e ) : F o r t h e f i r s t t i m e t h e s t u d e n t went to p e n c i l and p a p e r and q u i c k l y g o t the c o r r e c t i n i t i a l a n s w e r . Q u e s t i o n s #11, #12 ( t r a p e z o i d s ) , #13 ( t r i a n g l e ) : W o r k i n g on p a p e r t h e s t u d e n t c o r r e c t l y c a l c u l a t e d t h e i n i t i a l a r e a q u e s t i o n on a l l t h r e e p r o b l e m s and r e a c h e d t h e 80% e f f i c i e n c y l e v e l . The e l a p s e t i m e f o r t h e s e s s i o n was 10 m i n u t e s . He t h e n q u i c k l y and a c c u r a t e l y c a l c u l a t e d t h e 2 p r a c t i s e q u e s t i o n s w i t h o u t t h e a i d of t h e f o r m u l a s h e e t . Summary: T h i s s t u d e n t was o f t e n t e n t a t i v e and c o n f u s e d when w o r k i n g t h r o u g h t h e t u t o r i a l s e c t i o n of t h e s o f t w a r e . I t was o b v i o u s f r o m h i s r e s p o n s e s t h a t he d i d not u n d e r s t a n d t h e t a s k a l t h o u g h he gave a l l s u r f a c e i n d i c a t i o n s t h a t he had r e a d and u n d e r s t o o d i t . However h i s a c t i o n s , q u e s t i o n s , or 49 p l e a s f o r h e l p r e v e a l e d t h e e x t e n t t o w h i c h he had not c o m p r e h e n d e d t h e i n f o r m a t i o n . He u n d e r s t o o d most of the i s o l a t e d v o c a b u l a r y i n v o l v e d i n t h e t u t o r i a l but the s y n t a x on numerous o c c a s i o n s p r o v e d to be beyond h i s c o m p r e h e n s i o n . Thus the main c o n c e p t t h a t t h e t u t o r i a l s e t s out to e x p l a i n , (how t h e f o r m u l a e f o r t r a p e z o i d s and t r i a n g l e s a r e d e r i v e d ) was t o t a l l y m i s s e d by t h e s t u d e n t . A f t e r c o m p l e t i n g the t u t o r i a l he s t i l l g u e s s e d at the i n i t i a l a r e a q u e s t i o n s i n t h e p r a c t i c e , but he c o u l d a s s i g n t h e a p p r o p r i a t e d i g i t s t o t h e s y m b o l s f o r b a s e s , h e i g h t , and c a l c u l a t e B/2, B1+B2/2, and t h e a r e a s i n t h e r e m e d i a l p o r t i o n o f e a c h p r o b l e m . Once he s t a r t e d to work w i t h p e n c i l and p a p e r and was more c a r e f u l , he p r o v e d t h a t he c o u l d r e a d i l y c a l c u l a t e t he i n i t i a l a r e a s t o o . The e x p e r i m e n t e r f e l t t h a t i f t h e s t u d e n t had gone to p e n c i l and p a p e r e a r l i e r he w o u l d h a v e r e a c h e d the 80% e f f i c i e n c y s o o n e r . The s t u d e n t d e f i n i t e l y had no p r o b l e m a s s i g n i n g t h e b a s e s and h e i g h t s and e a s i l y c a l c u l a t e d B/2 o r B1+B2/2 i n t h e p r a c t i s e q u e s t i o n s . T h i s i s p r o b a b l y a d i r e c t r e s u l t of h i s e x p e r i e n c e w i t h the t u t o r i a l s e c t i o n . S t u d e n t s who d i d n o t have t u t o r i a l e x p e r i e n c e had a d i f f i c u l t t i m e a s s i g n i n g a p p r o p r i a t e b a s e s and h e i g h t s on t h e f i r s t few p r a c t i s e q u e s t i o n s . On the p o s t - t e s t t h i s s t u d e n t s c o r e d 9/10 d e m o n s t r a t i n g a d r a m a t i c i m p r o v e m e n t i n h i s a b i l i t y t o c a l c u l a t e t h e s e a r e a s . He was a l s o a b l e t o remember t h e c o r r e c t method of c a l c u l a t i o n one week a f t e r e x p o s u r e t o t h e c o m p u t e r s o f t w a r e . 50 CASE #2 S t u d e n t //2 w o u l d be r a n k e d i n the b o t t o m 25% of p a r t i c i p a n t s i n t h i s s t u d y as f a r as o v e r a l l a b i l i t y i s c o n c e r n e d . He i s c u r r e n t l y w o r k i n g a t t h e b e g i n n i n g of t h e g r a d e 8 math c u r r i c u l u m . He r e a d s at a g r a d e l e v e l of 3.1 ( S a t - H i J u n e 1 9 8 4 ) . On t h e p r e - t e s t he s c o r e d 1/10 g u e s s i n g a t t h e a r e a of t h e t r a p e z o i d s and u s i n g BxH f o r the a r e a of t h e t r i a n g l e s . A t t h e c o m p u t e r t h i s s t u d e n t had no p r o b l e m w i t h t h e i n i t i a l i n s t r u c t i o n s w i t h o u t h e s i t a t i o n he pushed the s p a c e b a r t o c o n t i n u e . He a l s o u n d e r s t o o d t h a t t h e g r a p h i c i n f r a m e #1 was a t r a p e z o i d . I n frame #2 he d i d not u n d e r s t a n d t h e word p a r a l l e l . The g r a p h i c s h e r e d e m o n s t r a t i n g t h e two p a r a l l e l l i n e s i n a p a r a l l e l o g r a m d i d not seem to g i v e him any c l u e s and he c o u l d not show t h e e x p e r i m e n t e r the two p a r a l l e l l i n e s i n t h e p i c t u r e g r a p h i c of t h e p a r a l l e l o g r a m on t h e m o n i t o r . I n frame #3 t h e s t u d e n t knew w h i c h one of t h e d i a g r a m s was t h e t r a p e z o i d , but he c o u l d not show the e x p e r i m e n t e r t h e p a r a l l e l s i d e s on t h e t r a p e z o i d . I n frame #5 t h e s t u d e n t ' r e a d ' t h e t e x t , t h e n the e x p e r i m e n t e r posed t h e q u e s t i o n "How i s a p a r a l l e l o g r a m d i f f e r e n t f r o m a t r a p e z o i d ? " The answer t o t h i s q u e s t i o n was c o n t a i n e d i n t h e f i r s t s e n t e n c e of t h i s f r a m e . The s t u d e n t c o u l d not answer t h i s q u e s t i o n and seemed v e r y c o n f u s e d . T h i s was a f a i r l y c l e a r i n d i c a t i o n t h a t he was h a v i n g p r o b l e m s w i t h the l a n g u a g e and v o c a b u l a r y p r e s e n t e d i n t h e t e x t . I n frame #5 t h e s t u d e n t i s a s k e d t o compare an o b v i o u s l y l a r g e r 51 p a r a l l e l o g r a m to a s m a l l e r t r a p e z o i d and d e c i d e w h i c h one i s l a r g e r . The s t u d e n t seemed t o u n d e r s t a n d t h e t a s k , but t h e n i n c o r r e c t l y d e c i d e d on the t r a p e z o i d . D i d he t h i n k the t r a p e z o i d was b i g g e r or d i d he m i s u n d e r s t a n d t h e t a s k ? I n f r a m e #6 t h e s t u d e n t w a t c h e d t he a n i m a t i o n but seemed c o n f u s e d . E v e n a f t e r t h e c o r r e c t answer was d i s p l a y e d he was n o t s u r e i f h i s answer was c o r r e c t o r wrong. I n frame #7 he a g a i n compared and i n c o r r e c t l y p i c k e d t h e s m a l l e r t r a p e z o i d t h i n k i n g t h a t i t was l a r g e r t h a n t h e p a r a l l e l o g r a m . A g a i n as i n f rame #6 he seemed v e r y c o n f u s e d when t h e c o r r e c t answer was r e v e a l e d i n frame #8. I n fr a m e #9 when the s t u d e n t was a s k e d t o f i n d t h e a v e r a g e b e t w e e n 4 and 8 he g u e s s e d i n c o r r e c t l y on b o t h a t t e m p t s . I n frame #9.5 t h e t e x t t e l l s and shows the s t u d e n t t h e c o r r e c t method f o r c a l c u l a t i n g the a v e r a g e . The s t u d e n t q u i c k l y l o o k e d i t o v e r (11 s e c o n d s ) , s t a r t e d t o ask a q u e s t i o n , but pushed t h e s p a c e b a r to c o n t i n u e . I n frame #10 t h e t a s k i s s i m i l a r to the two b e f o r e w h ere t h e s t u d e n t must compare a p a r a l l e l o g r a m and t r a p e z o i d and d e c i d e i f t h e y a r e the same s i z e o r n o t . The s t u d e n t had no p r o b l e m e n t e r i n g t h e d a t a , but gave an i n c o r r e c t r e s p o n s e . I n frame #11 t h e p r o g r a m u s e s a n i m a t i o n t o show t h a t t h e two a r e i n f a c t t h e same s i z e and g i v e s t h e f o r m u l a u s e d t o f i n d t h e a r e a s f o r t r a p e z o i d s . The s t u d e n t seemed c o n f u s e d a g a i n , s t a r t e d t o ask a q u e s t i o n and t h e n d e c i d e d t o c o n t i n u e and p u s h e d t h e s p a c e b a r . The t a s k i n frame #12 i s t o copy t he f o r m u l a w h i c h a p p e a r s i n a box on t h e m o n i t o r , o n t o t h e a p p r o p r i a t e s p o t on handout #4. The s t u d e n t r e a d t h e t e x t 52 and t h e n s t a r t e d t o push t h e s p a c e b a r t o c o n t i n u e , s h o w i n g t h a t he had not comprehended t h e t a s k . The e x p e r i m e n t e r s t o p p e d t h e s t u d e n t f r o m p u s h i n g t h e s p a c e b a r and i n s i g n l a n g u a g e t o l d h i m to r e a d i t c a r e f u l l y . The s t u d e n t l o o k e d o v e r t h e t e x t a g a i n and a p p e a r e d t o be v e r y c o n f u s e d and t o t a l l y a t a l o s s as t o what t o do. He a s k e d f o r g u i d a n c e s i g n i n g , "What d o ? " The e x p e r i m e n t e r t o l d t h e s t u d e n t t h a t he s h o u l d copy t h e f o r m u l a . The s t u d e n t d i d not know where t h e f o r m u l a was or where t o copy i t . A f t e r much d i s c u s s i o n t h e e x p e r i m e n t e r had t o show h i m what t o copy and where to co p y i t . T h i s was a n o t h e r e xample o f t h i s s t u d e n t ' s i n a b i l i t y to r e a d and comprehend t h e s y n t a x i n v o l v e d i n t h e t u t o r i a l p r o g r a m . I n frame #13 t h e s t u d e n t was c o n f u s e d a t f i r s t , but he d i d s u c c e s s f u l l y e n t e r t h e c o r r e c t d i g i t f o r B2 and H i n frame #14. I n frame #15 t h e B1+B2/2 f o r m u l a s t o p p e d h i m i n h i s t r a c k s . The e x p e r i m e n t e r r e m i n d e d t h e s t u d e n t of t h e f o r m u l a and e n c o u r a g e d him t o c o n t i n u e . He q u i c k l y e n t e r e d two i n c o r r e c t g u e s s e s a p p a r e n t l y w i t h l i t t l e t h o u g h t . I n f r a m e #16 t h e s t u d e n t a g a i n q u i c k l y g u e s s e d t w i c e a t t h e a r e a w i t h o u t much c o n t e m p l a t i o n . I n fr a m e #17 t h e c o r r e c t method of c a l c u l a t i n g t h e a r e a was e x p l a i n e d and the s t u d e n t a p p e a r e d t o c a r e f u l l y s t u d y t h i s d a t a (31 s e c o n d s ) . He s t a t e d he 'now u n d e r s t o o d t h e c o r r e c t way'. I n fr a m e #18 he d i d not u n d e r s t a n d t h e word " s h r i n k " . A t fr a m e #19 t h e s t u d e n t r e a d a b o u t t h e t r i a n g l e f o r m u l a and s i g n e d , " C o n f u s e d . " The e x p e r i m e n t e r s i g n e d , "Read a g a i n . " The s t u d e n t l o o k e d at i t a g a i n and c o n t i n u e d w i t h o u t a s k i n g f o r f u r t h e r c l a r i f i c a t i o n . 53 I n f r ame #20 t h e s t u d e n t c o n c e n t r a t e d h a r d , r e a d i n g he t e x t w h i c h gave an example of a r e a c o m p u t a t i o n f o r t r i a n g l e s . The s t u d e n t a s k e d f o r h e l p and the e x p e r i m e n t e r e x p l a i n e d how t h e t r i a n g l e f o r u m l a was u s e d u s i n g t h e example on t h e m o n i t o r . The s t u d e n t was not u s i n g t h e d a t a i n t h e g r a p h i c of t h e t r i a n g l e and the example f o r m u l a c a l c u l a t i o n to h e l p h i m s e l f u n d e r s t a n d how t h e f o r m u l a was s e t up and e x e c u t e d . He seemed s a t i s f i e d a f t e r t h i s e x p l a n a t i o n and c o n t i n u e d . The e x p e r i m e n t e r was f o r c e d t o s t o p t h e s t u d e n t a g a i n i n frame #21 and ask him t o r e a d i t a g a i n b e c a u s e he a t t e m p t e d t o push t h e s p a c e b a r t o c o n t i n u e b e f o r e c o p y i n g t h e f o r m u l a o n t o h a n d o u t #4. A f t e r r e a d i n g i t f o r a s e c o n d t i m e the s t u d e n t s t i l l had no i d e a t h a t t h e t a s k was t h e same as b e f o r e i n f r a m e #12. The e x p e r i m e n t e r a g a i n e x p l a i n e d t h a t he must c o p y t h e f o r m u l a o n t o t h e s h e e t and t h e s t u d e n t d i d i t . I n f r a m e #22 and #23 t h e s t u d e n t e n t e r e d t h e a p p r o p r i a t e d i g i t s f o r B and H, but a t frame #24 when he i s a s k e d to c a l c u l a t e t h e a r e a , t h e s t u d e n t c o u l d n o t use t h e n u m e r i c a l v a l u e s and t h e f o r m u l a t o g e t t h e c o r r e c t a n s w e r . I n s t e a d he q u i c k l y g u e s s e d t w i c e w i t h l i t t l e t h o u g h t . I n frame #25 he q u i c k l y r e a d o v e r the c o r r e c t method f o r t r i a n g l e a r e a c a l c u l a t i o n i n 12 s e c o n d s . I n t h e s i g n e d q u e s t i o n i n g a f t e r t h e t u t o r i a l t h e s t u d e n t showed i n h i s a n s w e r s t h a t he had r e c e i v e d l i t t l e b e n e f i t f r o m t h e i n f o r m a t i o n p r e s e n t e d i n t h e t u t o r i a l . The words " b a s e " , " p a r a l l e l " , and " a v e r a g e " c a l c u l a t i o n a p p e a r e d to mean n o t h i n g t o him. He a l s o s t a t e d t h a t he u n d e r s t o o d o n l y a l i t t l e of what t h e c o m p u t e r had t r i e d t o t e a c h him. A l t h o u g h t h i s s t u d e n t seemed to u n d e r s t o o d a v e r y s m a l l p a r t o f t h e c o n t e n t p r e s e n t e d i n the t u t o r i a l , he d i d say t h a t he e n j o y e d i t and w o u l d l i k e t o work w i t h t h e c o m p u t e r a g a i n i n t h e f u t u r e . On t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e t h i s s t u d e n t c o n t i n u e d to have p r o b l e m s and c o n s i s t e n t l y t r i e d t o do t h e w o r k i n h i s h e a d , n e v e r u s i n g p a p e r o r p e n c i l . Q u e s t i o n #1 ( t r a p e z o i d ) : He was wrong on h i s i n i t i a l answer f o r t h e a r e a and he was a l s o wrong on a l l s u b s e q u e n t i n i t i a l a r e a q u e s t i o n s . He had p r o b l e m s i d e n t i f y i n g B l , B2, and H and c o u l d not c o r r e c t l y c a l c u l a t e B1+B2/2 o r the a r e a . Q u e s t i o n //2 ( t r i a n g l e ) : He c o r r e c t l y a s s i g n e d B and H, and c o r r e c t l y c a l c u l a t e d B/2 and the a r e a f o r t h i s t r i a n g l e . Q u e s t i o n #3,#4 ( t r a p e z o i d s ) : He c o u l d c o r r e c t l y a s s i g n d i g i t s t o B l , B2, and H, but was u n a b l e t o g e t p a s t B1+B2/2 m o r e o v e r once g i v e n t h e c o r r e c t answer f o r B1+B2/2 c o u l d n o t u s e t h e f o r m u l a t o c a l c u l a t e t h e a r e a . He w o u l d j u s t q u i c k l y g u e s s and make no a t t e m p t t o use t h e f o r m u l a . Q u e s t i o n #5 ( t r a p e z o i d ) : A g a i n he c o u l d g e t B l , B2, H, but was u n a b l e to c a l c u l a t e B1+B2/2. Once g i v e n the c o r r e c t a n s w e r f o r B1+B2/2 he d i d c a l c u l a t e t h e c o r r e c t a r e a f o r t h e f i r s t t i m e . H o w e v e r , t h i s was a l s o h i s l a s t s u c c e s s f u l a r e a c a l c u l a t i o n . Q u e s t i o n #6 ( t r a p e z o i d ) : The s t u d e n t c o u l d a s s i g n B l , B2, H, b u t c o u l d not c a l c u l a t e B1+B2/2 o r the a r e a even g i v e n the c o r r e c t answer f o r B1+B2/2. He a l s o had c o m p u t a t i o n a l 55 p r o b l e m s m u l t i p l y i n g by .5. Q u e s t i o n #7,#8 ( t r a p e z o i d s ) : A f t e r a s s i g n i n g B l , B2, H, t h e s t u d e n t c o u l d n o t c a l c u l a t e B1+B2/2, but g i v e n t h e c o r r e c t a n s w e r f o r B1+B2/2 he c o u l d use Bl+B2/2xH and c a l c u l a t e t h e c o r r e c t a r e a . A t t h i s s t a g e t h e s t u d e n t was v e r y t i r e d of t h e work and s i g n e d " I d o n ' t know how n e v e r u s e d t h i s b e f o r e . " Q u e s t i o n #9 ( t r a p e z o i d s ) : The s t u d e n t was r i g h t on B l , B2, H, and wrong on b o t h B1+B2/2 and a r e a c a l c u l a t i o n s . A g a i n he had p r o b l e m s w i t h .5 i n c o m p u t a t i o n , Bl+B2/2=6.5. Q u e s t i o n #10 ( t r i a n g l e ) : The s t u d e n t had p r o b l e m s w i t h d i v i s i o n i n v o l v i n g .5 i n the q u o t i e n t , r e s u l t i n g i n i n c o r r e c t a n s w e r s a t B/2 ( 3 . 5 ) and a r e a . Q u e s t i o n s # 11 , #12 , #13 , #14 ( t r a p e z o i d s ) : The s t u d e n t had no p r o b l e m a s s i g n i n g B l , B2, and H. But now the s t u d e n t a p p e a r e d t o be more f a t i g u e d and f r u s t r a t e d and c o u l d not c o r r e c t l y c a l c u l a t e B1+B2/2 f o r any of t h e s e p r o b l e m s and w o u l d q u i c k l y g u e s s a t t h e a r e a s . Due t o t h e t i m e l i m i t of a p p r o x i m a t e l y t w e n t y m i n u t e s , t h e f a t i g u e and f r u s t r a t i o n of t h e s t u d e n t , and t h e f e e l i n g t h a t t h e s t u d e n t w o u l d not r e a c h t h e e x p e c t e d l e v e l of e f f i c i e n c y , t h e t r e a t m e n t was s t o p p e d a t t w e n t y m i n u t e s . Summary: T h i s s t u d e n t had a v e r y h a r d t i m e w o r k i n g t h r o u g h t h e p r a c t i s e p o r t i o n o f t h e s o f t w a r e . He c o u l d r e a d i l y o b t a i n B l , B2, H, o r B, H, but he c o u l d not g e t p a s t t h e c a l c u l a t i o n f o r B1+B2/2 o r B/2. He a l s o had p r o b l e m s i n c o m p u t a t i o n when 56 .5 was i n v o l v e d i n t h e q u o t i e n t . He d e f i n i t e l y needed e x t r a h e l p a t t h e p o i n t where B1+B2/2 o r B/2 was demanded. U n f o r t u n a t e l y t h i s p r o g r a m was u n a b l e t o r e c o g n i z e or p r o v i d e r e m e d i a t i o n w i t h t h e s e d i f f i c u l t i e s . I n t h e t u t o r i a l s e c t i o n he r a r e l y a s k e d f o r c l a r i f i c a t i o n of t h e d a t a p r e s e n t e d . A t t h e p o i n t s where t h e e x p e r i m e n t e r c o u l d j u d g e h i s u n d e r s t a n d i n g of the t e x t t h r o u g h h i s a c t i o n s he i n e v i t a b l y d i s p l a y e d t o t a l l a c k o f c o m p r e h e n s i o n . I t can be assumed t h a t i n t h e i n s t a n c e s where h i s c o m p r e h e n s i o n c o u l d n o t be j u d g e d by a c t i o n s , t h a t t h e r e t o o he u n d e r s t o o d l i t t l e of the m a t e r i a l . A l t h o u g h t h e c o n c e p t s p r e s e n t e d were at h i s l e v e l of math a b i l i t y , t h e s y n t a x w i t h w h i c h i t was p r e s e n t e d was beyond h i s c o m p r e h e n s i o n . The l a c k o f d i a g n o s t i c and r e m e d i a t i o n c a p a b i l i t i e s i n t h e p r a c t i s e p o r t i o n l e f t him f r u s t r a t e d and u n s u c c e s s f u l . On t h e p o s t - t e s t t h i s s t u d e n t s c o r e d 2/10 g u e s s i n g a t t h e a r e a of t h e t r a p e z o i d s and u s i n g BxH f o r t h e a r e a of t h e t r i a n g l e s . C a s e #3 S t u d e n t #3 w o u l d be r a n k e d a t o r b e l o w t h e 3 0 t h p e r c e n t i l e f o r o v e r a l l a b i l i t y when compared t o t h e o t h e r p a r t i c i p a n t s i n t h i s s t u d y . She i s p r e s e n t l y w o r k i n g h a l f way t h r o u g h t h e g r a d e s e v e n math c u r r i c u l u m . She r e a d s a t a g r a d e l e v e l of 3.0 ( t h i s i s an e s t i m a t e : no S a t - H i d a t a a r e a v a i l a b l e on t h i s s t u d e n t ) . On t h e p r e - t e s t she s c o r e d 0/10, 57 summing t h e d i g i t s t o f i n d t h e a r e a f o r b o t h t r i a n g l e s and t r a p e z o i d s . I n f r a m e #1 t h e s t u d e n t d i d not know what the p i c t u r e on t h e m o n i t o r r e p r e s e n t e d ( t r a p e z o i d ) and she a l s o d i d not u n d e r s t a n d t h e i n s t r u c t i o n " p r e s s s p a c e bar t o c o n t i n u e " . I n f r a m e #2 she c o u l d p o i n t to t h e two p a r a l l e l l i n e s i n the p a r a l l e l o g r a m s h o w i n g h e r u n d e r s t a n d i n g of t h e t e r m p a r a l l e l w h i c h she had r e c e n t l y l e a r n e d i n math c l a s s . I n frame #3 she g u e s s e d and i d e n t i f i e d t h e t r a p e z o i d and c o u l d a l s o show t h e p a r a l l e l s i d e s on t h e t r a p e z o i d . L a t e r i n frame #10 she a s k e d , "What does t h i s word mean - t r a p e z o i d ? " I n frame #4 she c o u l d not say how a p a r a l l e l o g r a m was d i f f e r e n t f r o m a t r a p e z o i d , e v e n a f t e r t h e e x p e r i m e n t e r had t o l d h e r t h a t t h e a n s w e r c o u l d be f o u n d on t h e s c r e e n . The s t u d e n t s a i d , " I d o n ' t u n d e r s t a n d ( t h e t a s k ) . " T h i s was a n o t h e r o b v i o u s e x a m p l e t h a t she c o u l d not h a n d l e t h e s y n t a x p r e s e n t e d , as t h e c o r r e c t a n swer a p p e a r e d i n t h e f i r s t s e n t e n c e of the t e x t she was v i e w i n g . I n frame #5 she t h o u g h t t h a t she had to p i c k A o r B, but w a n t e d r e a s s u r a n c e . She d i d not u n d e r s t a n d t h e word l a r g e r and a s k e d f o r i t t o be d e f i n e d . She was v e r y t e n t a t i v e w i t h h e r a n s w e r s and a c t i o n s . She was c o r r e c t i n o b s e r v i n g t h a t t h e p a r a l l e l o g r a m was l a r g e r t h a n the t r a p e z o i d . I n frame #6 she w a t c h e d t h e a n i m a t i o n and i n f r a m e #7 w a s t e d no t i m e m a k i n g h e r c h o i c e , but d i d not push r e t u r n . Then a f t e r w a i t i n g , she remembered t o push t h e r e t u r n k e y . I n f r a m e #8 she was s u r p r i s e d to f i n d out t h a t she had made a wrong c h o i c e i n f r a m e #7. She u n d e r s t o o d t h a t 58 she was w r o n g . I n frame #9 she r a n i n t o a number of l a n g u a g e r e l a t e d p r o b l e m s . I n t h i s f rame t h e s t u d e n t i s r e q u i r e d to g i v e t h e a v e r a g e of 8 and 4. She d i d not u n d e r s t a n d the w o r d s " r e c t a n g l e " or " a v e r a g e " and needed d i r e c t i o n s on how t o e n t e r h e r two g u e s s e s of 5 and 7, b o t h i n c o r r e c t . The s t u d e n t c a r e f u l l y r e a d frame #9.5 t h a t t e l l s h e r how to c a l c u l a t e t he a v e r a g e of two numbers. I n frame #10 t h e s t u d e n t a s k e d , "What does t r a p e z o i d mean?", s h o w i n g her c o n f u s i o n and a p p a r e n t m i s u n d e r s t a n d i n g of t h e t a s k s at hand. I n frame #10 she s a i d t h a t t h e p a r a l l e l o g r a m and t r a p e z o i d w e r e not the same s i z e and i n frame #11 she was a g a i n s u r p r i s e d t h a t she was wrong but she u n d e r s t o o d t h a t h e r r e s p o n s e had been i n c o r r e c t . A t f r a m e #11 t h e e x p e r i m e n t e r was f o r c e d t o s t o p t h e s t u d e n t f r o m p u s h i n g t h e space bar and s i g n e d , "Read i t c a r e f u l l y . " The s t u d e n t a s k e d a b o u t ' f o r m u l a ' and the t e a c h e r showed and e x p l a i n e d the f o r m u l a i n t h e box on t h e s c r e e n . The s t u d e n t r e a d the t e x t a g a i n and d i d n o t u n d e r s t a n d what t o c o p y . The e x p e r i m e n t e r e x p l a i n e d t h e t a s k and had t o show t h e s t u d e n t t h e a p p r o p r i a t e s p o t to c o p y t h e f o r m u l a on h a n d o u t #4. She c o p i e d t h e f o r m u l a wrong and t h e e x p e r i m e n t e r c o r r e c t e d h e r m i s t a k e (B1+B2=H). She n e e d e d r e a s s u r a n c e a t e v e r y s t e p p r o b a b l y b e c a u s e the e x p e r i m e n t e r was t h e r e and a l s o b e c a u s e she was not f e e l i n g c o n f i d e n t a b o u t h e r c o m p r e h e n s i o n of t h e t e x t and t a s k s c o m i n g f r o m t h e t e x t . A t frame #13 and #14 t h e s t u d e n t a n a l y z e d t h e c o n t e n t and e n t e r e d the c o r r e c t v a l u e f o r b o t h B2 and H. I n frame #15 t h e s t u d e n t q u i c k l y g u e s s e d l e t t e r s 5 9 f o r B1+B2/2, f i r s t e n t e r i n g H, t h e n A. A t t h i s p o i n t i t was c l e a r t h a t she d i d n o t u n d e r s t a n d t h e t a s k , but when the c o r r e c t d i g i t a p p e a r e d she s i g n e d , " I u n d e r s t a n d now." H o w e v e r , a t fr a m e #16 she a g a i n e n t e r e d l e t t e r s f o r the a r e a i n s t e a d of d i g i t s on b o t h a t t e m p t s . She r e p o r t e d , " I d o n ' t u n d e r s t a n d a r e a . " The main c o n c e p t a l l a l o n g had been a r e a and she had n o t once a s k e d a b o u t t h e t e r m ' a r e a ' b e f o r e . I n f r a m e #17 when t h e c o r r e c t method f o r c a l c u l a t i n g the a r e a a p p e a r e d she q u i c k l y g l a n c e d a t i t and c o n t i n u e d o n t o t h e n e x t f r a m e . She c o u l d not have g r a s p e d t h e c o n c e p t w i t h s u c h a q u i c k r e a d o v e r t h e t e x t and c a l c u l a t i o n . A t frame #18 she d i d not know t h e word " s h r i n k " . She r e a d t h r o u g h t h e t e x t c o n c e r n i n g t h e a r e a of t r i a n g l e s i n f r a m e s #18, #19, and #20. I n frame #20 she s t a r t e d t o push t h e s p a c e b a r and t h e n h e s i t a t e d and t h e n c o p i e d t h e t r i a n g l e f o r m u l a o n t o t h e a p p r o p r i a t e s p o t on h a n d o u t #4. She had l e a r n e d t h i s f r o m h e r p r e v i o u s e x p e r i e n c e a t frame #12. On t h e p r a c t i s e t r i a n g l e q u e s t i o n i n f r a m e s #22, #23, and #24 she g u e s s e d i n c o r r e c t l y a t B and H and t h e n had no i d e a on t h e a r e a q u e s t i o n , r e s p o n d i n g a r e a = H. She o b v i o u s l y d i d not u n d e r s t a n d what t a s k s were i n v o l v e d a t t h i s j u n c t u r e i n the p r o g r a m . I n fr a m e #25 she q u i c k l y ( 1 0 s e c o n d s ) l o o k e d o v e r t h e e x p l a n a t i o n of t h e c o r r e c t method f o r s o l v i n g t h e a r e a of t r i a n g l e s and t h e n pushed t h e s p a r e b a r and was f i n i s h e d . I n t h e s i g n e d q u e s t i o n i n g a f t e r t h e t u t o r i a l i t was o b v i o u s t h a t she had u n d e r s t o o d v e r y l i t t l e of e i t h e r the v o c a b u l a r y u s e d o r t h e c o n c e p t s p r e s e n t e d i n t h e t u t o r i a l . 60 She s a i d t h a t she u n d e r s t o o d a l i t t l e of what t h e computer had t a u g h t h e r but a l t h o u g h she f e l t t h a t i t was h a r d to u n d e r s t a n d t h e c o m p u t e r , she l i k e d w o r k i n g w i t h i t and t h o u g h t she m i g h t l i k e to work w i t h t h e c o m p u t e r a g a i n i n t h e f u t u r e . I n t h e p r a c t i s e p o r t i o n she had d i f f i c u l t y w i t h t h e f i r s t t r a p e z o i d a s s i g n i n g t h e wrong v a l u e s t o B l , B2, and H, b u t i n e v e r y t r a p e z o i d a f t e r t h a t she c o u l d e a s i l y i d e n t i f y t h e c o r r e c t v a l u e s f o r t h e s e t h r e e c o m p o n e n t s . The same h a p p e n e d w i t h t h e t r i a n g l e s . On q u e s t i o n #2 she was way o f f on t h e v a l u e s f o r B and H, but on q u e s t i o n #10 and #13 she had no p r o b l e m g i v i n g t h e c o r r e c t v a l u e s to B and H. She c o n s i s t e n t l y e n t e r e d a q u i c k g u e s s f o r t h e i n i t i a l a r e a q u e s t i o n and at q u e s t i o n #9 s a i d t h a t she e n j o y e d w o r k i n g t h r o u g h t h e s e c t i o n where the t a s k was b r o k e n down i n t o i t s c o m p o n e n t s . T h i s was p r o b a b l y b e c a u s e i n t h i s s e c t i o n she was v e r y s u c c e s s f u l a t a s s i g n i n g t h e v a l u e s . H owever, she d i d n o t u n d e r s t a n d t h e f o r m u l a B1+B2/2, o r t h e c o n c e p t of AREA. She w o u l d q u i c k l y e n t e r a g u e s s when she came t o t h e s e p a r t s i n t h e br e a k d o w n of t h e t a s k . I n q u e s t i o n #10 ( t r i a n g l e ) she s a i d B/2=H, s h o w i n g h e r c o n t i n u e d c o n f u s i o n w i t h t h i s t a s k . She c o n t i n u e d t o g u e s s a t v a l u e s , n ot u n d e r s t a n d i n g where she was wrong o r how t o become s u c c e s s f u l . Due t o the t i m e l i m i t o f a p p r o x i m a t e l y t w e n t y m i n u t e s , t h e f a t i g u e of t h e s t u d e n t , and t h e f e e l i n g t h a t t h e s t u d e n t w o u l d not r e a c h t h e e x p e c t e d l e v e l of e f f i c i e n c y , the t r e a t m e n t was s t o p p e d a f t e r t w e n t y m i n u t e s ( i e . q u e s t i o n 61 #15). Summary: T h i s s t u d e n t s t r u g g l e d w i t h t h e s y n t a x and t h e r e f o r e the i n f o r m a t i o n and e x p l a n a t i o n s f o u n d i n t h e t u t o r i a l . I n the p r a c t i c e she q u i c k l y p i c k e d out t h e i n d i v i d u a l c o m p o nents, b u t when a s k e d t o c a l c u l a t e B/2, B1+B2/2, o r a r e a , she c o u l d n o t s o l v e t h e s e p r o b l e m s . She d i d not a p p e a r to put a g r e a t d e a l of t h o u g h t i n t o h e r a n s w e r s n o r use p e n c i l and p a p e r to t r y t o c a l c u l a t e them. She a l s o skimmed o v e r t h e v e r y i m p o r t a n t d e t a i l e d e x p l a n a t i o n s on how t o use the f o r m u l a and v a l u e s t o c o r r e c t l y c a l c u l a t e t h e a r e a s e x p l a i n e d i n the t u t o r i a l . The s y n t a x i n t h e t u t o r i a l was f a r beyond her a b i l i t y and the p r a c t i s e p o r t i o n d i d not p r o v i d e d her w i t h r e m e d i a t i o n and h e l p a t the B1+B2/2, B/2, o r a r e a c a l c u l a t i o n s where she needed e x t r a h e l p . O v e r a l l t h i s s o f t w a r e p r o v e d t o be u n s a t i s f a c t o r y f o r the needs and a b i l i t i e s of t h i s i n d i v i d u a l . On t h e p o s t - t e s t she s c o r e d 0/10 u s i n g t h e same s u m m a t i o n methods as she u s e d i n t h e p r e - t e s t . I n o t h e r w o r d s h e r e x p o s u r e t o t h i s s o f t w a r e had no e f f e c t on h e r s t r a t e g i e s f o r s o l v i n g t h e s e p r o b l e m s . C a s e #4 T h i s s t u d e n t w o u l d be p l a c e d i n t h e t o p 10% i n a r a n k i n g o f o v e r a l l a b i l i t i e s f o r p a r t i c i p a n t s i n v o l v e d i n t h i s s t u d y . He was r e c e n t l y a c c e p t e d i n t o t h e f r e s h m a n c l a s s a t G a l l a u d e t C o l l e g e and i s p r e s e n t l y w o r k i n g a t t h e m i d - p o i n t of t h e 62 g r a d e 12 A l g e b r a c u r r i c u l u m . He r e a d s a t a g r a d e l e v e l of 6.8 ( S a t H i J u n e 8 4 ) . T h i s s t u d e n t s c o r e d 5/10 on the p r e - t e s t . He knew how t o g e t t h e a r e a of t r i a n g l e s but g u e s s e d a t a l l t h e t r a p e z o i d s p r o b l e m s . A t t h e c o m p u t e r t h i s s t u d e n t b r e e z e d t h r o u g h t h e t u t o r i a l e x p e r i e n c i n g o n l y a few d i f f i c u l t i e s . T h i s s t u d e n t had no t r o u b l e w i t h t h e m e c h a n i c s of e n t e r i n g d a t a i n t o t h e c o m p u t e r . He u n d e r s t o o d most o f t h e v o c a b u l a r y and c o u l d a n s w e r a l l q u e s t i o n s posed by the e x p e r i m e n t e r i n c l u d i n g the one a t frame #4 w h e r e he s t a t e d f r o m t h e d a t a i n t h e f i r s t s e n t e n c e of t h e fr a m e t h a t a p a r a l l e l o g r a m i s d i f f e r r e n t f r o m a t r a p e z o i d b e c a u s e of the d i f f e r e n t l e n g t h of t h e b a s e s i n a t r a p e z o i d . A t f r a m e #5 he was a l i t t l e c o n f u s e d . He a s k e d i f he s h o u l d d e c i d e w h i c h one was l a r g e r ( t r a p e z o i d o r r e c t a n g l e ) and the e x p e r i m e n t e r s a i d , "Yes d e c i d e w h i c h one i s l a r g e r . " He h e s i t a t e d , compared t h e two and e n t e r e d h i s c o r r e c t g u e s s . He went t h r o u g h t h e n e x t c o m p a r i s o n a t frame #7 and #8 q u i c k l y and e a s i l y . On frame #9 he e a s i l y c a l c u l a t e d and e n t e r e d t h e a v e r a g e . A t frame #10 he t o o k a l o n g t i m e t o compare t h e p a r a l l e l o g r a m and t r a p e z o i d b e f o r e i n c o r r e c t l y d e c i d i n g t h a t t h e y d i d not have t h e same a r e a . He l a u g h e d when i n frame #11 he f o u n d t h a t t h e y d i d have t he same a r e a and he r e a d t h e t e x t and compared t h e two f o r m u l a e ( t r a p e z o i d and p a r a l l e l o g r a m ) c a r e f u l l y . He was emb a r a s s e d t h a t he had made a m i s t a k e . I n f r a m e #12 he a s k e d f o r c o n f i r m a t i o n of h i s u n d e r s t a n d i n g of the t a s k "Copy f o r m u l a ? " The e x p e r i m e n t e r s a i d n o t h i n g . The s t u d e n t h e s i t a t e d and 6 3 s i g n e d , "What do I do" t o h i m s e l f , but t h e n c o p i e d the f o r m u l a and added a B and H o n t o t h e d r a w i n g of the t r a p e z o i d on handout #4. He was c o n f u s e d as t o the p l a c e m e n t of l i n e s B and H on t h e t r a p e z o i d d r a w i n g . I n f r a m e s #13, #14, and #15 he had no p r o b l e m e n t e r i n g t h e c o r r e c t v a l u e s B2, H, and q u i c k l y a n s w e r e d B1+B2/2. I n frame #16 he t o o k a l i t t l e t i m e and c o r r e c t l y c a l c u l a t e d t h e a r e a i n h i s h e a d . A t frame #17 he q u i c k l y r e a d o v e r t h e e x p l a n a t i o n of how t o c a l c u l a t e t h e a r e a . He u n d e r s t o o d t h e t e r m " s h r i n k " a t frame #18. I n f r a m e #19 t h e s t u d e n t i s shown a t r i a n g l e and an example of an a r e a c a l c u l a t i o n i s w o r k e d out f o r him u s i n g t h e t r a p e z o i d f o r m u l a w i t h B2=0. T h i s s t u d e n t c a r e f u l l y c h e c k e d the numbers t o make s u r e e v e r y t h i n g was r i g h t . A t frame #21 he c o p i e d t h e f o r m u l a o n t o the c o r r e c t p l a c e on h a n d o u t #4. A l l t h e s t u d e n t s c o p i e d i t A=B/2xH=A, but t h i s s t u d e n t s t a r t e d t h i s way and t h e n e r r a s e d t h e l a s t =A r e a l i z i n g i t was the same as t h e f i r s t A. The h a n d o u t p r o v e d t o be a l i t t l e c o n f u s i n g f o r a l l t h e o t h e r s t u d e n t s t h a t w o r k e d t h r o u g h t h e t u t o r i a l . I n f r a m e s #22 and #23 he q u i c k l y e n t e r e d t h e c o r r e c t v a l u e s f o r B2 and H. I n fr a m e #24 t h e com p u t e r a s k s t h e s t u d e n t t o c a l c u l a t e t h e a r e a . T h i s s t u d e n t a s k e d i f t h e y 'wanted t h e a n s w e r * . The e x p e r i m e n t e r s a i d ' y e s ' . The s t u d e n t c o r r e c t l y w o r k e d out t h e v a l u e i n h i s head and e n t e r e d i t . He b r i e f l y l o o k e d a t t h e c o r r e c t method f o r c a l c u l a t i o n f o u n d i n frame #25. I n t h e s i g n e d q u e s t i o n i n g a f t e r t h e t u t o r i a l e x p e r i e n c e t h e s t u d e n t e a s i l y a n s w e r e d a l l t he q u e s t i o n s e x c e p t f o r the 64 one r e g a r d i n g t h e c o m p a r i s o n o f t h e t h r e e d i f f e r e n t p a r a l l e l o g r a m s and t r a p e z o i d s . T h i s s t u d e n t u n d e r s t o o d many o f the c o n c e p t s and v o c a b u l a r y d i s c u s s e d i n the t u t o r i a l but he c o u l d not d e c i p h e r t h e a t t e m p t i n the t u t o r i a l t o show how t h e f o r m u l a f o r t r a p e z o i d s was d e r i v e d . The s t u d e n t s t a t e d t h a t he u n d e r s t o o d a l l t h e i n f o r m a t i o n t h a t t h e co m p u t e r t a u g h t him. He s a i d t h a t i t was e a s y t o u n d e r s t a n d , and he w o u l d l i k e t o be t a u g h t by a c o m p u t e r a g a i n i n t h e f u t u r e . I n t h e p r a c t i s e s e c t i o n he w o r k e d out t h e i n i t i a l a r e a q u e s t i o n i n h i s head f o r q u e s t i o n #1 ( t r a p e z o i d ) , #2 ( t r i a n g l e ) , #3 and #4 ( t r a p e z o i d s ) , r e a c h i n g t h e 80% e f f i c i e n c y l e v e l i n one m i n u t e and f i f t y - f i v e s e c o n d s . He t h e n e a s i l y c a l c u l a t e d t h e c o r r e c t a r e a f o r a t r a p e z o i d and t r i a n g l e w i t h o u t v i e w i n g t h e f o r m u l a . S ummary: T h i s s t u d e n t had few p r o b l e m s w i t h t h e c o n t e n t and s y n t a x i n the t u t o r i a l and b r e e z e d t h r o u g h t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e t h a n k s t o the l e a r n i n g t h a t had h a p p e n e d d u r i n g h i s e x p o s u r e t o t h e t u t o r i a l . On t he p o s t - t e s t t h i s s t u d e n t s c o r e d 10/10 s h o w i n g an i m p r o v e m e n t o v e r h i s p r e - t e s t s c o r e s . C a s e #5 T h i s s t u d e n t w o u l d be r a n k e d a b o u t t h e 5 0 t h p e r c e n t i l e when c o m p a r i n g h e r g e n e r a l a b i l i t i e s t o o t h e r s t u d e n t s i n v o l v e d i n t h i s s t u d y . She i s p r e s e n t l y w o r k i n g h a l f way t h r o u g h t h e g r a d e 9 math c u r r i c u l u m i n . She r e a d s a t a gra d e 65 l e v e l of 7.6 ( S a t H i J u n e 8 4 ) . On t h e p r e - t e s t she s c o r e d 1/10 g u e s s i n g a t t h e a r e a of t r a p e z o i d s and u s i n g BxH f o r the a r e a of the t r i a n g l e s . I n frame #1 t h e s t u d e n t knew t h a t t h e g r a p h i c was a t r a p e z o i d and d i d not h e s i t a t e t o f o l l o w t h e d i r e c t i o n s and p u s h t h e s p a c e b ar t o c o n t i n u e . The s t u d e n t c o u l d show the two p a r a l l e l l i n e s ( s i d e s ) of the p a r a l l e l o g r a m , d e m o n s t r a t i n g t h a t she u n d e r s t o o d t h e t e r m p a r a l l e l i n frame #2. I n frame #3 she knew w h i c h d i a g r a m was t h e t r a p e z o i d and c o u l d show t h e p a i r of p a r a l l e l s i d e s . I n frame //4 t h e s t u d e n t r e a d t h e t e x t and when a s k e d f o r t h e d i f f e r e n c e b e t w e e n t r a p e z o i d s and p a r a l l o g r a m s s a i d 1 p a r a l l o g r a m s have two p a i r s of p a r a l l e l s i d e s , t r a p e o i d s o n l y have one p a i r of p a r a l l e l s i d e s ' . T h i s i s c o r r e c t , but i n t h e frame i t s t a t e d " i n a t r a p e z o i d t h e p a r a l l e l s i d e s have d i f f e r e n t l e n g t h s " . T h e r e f o r e a l t h o u g h t h e s t u d e n t had a c o r r e c t answer t he i n f o r m a t i o n was not f r o m t h e c o n t e n t of t h i s f r a m e . She a s k e d t h e e x p e r i m e n t e r i f h e r answer was r i g h t . I n c o m p a r i n g t h e a r e a s of a t r a p e z o i d and p a r a l l e l o g r a m i n frame #5, the s t u d e n t d i d not know what t o e n t e r i n t o t h e c o m p u t e r . She s t a t e d , " T h i n k e q u a l " and t h e n d e c i d e d B was l a r g e r and a s k e d , "What d o ? " The e x p e r i m e n t e r s t a t e d , " E n t e r B." The s t u d e n t e n t e r e d B and t h e n w a i t e d f o r a l o n g t i m e w h i l e n o t h i n g h a p p e n e d . F i n a l l y t h e e x p e r i m e n t e r t o l d h e r to push r e t u r n . I n f r a m e #6 t h e s t u d e n t u n d e r s t o o d t h a t the t r a p e z o i d (B) was n o t l a r g e r and u n d e r s t o o d t h a t h e r answer was wrong. H a v i n g l e a r n e d f r o m h e r e x p e r i e n c e i n frame #5 66 she q u i c k l y e n t e r e d h e r c h o i c e i n frame #7, pushed r e t u r n and s i g n e d , "Hope." The s t u d e n t saw i n frame #8 t h a t she had c o r r e c t l y p i c k e d t h e t r a p e z o i d as h a v i n g t h e l a r g e r a r e a . At f r a m e #9 t h e s t u d e n t r e a d t h e i n f o r m a t i o n about a v e r a g e s and a s k e d f o r e a c h word t o be e x p l a i n e d and a l s o a s k e d f o r more h e l p u n d e r s t a n d i n g t h e c o n c e p t of a v e r a g e . T h i s was a n o t h e r i n d i c a t i o n t h a t t h e s y n t a x was d i f f i c u l t f o r h e r . The s t u d e n t g u e s s e d 2 f i r s t and t h e n t h o u g h t a b o u t i t and d e c i d e d on 6, w h i c h was t h e c o r r e c t answer f o r t h e a v e r a g e b etween 4 and 8. I n frame #9.5 she saw t h a t h e r s e c o n d answer was c o r r e c t and she r e a d o v e r t h e i n f o r m a t i o n on c a l c u l a t i n g a v e r a g e s . A t frame #10 she s t a t e d t h a t the r e c t a n g l e and t r a p e z o i d were n o t t h e same s i z e and had no p r o b l e m e n t e r i n g h e r c h o i c e . She was s u r p r i s e d a t frame #11 when t o l d t h a t t h e two a r e the same s i z e . I n frame #12 where she was a s k e d t o copy t h e f o r m u l a , she a s k e d t h e e x p e r i m e n t e r i f she s h o u l d i g n o r e t h e i n f o r m a t i o n on t h i s f r a m e . The e x p e r i m e n t e r s t a t e d , "No." The s t u d e n t t h e n a s k e d , " S h o u l d I c o p y ? " and s t a r t e d t o copy t h e f o r m u l a o n t o t h e s c r a p p a p e r . The e x p e r i m e n t e r s t o p p e d the s t u d e n t and had t o show h e r e x a c t l y w here on h a n d o u t #4 t o copy t h e f o r m u l a . The s t u d e n t c o p i e d t h e f o r m u l a A= B l + B 2 / 2 x H =A, p u t t i n g i n t h e l a s t '=A' w h i c h was not needed and m i g h t have been c o n f u s i n g . H e r e the s t u d e n t u n d e r s t o o d t h e t a s k of c o p y i n g t h e f o r m u l a but d i d n o t u n d e r s t a n d t h a t i t was t o be c o p i e d on h a n d o u t #4, even t h o u g h i t was c l e a r l y s t a t e d i n t h e f r a m e . A t frame #13 t h e s t u d e n t was c o n f u s e d and h e s i t a t e d c o m p l a i n i n g , "Never seen 67 b e f o r e . " She d i d not u n d e r s t a n d t h e t a s k . The e x p e r i m e n t e r s a i d , " q u e s s . " She q u i c k l y e n t e r e d a quess and was t o l d t h a t i t was wrong. Then she q u e s s e d a g a i n and d i d not push r e t u r n k e y u n t i l t h e e x p e r i m e n t e r p r o m p t e d h e r . A t frame #14 she g o t t h e i d e a and q u i c k l y e n t e r e d t h e c o r r e c t d i g i t f o r H. Frame #15 a s k e d f o r t h e v a l u e of B1+B2/2. The s t u d e n t t h o u g h t a b o u t i t and t h e n q u i c k l y made two i n c o r r e c t q u e s s e s . She d i d not u n d e r s t a n d t h e t a s k h e r e and when t h e c o r r e c t a n s w e r a p p e a r e d , she q u i c k l y moved o n t o t h e n e x t frame w i t h o u t l o o k i n g a t i t c a r e f u l l y . A g a i n a t frame #16 she d i d n o t comprehend t h e t a s k and q u i c k l y g u e s s e d t w i c e a t the a r e a o f t h e t r a p e z o i d . A t frame #17 when t h e c o r r e c t method f o r c a l c u l a t i o n i s shown she b r i e f l y g l a n c e d a t i t (6 s e c o n d s ) and t h e n pushed t h e sp a c e b a r to c o n t i n u e . The computer s h o u l d have had a w a r n i n g h e r e t o t e l l p e o p l e who made two i n c o r r e c t g u e s s e s t o c a r e f u l l y r e v i e w t h e c o r r e c t method of c a l u l a t i o n . I t s h o u l d a l s o use a d e l a y l o o p to f o r c e the s t u d e n t t o s t u d y i t s t u d i o u s l y . Many s t u d e n t s d i d not r e a l i z e how i m p o r t a n t and h e l p f u l t h e d a t a i n t h i s f rame c o u l d be. A t frame #18 she u n d e r s t o o d t h e word " s h r i n k " . D u r i n g t h e t r i a n g l e i n f o r m a t i o n i n f r a m e s #19 and #20 she a p p e a r e d d e s p o n d e n t , f r u s t r a t e d , and c o n f u s e d . H a v i n g l e a r n e d f r o m f r a m e #12, she c o p i e d t h e f o r m u l a o n t o t h e a p p r o p r i a t e s p o t on h a n d o u t #4 a c c o r d i n g t o t h e i n s t r u c t i o n s i n frame #21. A g a i n she c o p i e d w i t h o u t t h o u g h t A=B/2xH=A d u p l i c a t i n g t h e *=A' p o r t i o n of the f o r m u l a . I n frame #22 and #23 she had no p r o b l e m e n t e r i n g the. c o r r e c t v a l u e s f o r B 68 and H. H o w e v e r , a t frame #25 she e n t e r e d two w i l d random g u e s s e s f o r the a r e a , a n s w e r i n g f i r s t '72' and t h e n '17'. When the c o r r e c t method was g i v e n she q u i c k l y g l a n c e d a t i t (4 s e c o n d s ) and c o n t i n u e d to t h e end by p u s h i n g the s p a c e b a r . I n the s i g n e d q u e s t i o n i n g a f t e r t h e t u t o r i a l i t was e v i d e n t t h a t she had u n d e r s t o o d l i t t l e o f t h e c o n t e n t of t h e t u t o r i a l . She c o u l d n o t remember how many p a r a l l e l s i d e s t h e r e were on a t r a p e z o i d , e v e n t h o u g h she d i d answer a s i m i l a r q u e s t i o n p o s e d d u r i n g the t u t o r i a l . She d i d not u n d e r s t a n d t h e c o n c e p t or t h e method u s e d t o show how the f o r m u l a e were d e r i v e d . She d i d not know how to c a l c u l a t e an a v e r a g e a l t h o u g h 6 h e was s u c c e s s f u l a t t h i s d u r i n g t h e p r o g r a m . She s t a t e d t h a t she u n d e r s t o o d some of t h e i n f o r m a t i o n t a u g h t by the c o m p u t e r . She t h o u g h t t h a t i t was h a r d t o u n d e r s t a n d the c o m p u t e r and she d i d not l i k e math. She d i d not t h i n k she w o u l d l i k e t o work w i t h c o m p u t e r s a g a i n a f t e r t h i s e x p e r i e n c e . D u r i n g t h e p r a c t i s e p o r t i o n she i m m e d i a t e l y got B l , B2, and H, but j u s t g u e s s e d a t B1+B2/2 and a r e a on q u e s t i o n #1 ( t r a p e z o i d ) . Q u e s t i o n #2 ( t r i a n g l e ) : She c o r r e c t l y i d e n t i f i e d B, H, and B/2, but f a i l e d to c a l c u l a t e t h e a r e a and was a n g r y and c o n f u s e d . Q u e s t i o n #3 ( t r a p e z o i d ) : She e n t e r e d H f o r B2 and t h e n c a r e f u l l y and c o r r e c t l y w o r k e d out B1+B2/2, but gave the same an s w e r (B1+B2/2) f o r the a r e a . She d i d not m u l t i p l y 69 B l + B 2 / 2 x H t o c a l c u l a t e t h e a r e a . Q u e s t i o n #4 ( t r a p e z o i d ) : She c o r r e c t l y e n t e r e d B l , B2, and H, and c a l c u l a t e d B1+B2/2. When A a p p e a r e d she a s k e d , "What i s t h i s ? " The e x p e r i m e n t e r s a i d , " F o l l o w t h e f o r m u l a " , and p o i n t e d t o the s h e e t . The s t u d e n t t h e n c o r r e c t l y e n t e r e d t h e a n s w e r . Q u e s t i o n #5 ( t r a p e z o i d ) : C a r e f u l l y she t r i e d to g e t t h e i n i t i a l q u e s t i o n r i g h t , but f a i l e d . Then u s i n g t h e r i g h t numbers and m e t h o d s , but i n c o r r e c t c o m p u t a t i o n she got b o t h B1+B2/2 and t h e a r e a w rong. Q u e s t i o n #6 ( t r a p e z o i d ) : She c o r r e c t l y e n t e r e d B l , B2, and H, b u t a c o m p u t a t i o n p r o b l e m (.5) r e s u l t e d i n an i n c o r r e c t B1+B2/2. She was s u c c e s s f u l a t t h e a r e a c a l c u l a t i o n u s i n g t h e c o r r e c t B l + B 2 / 2 x H . Now she r e a l l y u n d e r s t o o d t h e c o r r e c t method f o r c a l c u l a t i n g t h e a r e a s u 6 i n g t h e f o r m u l a . Q u e s t i o n #7 ( t r a p e z o i d ) : The i n i t i a l q u e s t i o n was w r o n g , but she had no d i f f i c u l t i e s w o r k i n g t h r o u g h the r m e d i a l s e c t i o n . Q u e s t i o n #8 ( t r a p e z o i d ) : F o r t h e f i r s t t i m e she got t h e i n i t i a l q u e s t i o n r i g h t . Q u e s t i o n #9 ( t r a p e z o i d ) : She u s e d t h e c o r r e c t methods and v a l u e s , b u t due t o c o m p u t a t i o n a l p r o b l e m s she e n t e r e d i n c o r r e c t a n swer to b o t h B1+B2/2 and a r e a . Q u e s t i o n #10 ( t r i a n g l e ) : She got t h e i n i t i a l a r e a w rong. T h e n w o r k i n g on p a p e r she c o r r e c t l y a n s w e r e d a l l t h e s t e p by s t e p ( r e m e d i a l ) q u e s t i o n s . Q u e s t i o n #11,#12 ( t r a p e z o i d s ) : She was c o r r e c t on the 70 i n i t i a l a r e a c a l c u l a t i o n on b o t h q u e s t i o n s . Q u e s t i o n s #13 ( t r i a n g l e ) : She made a s i l l y m i s t a k e i n a s s i g n i n g numbers c a u s i n g an i n c o r r e c t B/2, but she d i d c a l c u l a t e t h e a r e a u s i n g c o r r e c t l y u s i n g c o r r e c t e d d a t a . Q u e s t i o n #14,#15 ( t r a p e z o i d s ) : B o t h i n i t i a l a r e a s were c a l c u l a t e d c o r r e c t l y . Q u e s t i o n #16 ( t r i a n g l e ) : The i n i t i a l a r e a was c o r r e c t . The s t u d e n t had r e a c h e d 80% e f f i c i e n c y a f t e r 20 m i n u t e s and 10 s e c o n d s . I n t h e p r a c t i c e w i t h o u t t h e a i d of t h e f o r m u l a she c a l c u l a t e d b o t h t h e t r i a n g l e and t r a p e z o i d c o r r e c t l y on t h e f i r s t a t t e m p t . She w o u l d f i r s t f i n d B/2 o r B1+B2/2 and t h e n m u l t i p l y by the h e i g h t . S ummary: I n t h e t u t o r i a l p o r t i o n of t h e p r o g r a m t h i s s t u d e n t w o u l d have b e n e f i t e d i f she was f o r c e d to c a r e f u l l y s c r u t i n i z e t h e c o r r e c t methods of c a l c u l a t i o n f o r b o t h t r a p e z o i d s and t r i a n g l e s . She q u i c k l y p a s s e d o v e r t h e s e two v e r y i m p o r t a n t f r a m e s . She had a d i f f i c u l t t i m e w i t h t h e s y n t a x , c o n t e n t , and s i g n i f i c a n c e of t h e d a t a i n the t u t o r i a l , but seemed t o u n d e r s t a n d most of t h e i n s t r u c t i o n s . The r e s u l t s f r o m t h e p o s t t u t o r i a l q u e s t i o n i n g showed t h a t s he r e c e i v e d l i t t l e b e n e f i t f r o m e x p o s u r e t o the t u t o r i a l e x c e p t f o r t h e f a c t t h a t she was a b l e t o c o r r e c t l y a s s i g n v a l u e s t o B l , B 2 o r B and H on h e r f i r s t e x p o s u r e to t h e s e i n t h e p r a c t i s e s e c t i o n . She o b v i o u s l y p i c k e d up on t h e s e c o n c e p t s d u r i n g t h e t u t o r i a l . T h i s made h e r t a s k i n the p r a c t i c e e a s i e r t h a n f o r t h o s e s t u d e n t s who d i d not r e c i e v e 71 t u t o r i a l i n f o r m a t i o n . On t h e p o s t - t e s t she s c o r e d 0/10 u s i n g a summation method t o c a l c u l a t e a r e a f o r b o t h t r a p e z o i d s (a+b+c) and t r i a n g l e s ( a + b ) , s h o w i n g t h a t she had f o r g o t t e n how to c a l c u l a t e t h e s e a r e a s o v e r the one week p e r i o d between the t r e a t m e n t and the p o s t - t e s t . C a s e #6. S t u d e n t #6 was r a n k e d i n the b o t t o m 5% o f p a r t i c i p a n t s i n t h i s s t u d y as f a r as o v e r a l l a b i l i t y i s c o n c e r n e d . He i s p r e s e n t l y w o r k i n g a t t h e m i d - p o i n t of t h e g r a d e 7 math c u r r i c u l u m . He r e a d s a t a g r a d e l e v e l of 2.4 ( S a t - H i J u n e 8 4 ) . On the p r e - t e s t he s c o r e d 0/10 g u e s s i n g a t the a r e a of t h e t r a p e z o i d s and u s i n g BxH f o r t h e a r e a s of the t r i a n g l e s . T h i s s t u d e n t had an e x t r e m e l y d i f f i c u l t t i m e u n d e r s t a n d i n g t h e t u t o r i a l i n f o r m a t i o n . He d i d not u n d e r s t a n d the v o c a b u l a r y , i n s t r u c t i o n s , q u e s t i o n s , or t a s k s p r e s e n t e d t o him. He needed a g r e a t d e a l of g u i d a n c e and e v e n a f t e r i t e m s were e x p l a i n e d to him he d i d not appear to u n d e r s t a n d the i n f o r m a t i o n . D u r i n g the t u t o r i a l he was i n c o r r e c t on e v e r y r e s p o n s e e x c e p t f o r t h e p r a c t i s e s e c t i o n s w h e re he c o r r e c t l y i d e n t i f i e d B2, H, and B and H; and y e t he was t h e o n l y s t u d e n t who c o u l d v i s u a l l y see t h a t the ' a v e r a g e ' t r a p e z o i d was t h e same s i z e ( a r e a ) as the r e c t a n g l e i n f rame #10. I n f r a m e #12 he needed t o be shown what to c o p y and where to copy the f o r m u l a . At f i r s t he had no c o n c e p t of t h e t a s k and t h e e x p e r i m e n t e r t o l d him t h a t he 72 must copy t h e f o r m u l a . A f t e r t he e x p e r i m e n t e r had shown him t h e f o r m u l a he s t a r t e d to copy i t o n t o t h e s c r a p p a p e r . The s e c o n d t i m e ( f r a m e #21) he was a s k e d to copy t h e f o r m u l a , he s t a r t e d to push t h e s p a c e bar t o c o n t i n u e and the e x p e r i m e n t e r s t o p p e d him and t o l d him t o r e a d i t c a r e f u l l y . He t h e n c o p i e d t h e f o r m u l a by h i m s e l f . The s y n t a x and v o c a b u l a r y u s e d i n t h i s t u t o r i a l were at a c o m p r e h e n s i o n l e v e l beyond t h i s s t u d e n t ' s a b i l i t y . E v e n b e f o r e t h i s s t u d e n t s t a r t e d t he e x p e r i m e n t e r s u s p e c t e d t h a t t h i s w o u l d be a d i f f i c u l t t a s k f o r him. From t i m e to t i m e t h e s t u d e n t w o u l d however s t a t e t h a t he u n d e r s t o o d when i t was c l e a r f r o m h i s r e s p o n s e s t h a t he had no i d e a a b o u t t h e c o n t e n t of t h e p r o g r a m . He q u i c k l y l o o k e d t h r o u g h t h e t e x t n o t a c t u a l l y r e a d i n g the w o r d s . Words l i k e " s h r i n k " w h i c h he had r e c e n t l y w o r ked w i t h i n consumer e d u c a t i o n were not u n d e r s t o o d by him. He d i d not r e a l l y u n d e r s t a n d what he was l o o k i n g f o r or why. F o r example when an e x p l a n a t i o n of the c o r r e c t method f o r c a l c u l a t i o n of the t r a p e z o i d a r e a was g i v e n , he w o u l d n o t comprehend t h e s i g n i f i g a n c e of t h i s and q u i c k l y move o n t o the n e x t f r a m e . He u n d e r s t o o d the i n s t r u c t i o n " p r e s s s p a c e b a r t o c o n t i n u e " and had o n l y a few p r o b l e m s w i t h t h e m e c h a n i c s of e n t e r i n g h i s r e s p o n s e s . D u r i n g t h e o r a l q u e s t i o n s of t h e t u t o r i a l i t was c l e a r t h a t he had u n d e r s t o o d r e l a t i v e l y l i t t l e o f t h e d a t a p r e s e n t e d i n t h e t u t o r i a l . He c o u l d not a nswer any of t h e q u e s t i o n s r e p l y i n g 'not know'. He s a i d t h a t he u n d e r s t o o d o n l y a l i t t l e o f t h e d a t a and t h a t he f o u n d i t a ' l i t t l e 73 h a r d ' t o comprehend. However he s t a t e d t h a t he l i k e d the c o m p u t e r and w o u l d e n j o y w o r k i n g w i t h i t a g a i n i n the f u t u r e . Summary: I n the p r a c t i s e s e s s i o n he c o u l d s u c c e s s f u l l y e n t e r B l , B 2 , or H a f t e r the f i f t h t r a p e z o i d and c o n t i n u e d t o be s u c c e s s f u l a t t h i s s t e p on a l l s u b s e q u e n t t r a p e z o i d s up t o q u e s t i o n #24. On the t r i a n g l e s he was s u c c e s s f u l r i g h t f r o m t h e f i r s t one e n t e r i n g B and H c o r r e c t l y . T h i s was the o n l y p a r t of t h e p r a c t i c e a t w h i c h he was s u c c e s s f u l . Once he a r r i v e d a t B/2 o r B1+B2/2, he w o u l d h e s i t a t e and t h e n q u i c k l y g u e s s w i t h l i t t l e t h o u g h t and t h e n g u e ss a g a i n q u i c k l y a t t h e l a s t a r e a q u e s t i o n . He d i d not once l o o k e d c a r e f u l l y a t the c o r r e c t a n s w e r s t o t r y and see how t h e y were computed. He w o u l d s a y ' i t ' s h a r d ' and t h e n o b l i v i o u s t o t h e t a s k c o n t i n u e w i t h t h e p a r t s t h a t he c o u l d do s u c c e s s f u l l y w h i l e g u e s s i n g a t the o t h e r s . He c o u l d not see any p a t t e r n or use the d a t a a v a i l a b l e to him on t h e m o n i t o r to a i d him i n t h e t a s k . The l a n g u a g e and c o n c e p t s i n v o l v e d i n t h i s p r o g r a m were w e l l a b o v e t h i s s t u d e n t ' s l e v e l of c o m p r e h e n s i o n . He r e a l l y d i d n o t u n d e r s t a n d t h e t a s k , n o r d i d he f e e l c o n c e r n e d t h a t he was u n s u c c e s s f u l . F o r t h i s s t u d e n t t h i s p r o g r a m w o u l d need t o be f a r more d e t a i l e d , b r e a k i n g down t h e t a s k even more and p r o v i d i n g d i a g n o s t i c and r e m e d i a l h e l p a t e v e r y s t e p of t h e way. I n a n o r m a l s i t u a t i o n t h i s t y p e and l e v e l of CAI w o u l d n o t be u s e d by a t e a c h e r w i t h a s t u d e n t of t h i s a b i l i t y . H o w e v e r , i t was i n t e r e s t i n g t o see how he r e a c t e d and what he c o u l d comprehend of t h e i n f o r m a t i o n p r e s e n t e d to him. Due to 74 t h e t i m e l i m i t of a p p r o x i m a t e l y 20 m i n u t e s and t h e f e e l i n g t h a t he w o u l d n o t r e a c h the e x p e c t e d l e v e l o f e f f i c i e n c y , t h e t r e a t m e n t was s t o p p e d a f t e r q u e s t i o n //24. The e l a p s e d t i m e was 23 m i n u t e s . He s c o r e d 1/10 on the p o s t - t e s t t a k i n g l e s s t h a n 2 m i n u t e s t o c o m p l e t e i t r a n d o m l y g u e s s i n g a t t h e a r e a s of b o t h t r a p e z o i d s and t r i a n g l e s . Case #7 T h i s s t u d e n t w o u l d be p l a c e d a t t h e 6 0 t h p e r c e n t i l e b a s e d on o v e r a l l a b i l i t y , i n a r a n k i n g of p a r t i c i p a n t s i n v o l v e d i n t h i s s t u d y . He i s p r e s e n t l y w o r k i n g at the m i d - p o i n t of t h e g r a d e 8 math c u r r i c u l u m and r e a d s a t a g r a d e l e v e l of 3.8 ( S a t - H i J u n e 8 4 ) . On t h e . p r e - t e s t he s c o r e d 2/10, g u e s s i n g at the a r e a of t h e t r a p e z o i d s and u s i n g B x H f o r t he a r e a of t h e t r i a n g l e s . I n f rame #1 t h e s t u d e n t s t a t e d he d i d not know what the g r a p h i c was on t h e m o n i t o r . Then he used t h e c l u e f r o m the t i t l e t o d e t e r m i n e t h a t i t was a t r a p e z o i d . He w a i t e d and t h e n a s k e d i f he s h o u l d c o n t i n u e . The e x p e r i m e n t e r s a i d ' y e s ' . The s t u d e n t i n frame #2 s a i d t h a t he c o u l d n o t remember what p a r a l l e l means and c o u l d n o t show t h e p a r a l l e l l i n e s i n t h e g r a p h i c on t h e m o n i t o r . I n f r a m e #3 he c o u l d i d e n t i f y t h e t r a p e z o i d , but c o u l d n o t show t h e p a r a l l e l s i d e s on i t . When a s k e d i n frame #4 what t h e d i f f e r e n c e was b e t w e e n a p a r a l l e l o g r a m and a t r a p e z o i d he c o u l d not e x t r a c t and comprehend t h e d a t a i n t h e f i r s t s e n t e n c e of t h e frame to 75 g i v e an a n s w e r . T h i s was t h e f i r s t e v i d e n c e t h a t a l t h o u g h he had r e a d t h r o u g h t h e d a t a and s a i d t h a t he u n d e r s t o o d i t , he c o u l d n ot i n d e e d comprehend i t s m e a n i n g . I n frame #5 when t h e s t u d e n t had t o d e c i d e w h i c h o b j e c t was l a r g e r , he u n d e r s t o o d t h e t a s k and knew t h a t h i s c h o i c e was t h e r e c t a n g l e , but he d i d not know t h e m e c h a n i c s r e q u i r e d to e n t e r h i s r e s p o n s e . The s t u d e n t a s k e d ' s h o u l d push A' and t h e e x p e r i m e n t e r s a i d ' y e s ' . The s t u d e n t e n t e r e d h i s r e s p o n s e and t h e n p u s h e d t h e s p a c e b a r and n o t h i n g h a p p e n e d . The e x p e r i m e n t e r s t a t e d 'push r e t u r n ' . A f t e r r e a d i n g t h e t e x t i n frame #7 t h e s t u d e n t saw t h a t t h e t a s k was s i m i l a r to t h a t i n frame #5 and e n t e r e d t h e c o r r e c t answer and pushed r e t u r n . I n frame #9, t h e s t u d e n t r e a d and u n d e r s t o o d t h e t a s k and s t a t e d , " I t h i n k 6." The e x p e r i m e n t e r s t a t e d 'put i n y o u r a n s w e r ' . The s t u d e n t a s k e d , " I r i g h t ? " and the e x p e r i m e n t e r s a i d , "The c o m p u t e r w i l l t e l l you i f you a r e r i g h t or w r o n g . " The c o m p u t e r t o l d t h e s t u d e n t i n frame #9.5 t h a t he was c o r r e c t . I n frame #10 t h e s t u d e n t d i d not u n d e r s t a n d t h e t a s k . He r e a d t h e t e x t a g a i n and d e c i d e d t h a t t h e two f i g u r e s were not the same s i z e and e n t e r e d h i s answer ' n o ' , b u t f o r g o t t o push r e t u r n . The e x p e r i m e n t e r w a i t e d 10 s e c o n d s and t h e n t o l d t h e s t u d e n t t o push r e t u r n . The s t u d e n t d i s c o v e r e d t h a t he was wrong and t h a t i n f a c t t h e two f i g u r e s were t h e same s i z e . He was a b i t s u r p r i s e d and s a i d "So w h a t ! " A t fr a m e #12 t h e s t u d e n t r e a d t h r o u g h t h e t e x t and t h e n r e a c h e d t o push t h e s p a c e b ar and t h e e x p e r i m e n t e r s t o p p e d h i m , s a y i n g ' r e a d c a r e f u l l y ' . The s t u d e n t r e a d i t 76 a g a i n and t h e n a s k e d , "What do I d o ? " The s t u d e n t d i d not u n d e r s t a n d the t a s k . He a s k e d , "What i s f o r m u l a ? " The t e a c h e r e x p l a i n e d t h a t t h e f o r m u l a was u s e d t o f i n d t he a r e a and i t was t h e i n f o r m a t i o n i n s i d e t h e box on the m o n i t o r . The s t u d e n t r e a d t h e i n f o r m a t i o n a g a i n and was s t i l l c o n f u s e d . He u n d e r s t o o d t h e i s o l a t e d words ' c o p y ' and ' f o r m u l a ' , but c o u l d not put them t o g e t h e r and d i d not know what t o copy o r where t o copy i t . He was v e r y c o n f u s e d and u n a b l e t o do t h e t a s k . He r e a d t h e t e x t a g a i n and s t i l l was n o t s u r e what t o do. He s i g n e d a l l t h e words i n t h e f r a m e , b u t he was u n a b l e t o u n d e r s t a n d them. The s y n t a x seemed be y o n d h i s a b i l i t y t o c omprehend. The e x p e r i m e n t e r showed t h e s t u d e n t what t o copy and where i t must be c o p i e d on h a n d o u t #4. A t frame #13 t h e s t u d e n t was a s k e d to e n t e r a v a l u e f o r B2 ( t h e v a l u e f o r B l was a l r e a d y e n t e r e d on t h e m o n i t o r ) . The s t u d e n t s a i d "3" and w a i t e d . The e x p e r i m e n t e r t o l d t h e s t u d e n t t o e n t e r h i s g u e s s . A t frame #14 t h e s t u d e n t q u i c k l y e n t e r e d 4 f o r t h e h e i g h t ( H ) . I n frame #15 t h e s t u d e n t was a s k e d t o c a l c u l a t e B1+B2/2. The s t u d e n t l o o k e d a t i t , w o r k e d out t h e c o r r e c t answer i n h i s head and s a i d "5" t o the e x p e r i m e n t e r and w a i t e d . The e x p e r i m e n t e r a g a i n had t o t e l l t h e s t u d e n t t o e n t e r h i s a nswer i n t o t he c o m p u t e r . When t h e c o m p u t e r a s k e d f o r t h e a r e a i n frame #16 t h e s t u d e n t l o o k e d a t i t f o r a l o n g t i m e b e f o r e s i g n i n g , " A r e a d o n ' t know, d o n ' t u n d e r s t a n d . " The s t u d e n t p o i n t e d to t h e t r a p e z o i d and a s k e d , " A r e a of t h a t ? " The e x p e r i m e n t e r s a i d , " Y e s . " The s t u d e n t g u e s s e d a t the a r e a by e n t e r i n g a 77 5. The c o m p u t e r t o l d him t h a t h i s r e s p o n s e was wrong and he s h o u l d t r y a g a i n . The s t u d e n t s a i d , " I d o n ' t know." The e x p e r i m e n t e r s a i d "Guess a g a i n . " The s t u d e n t g u e s s e d 7. A t t h i s p o i n t he d i d n o t u n d e r s t a n d how t o use the f o r m u l a (B1+B2/2 X H) t o c a l c u l a t e t he a r e a . I n frame #17 t h e s t u d e n t c a r e f u l l y s t u d i e d t h e c o r r e c t method f o r 20 s e c o n d s and t h e n c o n t i n u e d . He d i d not u n d e r s t a n d the word " s h r i n k " , so t h e e x p e r i m e n t e r e x p l a i n e d i t t o h i m . A t frame #19 he r e a d i t , s t a t e d he d i d n ' t u n d e r s t a n d i t , l o o k e d c o n f u s e d and t h e n s a i d , "Why b o t h e r " and p u s h e d t h e s p a c e b a r t o c o n t i n u e . He was f r u s t r a t e d now and a c t e d as i f t h i s was w a s t i n g h i s t i m e b e c a u s e he c o u l d n o t comprehend the m e a n i n g of t h e s e few s e n t e n c e s . I n f r a m e #21 t h e s t u d e n t r e a d t h e t e x t , p o i n t e d t o t h e t r i a n g l e f o r m u l a and s i g n e d , " Copy?" and t h e n c o p i e d i t . I n f r a m e s #22 and #23 he q u i c k l y e n t e r e d the c o r r e c t B and H f r o m the t r i a n g l e g r a p h i c . I n frame #24 he s l o w l y t h o u g h t a b o u t the answer and t h e n i n p u t the c o r r e c t a r e a . I n f r a m e #25 he was v e r y happy t h a t he had c a l c u l a t e d t h e a r e a and b r i e f l y l o o k e d o v e r t h e c o r r e c t method of c a l c u l a t i o n b e f o r e c o n t i n u i n g t o t h e l a s t f r a m e . I n the s i g n e d q u e s t i o n i n g a f t e r the t u t o r i a l t h e s t u d e n t knew how many p a r a l l e l s i d e s a t r a p e z o i d had. He d i d n o t u n d e r s t a n d t h e t u t o r i a l ' s a t t e m p t t o show him how t h e f o r m u l a f o r a r e a c a l c u l a t i o n i n t r a p e z o i d s was c a l c u l a t e d . He c o u l d e x p l a i n how t o c a l c u l a t e an a v e r a g e f o r two numbers. He had l e a r n e d t h a t a t r a p e z o i d had two b a s e s w h i l e a t r i a n g l e had o n l y one. He a l s o knew t h e t e r m " b a s e " . He s t a t e d t h a t he 78 u n d e r s t o o d most of what t h e c o m p u t e r t a u g h t h i m . He s a i d t h a t i t was of medium d i f f i c u l t y , "Not e a s y , n o t h a r d . " He s a i d t h a t he e n j o y e d w o r k i n g on the c o m p u t e r and w o u l d l i k e t o do i t a g a i n i n t h e f u t u r e . I n t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e t h i s s t u d e n t d i d v e r y w e l l . A t t h e b e g i n n i n g of t h e p r a c t i c e he r e a d o v e r t h e f o r m u l a s h e e t #4 and t h e n p r o c e e d e d t o do q u e s t i o n s # 1 , #2, #3, and #4 i n h i s h e a d , q u i c k l y r e a c h i n g t h e 80% e f f i c i e n c y l e v e l i n 2 m i n u t e s and 25 s e c o n d s . S ummary: I n t h e t u t o r i a l p r a c t i c e he c o u l d c a l c u l a t e the t r i a n g l e a r e a , but c o u l d not c a l c u l a t e t he t r a p e z o i d a r e a ( f r a m e / / 1 6 ) . However he d i d c a r e f u l l y v i e w t h e e x p l a n a t i o n of the c o r r e c t method to c a l c u l a t e t he t r a p e z o i d a r e a . T h e r e f o r e , a l t h o u g h he had a number of d i f f i c u l t e x p e r i e n c e s c o m p r e h e n d i n g the d a t a and i n s t r u c t i o n s i n the t u t o r i a l , he d i d l e a r n enough t o be s u c c e s s f u l i n u s i n g t h e f o r m u l a to c a l c u l a t e t h e c o r r e c t a r e a s of t h e f i r s t f o u r q u e s t i o n s (3 t r a p e z o i d and 1 t r i a n g l e ) . He a l s o q u i c k l y a n s w e r e d t h e q u e s t i o n s on the a r e a of a t r a p e z o i d and t r i a n g l e w i t h o u t t h e a i d of t h e f o r m u l a s h e e t u s i n g t h e f o r m u l a t h a t he had now c o m m i t t e d to memory. I n h i s work on t h e s e two q u e s t i o n s he showed t h a t he was f o l l o w i n g t h e f o r m u l a ( 6 / 2 x 8 and 5+7=12/2; ( B l + B 2 / 2 ) = 6 x 6 = 3 6 ) . T h i s s u g g e s t e d t o t h e e x p e r i m e n t e r t h a t a s t u d e n t need n o t u n d e r s t a n d a l l f a c e t s of the t u t o r i a l p r o g r a m i n o r d e r t o a q u i r e enough i n s i g h t and i n f o r m a t i o n t o f a c i l i t a t e t h e i r 79 l e a r n i n g of t h e c o r r e c t a p p l i c a t i o n of t h e two f o r m u l a e . On t h e p o s t - t e s t t h i s s t u d e n t s c o r e d 0/10 and t o l d t h e e x p e r i m e n t e , " I f o r g o t a l o t . " He d i d not r e t a i n what he had l e a r n e d f r o m h i s e x p e r i e n c e d u r i n g t h e week between t h e t r e a t m e n t and p o s t - t e s t . He q u e s s e d a t b o t h t r a p e z o i d and t r i a n g l e q u e s t i o n s on the p o s t t e s t . C ase #8 T h i s s t u d e n t w o u l d be r a n k e d a t or b e l o w t h e 6 0 t h p e r c e n t i l e when c o n s i d e r i n g t h e o v e r a l l a b i l i t i e s of i n d i v i d u a l s i n v o l v e d i n t h i s s t u d y . She r e a d s a t a g r a d e l e v e l of 4.3 ( S a t - H i J u n e 8 4 ) and i s p r e s e n t l y a t the m i d - p o i n t of t h e g r a d e 9 math c u r r i c u l u l m . On t h e p r e - t e s t she s c o r e d 0/10 g u e s s i n g at t h e a r e a of the t r a p e z o i d s and u s i n g BxH f o r the a r e a of the t r i a n g l e s . I n frame #1 t h e s t u d e n t t h o u g h t t h a t the g r a p h i c was a t r i a n g l e . She d i d n o t know what t r i a n g l e s o r t r a p e z o i d s w e r e . She c o u l d show t h e 2 p a i r s of p a r a l l e l l i n e s i n t h e g r a p h i c of t h e p a r a l l e l o g r a m i n frame #2, so she d i d u n d e r s t a n d the t e r m p a r a l l e l . I n frame #3 she c o u l d now p i c k o u t t h e t r a p e z o i d and show t h e 2 p a r a l l e l s i d e s on t h e t r a p e z o i d . The s t u d e n t r e a d frame #4 and t h e n m i s t a k e n l y t h o u g h t t h a t she was r e q u i r e d t o p e r f o r m some t a s k and e n t e r some d a t a . She a s k e d "Add?" The e x p e r i m e n t e r t o l d h e r t o "Read a g a i n . " The s t u d e n t r e a d i t a g a i n and s a i d " P i c k a r e a ? " O b v i o u s l y t h e s y n t a x and v o c a b u l a r y i n v o l v e d i n t h i s f r a m e were beyond t h e c o m p r e h e n s i o n of t h i s s t u d e n t . The 80 d a t a i n t h i s f r a m e d i s c u s s e s the d i f f e r e n c e between p a r a l l e l o g r a m s and t r a p e z o i d s , s h o w i n g t h e B l , B2, and H on a t r a p e z o i d g r a p h i c and s a y i n g " L e t ' s see how we can use our k n o w l e d g e of r e c t a n g l e s and p a r a l l e l o g r a m s to f i n d t he a r e a o f a t r a p e z o i d . " Nowhere does i t ask t h e s t u d e n t to f i n d t h e a r e a . T h i s s t u d e n t o b v i o u s l y d i d n o t u n d e r s t a n d the i n f o r m a t i o n p r e s e n t e d . O t h e r e v i d e n c e of t h i s was the f a c t t h a t she c o u l d n o t a t t h i s s t a g e e x p l a i n t h e d i f f e r e n c e b e t w e e n a p a r a l l e l o g r a m and a t r a p e z o i d . Y e t t h e answer f o r t h i s q u e s t i o n came f r o m the f i r s t s e n t e n c e of t h e f r a m e . I n f r a m e #5 t h e s t u d e n t d e c i d e d t h a t t h e r e c t a n g l e was l a r g e r and t o l d t he e x p e r i m e n t e r . The e x p e r i m e n t e r t o l d t h e s t u d e n t t o e n t e r i t i n t o t h e c o m p u t e r . The s t u d e n t e n t e r e d i t and t h e n w a i t e d w h i l e n o t h i n g h a p p e n e d . The s t u d e n t a s k e d , "Push r e t u r n ? " and the e x p e r i m e n t e r r e p l i e d , " Y e s . " I n frame #6 t h e s t u d e n t w a t c h e d t h e a n i m a t i o n and o b s e r v e d t h a t h e r r e s p o n s e was c o r r e c t . I n frame HI she p i c k e d t h e t r a p e z o i d and had no p r o b l e m e n t e r i n g the d a t a i n t o t h e c o m p u t e r . I n f r a m e #8 she saw t h a t t h e t r a p e z o i d d i d have t h e l a r g e r a r e a . I n f rame #9 t h e s t u d e n t r e a d t h e t e x t w h i c h s t a t e d t h a t t h e 8cm r e c t a n g l e was t o o l a r g e and t h a t t h e 4cm r e c t a n g l e was t o o s m a l l and what was t h e a v e r a g e between 4 and 8. A f t e r r e a d i n g t h i s she a s k e d t h e e x p e r i m e n t e r "Between ?" ; " A v e r a g e 6 and 8." The e x p e r i m e n t e r s a i d " Y e s . " However, t h e s t u d e n t was s t i l l c o n f u s e d , as t o t h e t a s k i n v o l v e d and a s k e d f o r h e l p . The t e a c h e r e x p l a i n e d t h e l a n g u a g e i n the f r a m e and t o l d h e r t o f i n d t he a v e r a g e of 4 and 8. She was 81 d i s c o u r a g e d by h e r i n a b i l i t y t o u n d e r s t a n d t h e t e s t , but s t a t e d the a v e r a g e was 6. The e x p e r i m e n t e r had to t e l l h e r t o go on and e n t e r h e r c o r r e c t r e s p o n s e . The c o r r e c t method f o r c a l c u l a t i n g t h e a v e r a g e was e x p l a i n e d i n frame #9.5. The s t u d e n t i g n o r e d t h i s b e c a u s e she had e n t e r e d t h e c o r r e c t a n s w e r . L a t e r a f t e r t h e t u t o r i a l i n r e s p o n s e t o a q u e s t i o n f r o m the e x p e r i m e n t e r she e x p l a i n e d t h a t she l o o k e d a t the k e y s 4 5 6 7 8, saw t h a t 6 was i n t h e m i d d l e and p i c k e d i t f o r h e r a n s w e r . She d i d not use t h e method i l l u s t r a t e d i n f r a m e #9.5, n o r d i d she r e a d i t b e c a u s e she f e l t t h a t she knew how to do i t as she had a l r e a d y a n s w e r e d i t c o r r e c t l y . H e r a t t i t u d e was t h a t i t d i d not m a t t e r how she o b t a i n e d t h e c o r r e c t answer as l o n g as i t was r i g h t . I n frame #10 t h e s t u d e n t s a i d t h a t t h e r e c t a n g l e and t h e t r a p e z o i d d i d not have he same a r e a . I n frame #11 she was not s u r p r i s e d t h a t t h e y a c t u a l l y d i d have t he same a r e a . Her r e s p o n s e to t h i s i n f o r m a t i o n was " C o o l . " The e x p e r i m e n t e r had to s t o p the s t u d e n t f r o m p u s h i n g t h e s p a c e b a r t o c o n t i n u e i n frame #12, and i n s t r u c t h e r t o r e a d i t c a r e f u l l y . The s t u d e n t was c o n f u s e d , she had r e a d t h e t e x t and was p r o c e e d i n g l i k e b e f o r e . She had n o t u n d e r s t o o d t h e i n s t r u c t i o n s to copy t he f o r m u l a o n t o h a n d o u t #4. She a s k e d t h e e x p e r i m e n t e r t o e x p l a i n t h e t e x t . Then she r e a d i t a g a i n h e r s e l f , but was s t i l l c o n f u s e d . She a s k e d , "What i s f o r m u l a ? " The e x p e r i m e n t e r showed h e r t h e f o r m u l a i n t h e box on the m o n i t o r . She s a i d , " C o p y ? " She was s t i l l c o n f u s e d and s t a r t e d to copy t h e t e x t f r o m t h e s c r e e n o n t o t h e s c r a p 82 p a p e r . The e x p e r i m e n t e r s a i d "No, copy t h e f o r m u l a o n t o h a n d o u t #4." She was s t i l l t o t a l l y c o n f u s e d . The e x p e r i m e n t e r p o i n t e d t o t h e words 'handout #4'. She l o o k e d a t h a n d o u t #4 and t h e n s t a r t e d to copy t h e wrong d a t a o n t o t h e wrong p l a c e on t h e h a n d o u t . The e x p e r i m e n t e r f i n a l l y showed the s t u d e n t what t o copy and where to copy i t . The s t u d e n t was c o m p l e t e l y c o n f u s e d by t h e t a s k shown on t h i s f r a m e even t h o u g h she u n d e r s t o o d t h e v a c a b u l a r y ' c o p y ' and ' f o r m u l a ' . The s y n t a x of t h i s s e c t i o n seemed t o be beyond h e r a b i l i t y to c o m p r e h e n d . A t f r a m e #13 t h e s t u d e n t s was t o l d t he v a l u e f o r B l and was a s k e d t o e n t e r t h e v a l u e f o r B2. The s t u d e n t f i r s t a s k e d i f she s h o u l d t y p e i n t h e a n s w e r , t h e n l o o k e d a t t h e d i a g r a m and c o r r e c t l y e n t e r e d a 3. She q u i c k l y a n s w e r e d 4 i n frame #14 f o r H ( h e i g h t ) . I n frame #15 she s t a t e d , "Must answer add" and t h e n c a l c u l a t e d B1+B2/2 w i t h o u t any d i f f i c u l t y . I n f r a m e #17 she q u i c k l y u s e d t h e f o r m u l a to c a l c u l a t e t h e a r e a of t h e t r a p e z o i d . She was t h e o n l y s t u d e n t t o do a l l of t h i s c o r r e c t l y d u r i n g t h e t u t o r i a l p o r t i o n of t h e t r e a t m e n t . She was a b l e t o a s s i g n t h e c o r r e c t v a l u e s f o r B2 and H, u n d e r s t a n d t h e n o t a t i o n and c a l c u l a t e B1+B2/2, and use t h e f o r m u l a t o c a l c u l a t e t h e a r e a . The s t u d e n t b r e e z e d by f r a m e #17 w h i c h e x p l a i n e d t h e c o r r e c t method b e c a u s e she a l r e a d y had t h e answer r i g h t . I n frame #18 she u n d e r s t o o d t h e word " s h r i n k " a f t e r t h i n k i n g a b o u t i t f o r 20 s e c o n d s . Then she r e a d t h e t e x t and a s k e d , "Copy o r w h a t ? " She d i d not u n d e r s t a n d the t a s k h e r e and s a i d " C o n f u s e d . " The e x p e r i m e n t e r e x p l a i n e d t h a t t h e r e was no 83 t a s k h e r e and she o n l y needed to r e a d t h e i n f o r m a t i o n and t h e n c o n t i n u e . She w a t c h e d t h e t r a p e z o i d s h r i n k t o a t r i a n g l e i n frame //19. I n frame #21 she c o p i e d the t r i a n g l e f o r m u l a o n t o h a n d o u t #4. She had l e a r n e d f r o m h e r f i r s t e x p e r i e n c e i n frame #12. Then she q u i c k l y w o r k e d t h r o u g h the p r a c t i s e q u e s t i o n on t h e t r i a n g l e . She m i s t a k e n l y e n t e r e d t h e h e i g h t f o r the base i n f r a m e #22, but a g a i n had no p r o b l e m u s i n g the f o r m u l a t o c a l c u l a t e the a r e a c o r r e c t l y . She needed t o c a l c u l a t e B/2 h e r s e l f b e c a u s e t h i s p a r t i s not one of t h e demanded components i n t h e t u t o r i a l p r a c t i c e . She i g n o r e d the c o r r e c t method shown i n frame #24 and was f i n i s h e d the t u t o r i a l . I n the q u e s t i o n i n g a f t e r t h e t u t o r i a l t he s t u d e n t d e m o n s t r a t e d t h a t she had l e a r n e d the t e r m p a r a l l e l and knew t h a t a t r a p e z o i d had two p a r a l l e l s i d e s . She d i d not u n d e r s t a n d the c o m p l i c a t e d e x p l a n a t i o n t h a t t r i e d to r e v e a l t h e d e r i v a t i o n of the t r a p e z o i d f o r m u l a by c o m p a r i n g d i f f e r e n t s i z e d r e c t a n g l e s w i t h a t r a p e z o i d . She e x p l a i n e d t h a t to f i n d t he a v e r a g e of two numbers you p i c k t h e number i n the m i d d l e . By u s i n g t h i s m ethod, she l a b o r i o u s l y p i c k e d 8 as t h e a v e r a g e of 6 and 10. She was n o t u s i n g t h e a c c e p t e d method f o r c a l c u l a t i n g t h e a v e r a g e . She u n d e r s t o o d the t e r m b a s e and knew t h a t a t r a p e z o i d had two b a s e s and a t r i a n g l e h ad one b a s e . The s t u d e n t s a i d t h a t she u n d e r s t o o d some of t h e i n f o r m a t i o n t h a t t h e c o m p u t e r had t r i e d t o t e a c h h e r . She s t a t e d t h a t i t was n o t r e a l l y e a s y b e c a u s e she ' a l w a y s made m i s t a k e s ' . She e n j o y e d w o r k i n g on the c o m p u t e r but d i d 84 n o t know i f she w o u l d l i k e t o work w i t h i t a g a i n . A l t h o u g h t h i s s t u d e n t had a t r e m e n d o u s l y d i f f i c u l t t i m e w i t h t h e s y n t a x i n v o l v e d i n t h e t u t o r i a l she d i d manage to l e a r n a number of i m p o r t a n t t h i n g s . She c o n t i n u e d o n t o t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : When t h e i n i t i a l a r e a q u e s t i o n a p p e a r e d she a s k e d , "Do t h e y want t h e a n s w e r ? " The e x a m i n e r r e p l i e d , " Y e s . " She g o t t h e i n i t i a l q u e s t i o n wrong and a l s o had t r o u b l e i d e n t i f y i n g B2, but t h e n c o r r e c t l y c a l c u l a t e d B1+B2/2 and t h e a r e a . She a l s o knew how t o do t h i s d u r i n g t h e t u t o r i a l q u e s t i o n . Q u e s t i o n #2 ( t r i a n g l e ) : She l o o k e d a t the f o r m u l a s h e e t and c o r r e c t l y c a l c u l a t e d t h e i n i t i a l a r e a q u e s t i o n j u s t as she had done on the t u t o r i a l p r a c t i s e q u e s t i o n . Q u e s t i o n #3 ( t r a p e z o i d ) : She l o o k e d a t t h e f o r m u l a s h e e t a g a i n and t h i n k i n g i n h e r h e a d , g u e s s e d a t t h e i n i t i a l a r e a q u e s t i o n . She had no p r o b l e m w o r k i n g t h r o u g h t h e r e m e d i a l s e c t i o n o f t h e p r a c t i c e . Q u e s t i o n #4 ( t r a p e z o i d ) : A g a i n t h e s t u d e n t had p r o b l e m s w i t h t h e i n i t i a l q u e s t i o n f o l l o w e d by p r o b l e m s w i t h B1+B2/2 b e c a u s e she m u l t i p l i e d B l x B 2 i n s t e a d o f summing t h e two. However she us e d t h e c o r r e c t d a t a and method to c a l c u l a t e t h e a r e a . Q u e s t i o n #5,#6,#7 ( t r a p e z o i d s ) : A f t e r g u e s s i n g a t the i n i t i a l a r e a q u e s t i o n she had no p r o b l e m c o r r e c t l y i d e n t i f y i n g t h e r e s t o f t h e components of t h e s e p r a c t i s e q u e s t i o n s . She was s t i l l g u e s s i n g a t t h e i n i t i a l a r e a and 85 n o t u s i n g h e r e x p e r i e n c e t o s o l v e i t s t r a i g h t o f f . She d i d n o t seem to u n d e r s t a n d what t h e y were a s k i n g f o r w i t h t h i s i n i t i a l q u e s t i o n or she had not had enough p r a c t i c e at t h i s p o i n t to be a b l e to do a l l t h e s t e p s h e r s e l f w i t h o u t the c o m p u t e r ' s g u i d a n c e . She had no p r o b l e m s w i t h some of the d i f f i c u l t c o m p u t a t i o n s t h a t b o t h e r e d o t h e r s t u d e n t s . Q u e s t i o n #8 ( t r a p e z o i d ) : W o r k i n g on p a p e r she a l m o s t went o f f t r a c k , but t h e n c o r r e c t l y c a l c u l a t e d t h e i n i t i a l a r e a f o r t h e f i r s t t i m e . Q u e s t i o n #9 ( t r a p e z o i d ) : She f a i l e d to c a l c u l a t e the i n i t i a l a r e a and t h e l a s t a r e a q u e s t i o n d u r i n g t h e r e m e d i a l p o r t i o n due t o c o m p u t a t i o n a l p r o b l e m s . Q u e s t i o n # 10 ( t r i a n g l e ) : Her i n i t i a l a nswer was i n c o r r e c t ( B x H ) . She t h e n w o r k e d t h r o u g h the s t e p by s t e p r e m e d i a l s e c t i o n w i t h o u t any d i f f i c u l t i e s . She s i g n e d " H a r d ! " a t t h e l a s t a r e a q u e s t i o n . Q u e s t i o n #11,#12 ( t r a p e z o i d s ) : W o r k i n g on p a p e r and h e r f i n g e r s , she c o r r e c t l y c a l c u l a t e d t h e i n i t l i a l a r e a q u e s t i o n f o r b o t h t r a p e z o i d s . Q u e s t i o n #13 ( t r i a n g l e ) : A g a i n she used BxH t o g e t an i n c o r r e c t a n s w e r . She t h e n made a m i s t a k e a s s i g n i n g h e i g h t f o r B. A f t e r t h e s e p r o b l e m s she was a b l e t o use t h e f o r m u l a t o c a l c u l a t e t he a r e a . Q u e s t i o n #14,#15 ( t r a p e z o i d s ) : B o t h i n i t i a l a r e a s were c a l c u l a t e d w i t h o u t e r r o r . She now needed to c o r r e c t l y answer a t r i a n g l e q u e s t i o n t o r e a c h t h e 80% e f f i c i e n c y l e v e l , so the e x p e r i m e n t e r moved o n t o the n e x t t r i a n g l e q u e s t i o n . 86 Q u e s t i o n #16 ( t r i a n g l e ) : She c a l c u l a t e d t h e i n i t i a l a r e a w i t h o u t e r r o r , r e a c h i n g 80% e f f i c i e n c y a f t e r 21 m i n u t e s . T h e n she e a s i l y c a l c u l a t e d t h e a r e a s of the t r a p e z o i d and t r i a n g l e q u e s t i o n s w i t h o u t t h e a i d of the f o r m u l a s h e e t . Summary: T h i s s t u d e n t c o u l d use t h e c o r r e c t methods to c a l c u l a t e t h e a r e a f o r b o t h t r a p e z o i d s and t r i a n g l e s i n t h e p r a c t i s e q u e s t i o n s of the t u t o r i a l s e c t i o n . She knew how to o b t a i n t h e c o r r e c t a n s w e r s r i g h t f r o m t h e s t a r t . B u t she e i t h e r d i d n o t u n d e r s t a n d t h e s i g n i f i g a n c e of t h e i n i t i a l a r e a q u e s t i o n , o r she s i m p l y needed more p r a c t i c e w i t h t h e s t e p by s t e p r e m e d i a l g u i d a n c e b e f o r e she c o u l d s u c c e s s f u l l y do i t i n d e p e n d e n t l y d u r i n g t h e p r a c t i s e s e c t i o n . E i t h e r way, some e x t r a h e l p was needed f r o m t h e s o f t w a r e i n the r e m e d i a l s e c t i o n o f t h e p r o g r a m to e x p l a i n t h a t t h e i n i t i a l a r e a q u e s t i o n was t h e same as t h e l a s t a r e a q u e s t i o n i n t h e s t e p by s t e p p r o c e s s . T h i s w o u l d have been b e n e f i c i a l f o r t h i s s t u d e n t . I t may have h e l p e d h e r l e a r n t h e t a s k more s w i f t l y w i t h l e s s f r u s t r a t i o n . C a s e #9 S t u d e n t #9 w o u l d be p l a c e d a t o r b e l o w t h e 7 0 t h p e r c e n t i l e of a r a n k i n g f o r a l l t h e p a r t i c i p a n t s i n v o l v e d i n t h i s s t u d y . She r e a d s a t a g r a d e l e v e l of 7.6 ( S a t H i J u n e 8 4 ) and i s p r e s e n t l y w o r k i n g a t t h e s t a r t of t h e g r a d e 9 math c u r r i c u l u m . On t h e p r e - t e s t she s c o r e d 0/10 summing the t r a p e z o i d s (a+b+c) and u s i n g BxH f o r t h e a r e a of t h e 87 t r i a n g l e s . I n frame #1 t h e s t u d e n t s i g n e d t h a t she t h o u g h t the g r a p h i c on t h e m o n i t o r was a t r a p e z o i d . She had no p r o b l e m s w i t h t he i n s t r u c t i o n " p r e s s s p a c e b a r t o c o n t i n u e " . I n frame iH t h e s t u d e n t c o u l d p o i n t out t h e 2 p a i r s of p a r a l l e l l i n e s on t h e t r a p e z o i d , d e m o n s t r a t i n g h e r u n d e r s t a n d i n g of t h e word p a r a l l e l . She c o u l d p i c k out t h e t r a p e z o i d and show i t s s i d e s i n frame #3. I n f r a m e #4 s h e c o u l d l o g i c a l l y deduce t h e d i f f e r e n c e b e t ween a t r a p e z o i d and a p a r a l l e l o g r a m . "A p a r a l l e l o g r a m had 2 p a i r s o f p a r a l l e l s i d e s , t r a p e z o i d has o n l y 1 p a i r of p a r a l l e l s i d e s , o t h e r s n o t . " T h i s was a c o r r e c t e x p l a n a t i o n , but i t was n o t t h e same as t h e one g i v e n i n t h e t e x t o f t h i s f r a m e , " u n l i k e t h e p a r a l l e l o g r a m t he p a r a l l e l s i d e s o f a t r a p e z o i d have d i f f e r e n t l e n g t h s . " I n c o m p a r i n g the r e c t a n g l e and t r a p e z o i d i n frame #5 t h e s t u d e n t knew what to do but she had p r o b l e m s w i t h t he m e c h a n i c s of e n t e r i n g her r e s p o n s e s . She s i g n e d , "My answer i s A." The e x p e r i m e n t e r t o l d h e r to push t h e 'A' k e y . Then she w a i t e d , n o t h i n g happened and t h e e x p e r i m e n t e r t o l d h e r t o push t h e r e t u r n k e y . I n f r a m e //6 t h e s t u d e n t saw t h a t she had p i c k e d t h e c o r r e c t a n s w e r . The, t a s k a t f r a m e #7 was i d e n t i c a l to t h t a s k a t frame #5, p i c k t h e shape w i t h t h e l a r g e r a r e a , t h e r e c t a n g l e o r t h e t r a p e z o i d . The s t u d e n t seemed to have a d i f f i c u l t t i m e m a k i n g h e r d e c i s i o n . She compared t h e two f o r a l o n g t i m e b e f o r e d e c i d i n g . Then she l o o k e d t o t h e e x p e r i m e n t e r f o r p e r m i s i o n t o e n t e r t he d a t a , a s k i n g , " I s i t r i g h t o r w r o n g ? " The e x p e r i m e n t e r s t a t e d , " E n t e r y o u r d a t a . " 88 I n frame #8 she o b s e r v e d t h a t h e r d e c i s i o n was c o r r e c t and she was happy. A f t e r r e a d i n g f r a m e #9 ( a s k i n g f o r the a v e r a g e of 4 and 8 ) she s i g n e d , "Number i n t h e m i d d l e , 6." The e x p e r i m e n t e r a n s w e r e d , " Y e s . " She e n t e r e d h e r answer and was t o l d i t was r i g h t and was shown how to c a l c u l a t e t h e a v e r a g e i n frame #9.5. I n frame #10 she compared t he 2 f i g u r e s , t h e r e c t a n g l e whose s i d e s were t h e a v e r a g e l e n g t h of t h e t r a p e z o i d ' s l o n g e r and s h o r t e r base and t h e t r a p e z o i d . She d e c i d e d t h a t t h e y d i d n o t have t h e same a r e a . I n frame #11 she was e m b a r r a s s e d to d i s c o v e r t h a t she was wrong. The s t u d e n t d i d not u n d e r s t a n d t h e t a s k i n frame #12 and t h e e x p e r i m e n t e r had t o s t o p h e r f r o m p u s h i n g t h e s p a c e b ar to c o n t i n u e . The e x p e r i m e n t e r a s k e d , "What does i t s a y ? " She a n s w e r e d , "Don't u n d e r s t a n d . " Then she a s k e d , "Copy, what i s f o r m u l a ? i n box?" The e x p e r i m e n t e r r e p l i e d , "Yes t h i s i s t h e f o r m u l a " and he p o i n t e d a t t h e f o r m u l a . The s t u d e n t was s t i l l c o n f u s e d , "What d o ? " The e x p e r i m e n t e r a n s w e r e d , "You c o p y t h e f o r m u l a i n t h e box." The s t u d e n t s i g n e d , "Copy the f o r m u l a " and p o i n t e d to t h e s c r a p p a p e r . "No, what does i t s a y " r e p l i e d t h e e x p e r i m e n t e r . She a g a i n s i g n e d , "Don't u n d e r s t a n d " and t h e e x p e r i m e n t e r a n s w e r e d "Copy i t on h a n d o u t #4" and p o i n t e d t o t h e h a n d o u t . The s t u d e n t s t a r t e d t o copy i t on t h e wrong p l a c e on t h e h a n d o u t . The e x p e r i m e n t e r showed h e r where t o copy t h e f o r m u l a o n t o t h e h a n d o u t . The s t u d e n t u n d e r s t o o d some of t h e i n d i v i d u a l words i n t h e t e x t , b u t t h e s y n t a x seemed beyond h e r a b i l i t y to comprehend. Where some s t u d e n t s w o u l d h i d e t h e i r m i s u n d e r s t a n d i n g , she 89 was e x t r e m e l y c o n c i s e a b o u t what she d i d and d i d not u n d e r s t a n d . She was v e r y c o n f u s e d and needed a g r e a t d e a l of d i r e c t i o n and g u i d a n c e f r o m the e x p e r i m e n t e r to c o m p l e t e the t a s k . I n frame #13 w h e r e she was a s k e d to e n t e r B2 t h e s t u d e n t was c o n f u s e d and d i d n o t u n d e r s t a n d t h e t a s k , "What d o ? " The e x p e r i m e n t e r t o l d h e r t o g u e s s . The s t u d e n t a g a i n s i g n e d t h a t she was c o n f u s e d and d i d not know t h e a n s w e r . T h e n she c a r e f u l l y l o o k e d o v e r t h e d a t a on t h e s c r e e n and c o r r e c t l y e n t e r e d a 3 and q u i c k l y e n t e r e d a 4 f o r H. A t f r a m e #15 t h e s t u d e n t a s k e d , " A n s w e r ? " and w o rked out the c o r r e c t answer f o r B1+B2/2 on p a p e r . She u n d e r s t o o d the n o t a t i o n and had no p r o b l e m c a l c u l a t i n g i t even t h o u g h t h i s was the f i r s t t i m e she e n c o u n t e r e d i t . I n frame #16 she was a s k e d t o c a l c u l a t e t he a r e a and a g a i n she s t a t e d t h a t she d i d n o t know what to do. The e x p e r i m e n t e r e n c o u r a g e d h e r t o t r y i t . The s t u d e n t w o r k e d on p a p e r and h e r hands and computed 4x21=84 and e n t e r e d 84. Then t h e c o m p u t e r t o l d h e r t h i s was w r o n g and t o t r y a g a i n . On h e r s e c o n d a t t e m p t she added a l l t h r e e numbers t o g e t h e r t o compute a n o t h e r wrong a n s w e r . She d i d not u n d e r s t a n d t h e use of t h e f o r m u l a a t t h i s p o i n t . She c a r e f u l l y l o o k e d a t t h e c o r r e c t method f o r a r e a c a l c u l a t i o n i n t r a p e z o i d s shown i n f r a m e #17 (25 s e c o n d s ) . I n frame #18 she u n d e r s t o o d t h e word " s h r i n k " , but she d i d n o t u n d e r s t a n d " s h r i n k down". She was c o n f u s e d a f t e r r e a d i n g t h e t e x t and t h o u g h t t h a t t h e r e was a t a s k f o r h e r t o do i n t h i s f r a m e . She s h e e p i s h l y a s k e d i f she s h o u l d p r e s s t h e s p a c e b a r to c o n t i n u e and t h e e x p e r i m e n t e r gave h e r t h e g r e e n l i g h t . The 90 s t u d e n t r e a d frame #19 and seemed t o u n d e r s t a n d the c o n c e p t t h a t a t r i a n g l e was l i k e a t r a p e z o i d w i t h one base t h a t e q u a l l e d l e n g t h z e r o . She r e a d frame #20 and l o o k e d to the e x p e r i m e n t e r b e f o r e p u s h i n g t h e s p a c e b a r . I n frame #21 she showed t h a t she had l e a r n e d f r o m h e r e x p e r i e n c e a t frame #12 and c o p i e d t h e t r i a n g l e f o r m u l a o n t o t h e a p p r o p r i a t e s p o t on h a n d o u t #4. I n f r a m e #22 she c a r e f u l l y l o o k e d at the t r i a n g l e g r a p h i c b e f o r e p i c k i n g t h e v a l u e 8 t h a t c o r r e s p o n d e d t o B. I n frame #23 she q u i c k l y p i c k e d H=9. I n frame #24 she c o m puted t h e t r i a n g l e ' s a r e a i n h e r head and e n t e r e d the c o r r e c t a n s w e r . I t was o b v i o u s she u n d e r s t o o d the f o r m u l a h e r e b e c a u s e i n t h e p r a c t i c e t h e s t u d e n t was not r e q u i r e d to g i v e the B/2 v a l u e . She had to compute t h i s and t h e n m u l t i p l y by the h e i g h t w h i c h she d i d s u c c e s s f u l l y on h e r f i r s t e n c o u n t e r . I n frame #25 she q u i c k l y l o o k e d o v e r the c o r r e c t method of t r i a n g l e a r e a c a l c u l a t i o n . I n the s i g n e d q u e s t i o n i n g a f t e r t he t u t o r i a l t h e s t u d e n t showed, as was s e e n i n h e r work on t h e t u t o r i a l , t h a t she u n d e r s t o o d the word p a r a l l e l and t h a t she a l s o knew how many s i d e s a t r a p e z o i d h a d . She was u n a b l e t o see the r e a s o n i n g f o r c o m p a r i n g the t h r e e d i f f e r e n t r e c t a n g l e s to the t r a p e z o i d . She d i d n o t u n d e r s t a n d t h e s o f t w a r e s a t t e m p t to show h e r how t h e t r a p e z o i d f o r m u l a was d e r i v e d . She c o u l d n o t e x p l a i n how an a v e r a g e f o r 2 numbers was c a l c u l a t e d , but she c o u l d g i v e t h e a v e r a g e f o r t h e numbers 6 and 10. The s t u d e n t t h o u g h t t h a t a t r a p e z o i d and t r i a n g l e b o t h had one b a s e . She i n d i c a t e d t h a t i t was e a s y t o u n d e r s t a n d what the 91 c o m p u t e r had t a u g h t h e r , and t h a t some p a r t s were s i m p l e w h i l e o t h e r s were q u i t e h a r d . She e n j o y e d w o r k i n g w i t h t h e c o m p u t e r , but p r e f e r r e d t e a c h e r s b e c a u s e t h e y were e a s i e r t o c o m m u n i c a t e w i t h . On the p r a c t i s e p o r t i o n she had p r o b l e m s a s s i g n i n g t h e v a l u e s f o r B l , B2, and H on q u e s t i o n #1 ( t r a p e z o i d ) . Then she m u l t i p l i e d B l x B 2 / 2 t o g e t an i n c o r r e c t v a l u e . However, she was a b l e to use t h e c o r r e c t v a l u e f o r B1+B2/2 and H to c a l c u l a t e t h e a r e a . She was a b l e t o f o l l o w B1+B2/2 on the t u t o r i a l p r a c t i c e , but was c o n f u s e d by i t h e r e . Q u e s t i o n #2 ( t r i a n g l e ) : F o r the i n i t i a l a r e a she m u l t i p l i e d BxH. She a p p e a r e d o v e r t h e s e f i r s t two p r a c t i s e q u e s t i o n s t o ha v e f o r g o t t e n what she d i d on t h e t u t o r i a l p r a c t i s e q u e s t i o n s . She t h e n w o r k e d - t h r o u g h t h e r e m e d i a l p o r t i o n q u i c k l y w i t h o u t e r r o r . Q u e s t i o n #3 ( t r a p e z o i d ) : She g u e s s e d a t the i n i t i a l a r e a and t h e n had no p r o b l e m w o r k i n g t h r o u g h t h e s t e p by s t e p b r e a k d o w n of the p r o p e r method. Q u e s t i o n / / 4 , / / 5 ( t r a p e z o i d s ) : W o r k i n g w i t h pen and p a p e r , she had no d i f f i c u l t y c a l c u l a t i n g t h e i n i t i a l a r e a s f o r t h e f i r s t ( # 4 ) and s e c o n d ( # 5 ) t i m e . Q u e s t i o n #6 ( t r a p e z o i d ) : She a s k e d a b o u t a c r o o k e d l i n e on t h e g r a p h i c o f t h e t r a p e z o i d . The e x p e r i m e n t e r t o l d h e r i t d i d not m a t t e r . She had p r o b l e m s c o m p u t a t i n g q u o t i e n t s and p r o d u c t s i n v o l v i n g . 5 Q u e s t i o n #7,#8 ( t r a p e z o i d s ) : The s t u d e n t had no d i f f i c u l t y c a l c u l a t i n g t h e i n i t i a l a r e a s . 92 Q u e s t i o n #9 ( t r a p e z o i d ) : A g a i n she had c o m p u t a t i o n a l d i f f i c u l t y i n v o l v i n g .5 as b o t h a q u o t i e n t and p r o d u c t . She u n d e r s t o o d e v e r y a s p e c t needed t o s o l v e t h e s e p r o b l e m s but had f o r g o t t e n how t o d i v i d e y e i l d i n g a .5 q u o t i e n t or how to m u l t i p l y w i t h .5. I f she had r e c e i v e d some r e m e d i a l h e l p h e r e she w o u l d have r e a c h e d 8 0 % e f f i c i e n c y . Q u e s t i o n #10 ( t r i a n g l e ) : She made a w i l d g u e s s a t the i n i t i a l a r e a and t h e n p r o c e e d e d t o c o r r e c t l y work t h r o u g h t h e r e m e d i a l s e c t i o n o f t h e p r o g r a m w h i c h i n v o l v e d .5 as a q u o t i e n t and p r o d u c t . Q u e s t i o n #11,#12, ( t r a p e z o i d s ) : W o r k i n g c a r e f u l l y on pap e r she c a l c u l a t e d t h e i n i t i a l a r e a f o r e a c h t r a p e z o i d . Q u e s t i o n #13 ( t r i a n g l e ) : She had no p r o b l e m c a l c u l a t i n g t h e i n i t i a l a r e a u s i n g t h e f o r m u l a . Q u e s t i o n #14 ( t r a p e z o i d ) : She e n c o u n t e r e d no d i f f i c u l t i e s w h i l e c a l c u l a t i n g the i n i t i a l a r e a u s i n g the f o r m u l a . A f t e r 15 m i n u t e s and 10 s e c o n d s she had r e a c h e d t h e 80% e f f i c i e n c y l e v e l . Then w i t h o u t t h e a i d of the f o r m u l a s h e e t she had no p r o b l e m s u s i n g t h e m e m o r i z e d f o r m u l a e t o answer e i t h e r q u e s t i o n . On t h e p o s t - t e s t she s c o r e d 4/10 g u e s s i n g a t t h e t r a p e z o i d a r e a s , but r e m e m b e r i n g how t o c o r r e c t l y c a l c u l a t e t h e a r e a f o r t r i a n g l e s . Summary: T h i s s t u d e n t had no p r o b l e m s a s s i g n i n g B l , B2, H, o r B and H and c o u l d u n d e r s t a n d and c a l c u l a t e B1+B2/2 and B/2. She c o u l d a l s o use the a p p r o p r i a t e f o r m u l a c o r r e c t l y to c a l c u l a t e t h e a r e a of e i t h e r f i g u r e . The o n l y t h i n g s t o p p i n g 93 h e r s u c c e s s was the p r o b l e m she had d i v i d i n g two i n t o odd numbers to p r o d u c e a .5 q u o t i e n t or m u l t i p l y i n g w i t h t h i s .5. I f t h e p r o g r a m was somehow s e n s i t i v e to t h i s p r o b l e m and gave h e r r e m e d i a l h e l p on t h i s s k i l l , 6 h e w o u l d have e a s i l y r e a c h e d t h e 80% e f f i c i e n c y e a r l i e r . Her p r o b l e m w i t h .5 was s i m p l y b e c a u s e she had f o r g o t t e n how to work w i t h i t . She n e e d e d a l i t t l e g u i d a n c e and p r a c t i c e t o r e m i n d h e r how t h e s e c o m p u t a t i o n s were p e r f o r m e d . 94 5.3 N o n - T u t o r i a l G r o u p Case S t u d i e s C a s e ifl S t u d e n t #1 w o u l d be r a n k e d i n t h e b o t t o m 25% of p a r t i c i p a n t s i n t h i s s t u d y as f a r as o v e r a l l a b i l i t y i s c o n c e r n e d . She i s p r e s e n t l y w o r k i n g a t t h e b e g i n n i n g of the g r a d e 8 math c u r r i c u l u m i n . On t h e p r e - t e s t she s c o r e d 1/10, g u e s s i n g at the a r e a of t h e t r a p e z o i d s and u s i n g BxH f o r the a r e a of t h e t r i a n g l e s . I n i t i a l l y on t h e c o m p u t e r she had d i f f i c u l t y w i t h t h e r e q u i r e d p r o c e d u r e t o e n t e r a n s w e r s and f a i l e d t o comprehend s i m p l e i n s t r u c t i o n s l i k e " p r e s s s p a c e b a r " . But a f t e r t he f i r s t t r i a l t h i n g s went s m o o t h l y . B e l o w i s a d e t a i l e d o u t l i n e of h e r e x p e r i e n c e w i t h t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : On t h i s and e v e r y s u b s e q u e n t q u e s t i o n she was u n a b l e to c o r r e c t l y answer t h e i n i t i a l a r e a q u e s t i o n posed a t the s t a r t of e v e r y p r a c t i s e q u e s t i o n . She w o u l d i n c o r r e c t l y answer t h e i n i t i a l q u e s t i o n and t h e n c o n t i n u e w i t h the more s t r u c t u r e d p a r t of t h e p r a c t i s e s e s s i o n . As e x p e c t e d t h e s t u d e n t s i m p l y g u e s s e d a t B l , B2, and H. At B1+B2/2 she a s k e d , "Do I add t h e s e a l l t o g e t h e r ? " The e x p e r i m e n t e r t o l d h e r t h a t he c o u l d not h e l p . The s t u d e n t m u l t i p l i e d B l x B 2 t o g e t an i n c o r r e c t answer and t h e n i n c o r r e c t l y g u e s s e d a t t h e a r e a . Q u e s t i o n #2 ( t r i a n g l e ) : The s t u d e n t g u e s s e d i n c o r r e c t l y on b o t h B and B/2. When th e c o r r e c t answer f o r B/2 was g i v e n she c o u l d not u n d e r s t a n d how t h i s number was c a l c u l a t e d . B u t 95 o nce g i v e n B/2 and H she was a b l e t o compute t h e c o r r e c t a n s w e r f o r t h e a r e a o f t h e t r i a n g l e . Q u e s t i o n #3 ( t r a p e z o i d ) : On t h e s e c o n d t r a p e z o i d t h e s t u d e n t c o r r e c t l y a s s i g n e d t h e a p p r o p r i a t e numbers t o B l , B2, and H. And she c o n t i n u e d t o c o r r e c t l y a s s i g n t h e s e on a l l s u b s e q u e n t t r a p e z o i d s . She was however v e r y c o n f u s e d when a s k e d to compute B1+B2/2 and i n d e e d added a l l t h r e e d i g i t s t o g e t h e r . The s t u d e n t a f t e r t h i n k i n g l o n g and h a r d i n c o r r e c t l y a r r i v e d a t t h e a r e a by m u l t i p l y i n g B2xH. Q u e s t i o n s #4,#5 , #6 , #7,#8,#9 ( t r a p e z o i d s ) : The s t u d e n t was u n a b l e to g e t p a s t t h e B1+B2/2 p o r t i o n on e a c h of t h e s e q u e s t i o n s . T h i s component o f t h e s o l u t i o n p r o c e s s was a m a j o r h u r d l e to t h e s u c c e s s f u l c o m p l e t i o n of t h e q u e s t i o n s . On q u e s t i o n #4 she s i g n e d , " I d o n ' t know what t h i s means" ( B 1 + B 2 / 2 ) . T h i s seemed t o be a v e r y f r u s t r a t i n g e x p e r i e n c e f o r h e r . On q u e s t i o n #7 she t r i e d to e l i m i n a t e a l l p o s s i b l e ways f o r c a l c u l a t i n g B1+B2/2 u s i n g p e n c i l and p a p e r . But a f t e r l o o k i n g a t t h e f o r m u l a and o t h e r d a t a on the s c r e e n f o r 1.5 m i n u t e s she a g a i n a r r i v e d a t an i n c o r r e c t a n s w e r . She a p p e a r e d to become more f r u s t r a t e d and m u l t i p l i e d B l x B 2 t o g e t an i n c o r r e c t answer f o r t h e a r e a . Q u e s t i o n #10 ( s e c o n d t r i a n g l e ) : The s t u d e n t was i n c o r r e c t i n i d e n t i f y i n g B and c a l c u l a t i n g B/2, but once g i v e n t h e c o r r e c t H and B/2 d a t a she was a b l e t o c a l c u l a t e t h e a r e a . Q u e s t i o n #11 ( 9 t h t r a p e z o i d ) : A g a i n t h e s t u d e n t was stumped by t h e e x p r e s s i o n B1+B2/2, but she was a b l e t o c a l c u l a t e t h e c o r r e c t a r e a once t h e answer f o r B1+B2/2 was g i v e n . She 96 d e c l a r e d , "But I d o n ' t u n d e r s t a n d B1+B2/2!" The s t u d e n t now u n d e r s t o o d t h a t Bl+B2/2xH gave t h e c o r r e c t a n s w e r , but she was u n a b l e t o c a l c u l a t e B1+B2/2. Q u e s t i o n #12 ( t r a p e z o i d ) : The s t u d e n t a g a i n c o u l d not s u c c e s s f u l l y s o l v e the e q u a t i o n B1+B2/2. Once g i v e n the a n s w e r t o B1+B2/2 ( 6 . 5 ) , c o m p u t a t i o n a l p r o b l e m s ( m u l t i p l y i n g by .5) r e s u l t e d i n an i n c o r r e c t a n swer when she t r i e d to compute t h e a r e a of t h e t r a p e z o i d . The e x p e r i m e n t e r c o u l d s e e t h a t the s t u d e n t u n d e r s t o o d the c o r r e c t method f o r s o l v i n g t h e p r o b l e m , but t h e h u r d l e of B1+B2/2 s t i l l e x i s t e d . Q u e s t i o n #13 ( 3 r d t r i a n g l e ) : The s t u d e n t c o u l d not compute B/2, but once g i v e n t h e c o r r e c t v a l u e f o r B/2 had no p r o b l e m c a l c u l a t i n g t h e a r e a . E v e n a f t e r b e i n g g i v e n B/2 she c o u l d n o t see how i t was c a l c u l a t e d (B=6 B/2=3). Q u e s t i o n #14 ( 1 1 t h t r a p e z o i d ) : The s t u d e n t r e a l i z e d t h a t B1+B2 was 13 and t h e n c o r r e c t l y p r o c e e d e d to d i v i d e i t by 2, b u t a g a i n d i f f i c u l t i e s w i t h c o m p u t a t i o n (.5) p r e v e n t e d her f r o m b e i n g s u c c e s s f u l . Then she had more c o m p u t a t i o n a l d i f f i c u l t i e s r e s u l t i n g i n an i n c o r r e c t a r e a c a l c u l a t i o n . Due t o t h e s e d i f f i c u l t i e s i n o b t a i n i n g t h e c o r r e c t answer she was u n a w a r e t h a t she had f o l l o w e d the c o r r e c t method. U n f o r t u n a t e l y t h e c o m p u t e r p r o g r a m gave h e r no i n d i c a t i o n s t h a t she was on t h e r i g h t t r a c k n o r c o u l d i t t e l l h e r where she was m a k i n g c o m p u t a t i o n a l e r r o r s . Q u e s t i o n #15,#16 ( t r a p e z o i d s ) : The s t u d e n t s u c c e s s f u l l y c a l c u l a t e d B1+B2/2 and t h e a r e a of t h e s e two t r a p e z o i d s . Q u e s t i o n #17 ,#18 ,#19 ( t r a p e z o i d s ) : C o m p u t a t i o n a l p r o b l e m s 97 p o s s i b l y due to f a t i g u e and f r u s t r a t i o n with the exercise r e s u l t e d i n i n c o r r e c t answers to B1+B2/2 but the student was able to c a l c u l a t e the c o r r e c t area f o r a l l three trapezoids once given the s o l u t i o n to B1+B2/2. Due to a time l i m i t of approximately 30 minutes, the f a t i g u e and f r u s t r a t i o n of the student, and the f e e l i n g that the student would not reach the expected l e v e l of e f f i c i e n c y , the treatment was stopped at 31 minutes and 30 seconds. Summary: From these observations i t was obvious that the student had learned the c o r r e c t method f o r s o l v i n g the problems. From the s t a r t she could place the c o r r e c t values for the bases and h e i g h t s , but the major hurdle was understanding the task and the steps i n v o l v e d i n c a l c u l a t i n g B/2 or B1+B2/2. If t h i s weakness could have been detected by the program with d i r e c t i o n and remediation performed from the onset, t h i s student would have been more s u c c e s s f u l . The student could not understand the task when presented with these two d i v i s i o n procedures. In a classroom s i t u a t i o n i f these computational e r r o r s had been remedied the student could have reached 80% e f f i c i e n c y working one on one with the computer and no teacher i n t e r v e n t i o n would be neccessary. With a s l i g h t l y more elab o r a t e program t h i s student could have been given more s p e c i f i c help and learned t h i s task from the comput e r. On the p o s t - t e s t t h i s student scored 0/10 guessing at the areas f o r both t r a p e z o i d s and t r i a n g l e s . 98 Case #2 T h i s s t u d e n t w o u l d be r a n k e d i n t h e b o t t o m 15% of p a r t i c i p a n t s i n t h i s s t u d y as f a r as o v e r a l l a b i l i t y i s c o n c e r n e d . He i s p r e s e n t l y w o r k i n g a t t h e h a l f w a y p o i n t i n t h e g r a d e 7 math c u r r i c u l u m . On t h e p r e - t e s t he s c o r e d 3/10, r a n d o m l y g u e s s i n g a t t h e a r e a s of b o t h t r i a n g l e s and t r a p e z o i d s . He had no d i f f i c u l t i e s w i t h t h e m e c h a n i c s of e n t e r i n g d a t a or f o l l o w i n g t h e i n s t r u c t i o n of "push space b ar t o c o n t i n u e " . T h i s s t u d e n t s t a r t e d t o work u s i n g p e n c i l and p a p e r r i g h t f r o m t h e s t a r t . N o r m a l l y he i s e a s i l y d i s t r a c t e d and h a r d to keep on t a s k , but f o r t h e w h o l e t i m e he was on t h e c o m p u t e r he was v e r y s t u d i o u s and c o n c e n t r a t e d on the t a s k a t hand. B e l o w i s a d e t a i l e d o u t l i n e of h i s e x p e r i e n c e w h i l e w o r k i n g on t h e p r a c t i s e p o r t i o n of the s o f t w a r e . Q u e s t i o n it 1 ( t r a p e z o i d ) : H a v i n g had no p r e v i o u s e x p e r i e n c e w i t h t h i s m a t e r i a l , t h e s t u d e n t s i m p l y g u e s s e d i n c o r r e c t l y a t t h e a r e a of t h e t r a p e z o i d . He g u e s s e d i n c o r r e c t l y on a l l s u b s e q u e n t i n i t i a l a r e a q u e s t i o n s d u r i n g t h i s e x e r c i s e . He a l s o g u e s s e d a t B l , B2, and H. A t B1+B2/2 he was c o n f u s e d and m u l t i p l i e d two numbers t o come up w i t h an i n c o r r e c t r e s p o n s e . Then he g u e s s e d a t t h e a r e a . Q u e s t i o n #2 ( t r i a n g l e ) : F o r t h e i n i t i a l a r e a q u e s t i o n he m u l t i p l i e d BxH t o g e t an i n c o r r e c t a n s w e r . He t h e n c o r r e c t l y a s s i g n e d B and H. A t B/2 he was c o n f u s e d as t o the t a s k and e n t e r e d an i n c o r r e c t g u e s s . F o r t h e a r e a he g u e s s e d q u i c k l y and a g a i n i n c o r r e c t l y . 99 Q u e s t i o n #3 ( t r a p e z o i d ) : F o r B l t h e s t u d e n t gave the v a l u e f o r H. He t h e n went on t o g e t B2 and H c o r r e c t . At B1+B2/2 he m u l t i p l i e d B l x B 2 b u t once t h e c o r r e c t answer a p p e a r e d he saw h i s m i s t a k e and s i g n e d , " I t h o u g h t m u l t i p l y . " He q u i c k l y g u e s s e d a t t h e a r e a and was w r o n g . Q u e s t i o n #4, #5 ( t r a p e z o i d s ) : He c o r r e c t l y a s s i g n e d d i g i t s t o B l , B2, and H. A t B1+B2/2 he q u i c k l y g u e s s e d a p p a r e n t l y w i t h o u t t h i n k i n g . F o r t h e a r e a he a g a i n g u e s s e d i n c o r r e c t l y on b o t h q u e s t i o n s . A f t e r c o m p l e t i n g #5 he s i g n e d , " I u n d e r s t a n d H, but B1+B2/2 t i m e s ( m u l t i p l y ) ?" The e x p e r i m e n t e r made no r e s p o n s e . Q u e s t i o n #6 ( t r a p e z o i d ) : He c o r r e c t l y a s s i g n e d d i g i t s t o B l , B2, and H and a l s o c a l c u l a t e d B1+B2/2 ( 5 . 5 ) . He t h e n s t a r t e d t o d i v i d e H i n t o 5.5, but t h e n changed and m u l t i p l i l e d . H o w e v e r , due t o a c o m p u t a t i o n a l e r r o r he p r o d u c e d an i n c o r r e c t a n swer of 25.5 i n s t e a d of 2 7 . 5 . T h e r e f o r e on t h i s q u e s t i o n he was s u c c e s s f u l a t c a l c u l a t i n g b o t h B1+B2/2 and t h e a r e a f o r t h e t i m e . He now had d i s c o v e r e d t h e c o r r e c t method f o r s o l v i n g t h e q u e s t i o n s . Q u e s t i o n #7,#8 ( t r a p e z o i d s ) : The s t u d e n t c o r r e c t l y c a l c u l a t e d a l l t h e a n s w e r s d u r i n g t h e r e m e d i a l s e c t i o n s and ga v e t h e 'thumbs up' s i g n . Q u e s t i o n #9 ( t r a p e z o i d ) : A t B1+B2/2 t h e s t u d e n t g u e s s e d q u i c k l y and p r o d u c e d an i n c o r r e c t r e s p o n s e . To c a l c u l a t e t h e a r e a he u s e d t h e c o r r e c t method and v a l u e s , but made a s i l l y c o m p u t a t i o n a l e r r o r i n v o l v i n g .5. Q u e s t i o n 10 ( t r i a n g l e ) : The s t u d e n t was a t f i r s t s t u c k a t 100 B/2 and t h e n used t h e r i g h t v a l u e s and methods f o r the c a l c u l a t i o n . H o wever, he made a c o m p u t a t i o n a l e r r o r . Q u e s t i o n #11 ( t r a p e z o i d ) : He made a m i s t a k e a t B2, g i v i n g t h e v a l u e f o r H. He c o u l d n ot c a l c u l a t e B1+B2/2, but used t h e c o r r e c t d a t a t o c a l c u l a t e t h e a r e a a n s w e r . Q u e s t i o n #12 ( t r a p e z o i d ) : A g a i n t h e s t u d e n t was s t u c k a t B1+B2/2, p e r h a p s b e c a u s e t h e v a l u e i n v o l v e d .5 ( 7 . 5 ) . Then u s i n g t h e c o r r e c t v a l u e s and method he c a l c u l a t e d an i n c o r r e c t a r e a due t o a s i m p l e c o m p u t a t i o n a l p r o b l e m . Q u e s t i o n #13 ( t r i a n g l e ) : The s t u d e n t s t a t e d t h a t B/2=6 when i t s h o u l d have been B/2=3 b e c a u s e B=6. Then w i t h o u t t h i n k i n g he q u i c k l y g u e s s e d i n c o r r e c t l y a t t h e a r e a . Q u e s t i o n #14 ( t r a p e z o i d ) : W h i t o u t h e s i t a t i n g t h e s t u d e n t g u e s s e d a t B1+B2/2. He a p p e a r e d to be t i r e d a t t h i s p o i n t . He used t h e c o r r e c t v a l u e s and method but due to a c o m p u t a t i o n a l e r r o r he e n t e r e d an i n c o r r e c t a n s w e r . Q u e s t i o n #15 ( t r a p e z o i d ) : He w a i t e d and t h e n e n t e r e d a g u e s s not t h i n k i n g o r u s i n g p a p e r and p e n c i l a t B1+B2/2. He t h e n u s e d t h e c o r r e c t d a t a t o s o l v e t h e a r e a . Q u e s t i o n #16,#17 , #18 , #19 ( t r a p e z o i d s ) : The s t u d e n t c o r r e c t l y c a l c u l a t e d a n s w e r s t o a l l t h e p o r t i o n s of t h e s e 4 q u e s t i o n s e x c e p t f o r #18 where c o m p u t a t i o n a l p r o b l e m s r e s u l t e d i n a m i s t a k e a t B1+B2/2. Due t o t h e t i m e l i m i t o f a p p r o x i m a t e l y 30 m i n u t e s and t h e f e e l i n g t h a t the s t u d e n t w o u l d not r e a c h t h e e x p e c t e d l e v e l of e f f i c i e n c y , t h e t r e a t m e n t was s t o p p e d a f t e r 32 m i n u t e s had e l a p s e d . 101 Summary: T h i s s t u d e n t knew t h e c o r r e c t method f o r c a l c u l a t i n g t h e a r e a f o r t r a p e z o i d s ( B l + B 2 / 2 x H ) a f t e r q u e s t i o n #6, but he d i d n o t g e t enough p r a c t i c e to l e a r n how t o c a l c u l a t e t h e a r e a f o r t r i a n g l e s . I f he was h a v i n g c o m p u t a t i o n a l p r o b l e m s w i t h B1+B2/2, he c o u l d s t i l l use t h e g i v e n d a t a and f i n d t h e c o r r e c t a r e a . On s e v e r a l o c c a s s i o n s p r o b l e m s w i t h math c o m p u t a t i o n k e p t him f r o m b e i n g s u c c e s s f u l . He w o u l d o c c a s s i o n a l l y guess at B1+B2/2 o r the a r e a , but most of the t i m e he c a r e f u l l y w o r k e d out t h e answer u s i n g p e n c i l and p a p e r . The s t u d e n t d i d not g e t t o t h e p o i n t where he u n d e r s t o o d the s i g n i f i c a n c e of t h e i n i t i a l a r e a q u e s t i o n . He c o n s i s t e n t l y g u e s s e d at the f i r s t q u e s t i o n and t h e n s u c c e s s f u l l y work t h r o u g h t h e s t e p by s t e p p r o c e s s where the c o m p l e t e t a s k was b r o k e n down. I f he had been t o l d t h a t t he f i r s t ( i n i t i a l ) a r e a q u e s t i o n was t h e same as t h e l a s t a r e a q u e s t i o n i t may have h e l p e d him. However t h i s i s a s t u d e n t who a l s o needs a g r e a t d e a l of s t r u c t u r a l h e l p i n h i s day to day p r o b l e m s o l v i n g . I f he had r e c e i v e d more p r a c t i c e on t h e t r i a n g l e q u e s t i o n s he w o u l d have been a b l e t o s u c c e s s f u l l y c a l c u l a t e them. He had a h a r d t i m e d e c i p h e r i n g B/2 and n e e d e d some more p r a c t i c e t o c l e a r up t h i s m i s u n d e r s t a n d i n g . T h i s s t u d e n t d i d v e r y w e l l c o n s i d e r i n g h i s o v e r a l l a b i l i t y . I f t h i s p r o g r a m had a l i t t l e more i n t h e way of d i a g n o s t i c s and r e m e d i a t i o n t h i s s t u d e n t c o u l d have been more s u c c e s s f u l . He c e r t a i n l y e n j o y e d t h e e x p e r i e n c e and s t a y e d on t a s k c o n t i n u o u s l y f o r l o n g e r t h a n he w o u l d have i n a n o t h e r 102 l e a r n i n g s i t u a t i o n . On t h e p o s t - t e s t he s c o r e d 0/10. On b o t h t r i a n g l e s and t r a p e z o i d s he w o u l d add t h e h e i g h t and base o r b a s e s t o c a l c u l a t e t h e a r e a . Case #3 T h i s s t u d e n t w o u l d be p l a c e d a t o r b e l o w t h e 3 0 t h p e r c e n t i l e i n a r a n k i n g of i n d i v i d u a l s i n v o l v e d i n t h i s s t u d y b a s e d on o v e r a l l a b i l i t y . He i s p r e s e n t l y t h r e e q u a r t e r s of t h e way t h r o u g h t h e g r a d e 9 math c u r r i c u l u m . He s c o r e d 2/10 on t h e p r e - t e s t g u e s s i n g a t t h e a r e a of t h e t r a p e z o i d s and u s i n g the BxH method t o s o l v e t h e t r i a n g l e a r e a s . B e l o w i s a d e t a i l e d o u t l i n e of h i s e x p e r i e n c e w i t h t h e p r a c t i s e p o r t i o n o f t h e s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : From q u e s t i o n #1 t o #20 t h i s s t u d e n t w o u l d i n c o r r e c t l y g u e s s a t t h e i n i t i a l a r e a q u e s t i o n and t h e n work t h r o u g h t h e s t e p by s t e p b r eakdown of the t a s k . F o r B l he was c o n f u s e d and e n t e r e d 3 5. A f t e r l o o k i n g over t h e f o r m u l a on h a n d o u t #4 he e n t e r e d t h e a p p r o p r i a t e v a l u e s f o r B2 and H. He was a l s o s u c c e s s f u l a t B1+B2/2 and the a r e a . R i g h t f r o m t h e b e g i n i n g he knew how t o do t h e s e c a l c u l a t i o n s . Q u e s t i o n #2 ( t r i a n g l e ) : He c o r r e c t l y a n s w e r e d a l l p a r t s of t h e r e m e d i a l s e c t i o n f o r t h i s p r o b l e m . Q u e s t i o n #3,#4,#5 ( t r a p e z o i d s ) : The s t u d e n t had no d i f f i c u l t y a n s w e r i n g t h e s e q u e s t i o n s a f t e r g e t t i n g t h e i n i t i a l a r e a q u e s t i o n wrong on e a c h one. 1 0 3 Q u e s t i o n #6,#7 ( t r a p e z o i d s ) : I n b o t h p r o b l e m s he was i n c o r r e c t on t h e a r e a c a l c u l a t i o n due to s i l l y c o m p u t a t i o n a l e r r o r s . He u s e d t h e c o r r e c t method t o c a l c u l a t e t h e a r e a , b u t c o m p u t a t i o n a l p r o b l e m s k e p t h i m f r o m b e i n g s u c c e s s f u l . On t h e i n i t i a l a r e a q u e s t i o n s he was becomming f r u s t r a t e d s i n g i n g , " I d o n ' t know how t o do t h i s p a r t . " Q u e s t i o n #8 ( t r a p e z o i d ) : The s t u d e n t made a s t u p i d m i s t a k e a t H and t h e n a p p a r e n t l y w o r k i n g t o o q u i c k l y he made a c a r e l e s s e r r o r a t B1+B2/2. H o w e v e r , he u s e d t h e c o r r e c t d a t a t o c a l c u l a t e t h e a r e a . Q u e s t i o n #9 ( t r a p e z o i d ) : He made a s i l l y e r r o r a t B1+B2/2, b u t t h e n a g a i n used t h e c o r r e c t d a t a t o c a l c u l a t e the a r e a . Q u e s t i o n #10 ( t r i a n g l e ) : The s t u d e n t had no p r o b l e m s w o r k i n g t h r o u g h t h e r e m e d i a l s e c t i o n of t h i s q u e s t i o n . Q u e s t i o n #11,#12,(#13 t r i a n g l e ) , #14 , #15 , #16 ( t r a p e z o i d s ) : He c o r r e c t l y p l a c e d t h e v a l u e s and d i d t h e c a l c u l a t i o n s on e a c h of t h e s e p r o b l e m s a f t e r g e t t i n g t h e i n i t i a l a r e a q u e s t i o n s w rong. On q u e s t i o n #15 he a s k e d , "Where i s t h i s AREA = ( i n i t i a l a r e a ) f r o m ? " The e x p e r i m e n t e r e x p l a i n e d i t was t h e same as t h e f i n a l a n s w e r . The s t u d e n t d i d not seem t o u n d e r s t a n d t h i s e x p l a n a t i o n . Q u e s t i o n #17 ( t r a p e z o i d ) : The s t u d e n t made c o m p u t a t i o n a l e r r o r s a t B1+B2/2 and on t h e a r e a c a l c u l a t i o n . Q u e s t i o n #18,#19 ( t r a p e z o i d s ) : He had no p r o b l e m s w o r k i n g t h r o u g h t h e r e m e d i a l p o r t i o n s f o r t h e s e q u e s t i o n s . The e x p e r i m e n t e r s a i d , " T r y t o g e t t h e f i r s t q u e s t i o n ( i n i t i a l a r e a ) c o r r e c t now." 104 Q u e s t i o n #20 ( t r i a n g l e ) : H i s a nswer was wrong on the i n i t i a l a r e a , but c o r r e c t on t h e b r o k e n down r e m e d i a l s e c t i o n . Q u e s t i o n s #21,#22,#23 ( t r i a n g l e s ) : He was c o r r e c t on a l l t h e i n i t i a l a r e a q u e s t i o n . Now t h e s t u d e n t had t o get two t r a p e z o i d q u e s t i o n s r i g h t t o r e a c h t h e 80% e f f i c i e n c y l e v e l . Q u e s t i o n #24,#25 ( t r a p e z o i d s ) : The s t u d e n t a n s w e r e d b o t h i n i t i a l a r e a q u e s t i o n s c o r r e c t l y t h u s r e a c h i n g t h e 80% e f f i c i e n c y l e v e l . On t h e p r a c t i s e q u e s t i o n s w i t h o u t t h e f o r m u l a , the f i r s t and s e c o n d t r a p e z o i d s were wrong due to c o m p u t a t i o n a l m i s t a k e s . The t h i r d t r a p e z o i d and the f i r s t t r i a n g l e a r e a s w e r e c o r r e c t . Summary: T h i s s t u d e n t had the c o r r e c t method r i g h t f r o m the s t a r t . He s i m p l y c o u l d not see t h a t t h e f i r s t ( i n i t i a l ) a r e a q u e s t i o n was t h e same as t h e l a s t a r e a q u e s t i o n t h a t he w o r k e d out s u c c e s s f u l l y i n t h e r e m e d i a l s e c t i o n e a c h t i m e . He seemed s a t i s f i e d g e t t i n g t h e i n i t i a l a r e a q u e s t i o n wrong and t h e n w o r k i n g t h r o u g h t h e p r o b l e m s t e p by s t e p . L a t e r he became f r u s t r a t e d (#15) and a s k e d a b o u t t h e i n i t i a l a r e a q u e s t i o n , w o n d e r i n g what i t meant and where i t f i t i n t o t he o v e r a l l p i c t u r e . He d i d n o t see t h e r e l a t i o n s h i p between the f i r s t a r e a q u e s t i o n and t h e answer he w o u l d g e t at the end of t h e c o m p u t a t i o n s . The e x p e r i m e n t e r c o u l d see t h a t he had no p r o b l e m f i g u r i n g t h e t a s k out and e n c o u r a g e d him a t q u e s t i o n #15 t o t r y and g e t t h e i n i t i a l q u e s t i o n c o r r e c t . T h i s 105 s t u d e n t c o u l d comprehend the n o t a t i o n B/2 and B1+B2/2 and knew how t o use t h e f o r m u l a e t o c o r r e c t l y c a l c u l a t e the a r e a s . He c o u l d have r e a c h e d t h e 80% e f f i c i e n c y l e v e l much e a r l i e r i f t h e e x p e r i m e n t e r had e n c o u r a g e d him e a r l i e r on to g e t t h e i n i t i a l a r e a q u e s t i o n c o r r e c t . T h i s s t u d e n t was s u c c e s s f u l b e c a u s e he u n d e r s t o o d the t a s k a t B/2 o r B1+B2/2 and he c o u l d use t h e f o r m u l a e s u c c e s s f u l l y . I f t h e p r o g r a m had been a b l e t o h e l p him see t h e r e l a t i o n s h i p between t he q u e s t i o n s he w o r k e d t h r o u g h s t e p by s t e p and t h e i n i t i a l a r e a q u e s t i o n , he w o u l d have been s u c c e s s f u l on the i n i t i a l a r e a q u e s t i o n s much s o o n e r . The r e a s o n f o r t h i s p r o b l e m was b e c a u s e he was c o n f u s e d by the i n i t i a l n o t a t i o n (AREA= _) a l t h o u g h he u n d e r s t o o d t h e p r o c e d u r e f o r i t s c a l c u l a t i o n f r o m t h e s t a r t . A l i t t l e more i n f o r m a t i o n f r o m t h e s o f t w a r e w o u l d have h e l p e d him i m m e n s e l y . On t h e p o s t - t e s t t h i s s t u d e n t s c o r e d 1/10 u s i n g t h e same s t r a t e g i e s as t h o s e he us e d on t h e p r e - t e s t . He g u e s s e d a t t h e a r e a f o r t h e t r a p e z o i d s and u s e d BxH f o r the a r e a of t h e t r i a n g l e s . He had not r e t a i n e d t h e c o r r e c t method of c a l c u l a t i o n t h a t he had l e a r n e d a week e a r l i e r . C a s e #4 T h i s s t u d e n t w o u l d be r a n k e d a t a b o u t t he 50% l e v e l i n o v e r a l l a b i l i t i e s when compared t o t h e o t h e r p a r t i c i p a n t s i n t h i s s t u d y . She was r e c e n t l y a c c e p t e d i n t o t h e p r e p a r a t o r y y e a r a t G a l l a u d e t C o l l e g e and i s p r e s e n t l y w o r k i n g a t t h e 106 b e g i n n i n g of t h e g r a d e 10 c u r r i c u l u m i n math. On the p r e - t e s t she s c o r e d 1/10 g u e s s i n g a t t h e a r e a of the t r a p e z o i d s and u s i n g BxH f o r t h e a r e a of t h e t r i a n g l e s . B e l o w i s a d e t a i l e d a c c o u n t of h e r e x p e r i e n c e w i t h the p r a c t i s e p o r t i o n of t h i s s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : On t h i s and e v e r y o t h e r q u e s t i o n she e n t e r e d an i n c o r r e c t g u e s s f o r t h e i n i t i a l a r e a q u e s t i o n . T hen she w o u l d p r o c e e d t h r o u g h t h e s t e p by s t e p r e m e d i a l p r o c e d u r e s h o w i n g t h e a p p r o p r i a t e method f o r c a l c u l a t i n g the a n s w e r . T h i s s t u d e n t had no p r o b l e m s w i t h t h e m e c h a n i c s of e n t e r i n g h e r r e s p o n s e s . A t B l she e n t e r e d 35 as h e r guess f o r the a r e a . She was c o r r e c t a t B l and H, but v e r y c o n f u s e d a t B1+B2/2, e n t e r i n g 4B as an a n s w e r . Then she q u i c k l y g u e s s e d a t the a r e a and j u s t as q u i c k l y moved o n t o t h e n e x t q u e s t i o n w i t h o u t a t t e m p t i n g to see how t h e answer was d e r i v e d . Q u e s t i o n #2 ( t r i a n g l e ) : F o r B she e n t e r e d 12 and t h e n f o r H and B/2 she e n t e r e d t h e a p p r o p r i a t e d i g i t s . Then f o r the a r e a she e n t e r e d 6 w h i c h was t h e v a l u e f o r B o r H. She u n d e r s t o o d t h e t a s k a t B/2, but d i d n o t know how to use the f o r m u l a t o c a l c u l a t e t h e a r e a . Q u e s t i o n //3 ( t r a p e z o i d ) : She was wrong on b o t h B l and B2, c o r r e c t on H, but i n c o r r e c t a t B1+B2/2 and a r e a . She was not w o r k i n g t h e answer out on p a p e r and d i d not a p p e a r to u n d e r s t a n d t h e t a s k i n v o l v e d t o o b t a i n a c o r r e c t a n s w e r . Q u e s t i o n #4 ( t r a p e z o i d ) : She was g e t t i n g r e s t l e s s at t h i s p o i n t . F o r t h e f i r s t t i m e she e n t e r e d t h e a p p r o p r i a t e v a l u e s 107 f o r B l , B2, and H, but a g a i n she q u i c k l y g u e s s e d a t B1+B2/2 and the a r e a . Q u e s t i o n #5,#6 ( t r a p e z o i d s ) : She p l a c e d i n c o r r e c t v a l u e s at B2, B1+B2/2, and a r e a on b o t h q u e s t i o n s . She s t i l l a p p e a r e d t o have no u n d e r s t a n d i n g of t h e t a s k s r e q u i r e d to compute B1+B2/2 o r a r e a . She j u s t r a n d o m l y g u e s s e d a t t h e i r v a l u e . Q u e s t i o n #7,#8,#9 ( t r a p e z o i d s ) : The s t u d e n t had no p r o b l e m p l a c i n g the a p p r o p r i a t e v a l u e s on B l , B2, and H. However she was u n a b l e to c a l c u l a t e B1+B2/2 and c o u l d not see t h a t by f o l l o w i n g t h e f o r m u l a the answer c o u l d be c a l c u l a t e d by B l + B 2 / 2 x H . She a p p e a r e d to work c a r e f u l l y , but d i d not c omprehend the t a s k s i n v o l v e d i n e i t h e r of t h e s e c o m p u t a t i o n s . Sometimes she s i m p l y g u e s s e d u s i n g the numbers p r e s e n t and o t h e r t i m e s she p i c k e d numbers out of the a t m o s p h e r e . She d i d not l o o k e d a t the f o r m u l a s h e e t and was becomming f r u s t r a t e d . Q u e s t i o n #10 ( t r i a n g l e ) : F o r t h e i n i t i a l a r e a q u e s t i o n the s t u d e n t e n t e r e d TRIANGLE. The e x p e r i m e n t e r t o l d her t h a t i t must be a number. She e r r a s e d i t and q u i c k l y e n t e r e d an i n c o r r e c t g u e s s f o r the i n i t i a l a r e a , o t h e r i n c o r r e c t v a l u e s f o r B and B2 and t h e n the a r e a a g a i n . She d i d not l o o k at t h e c o r r e c t a n s w e r s and t r y t o l o g i c a l l y deduce how e a c h was c a l c u l a t e d . She j u s t q u i c k l y e n t e r e d a g u e s s and when the c o r r e c t answer a p p e a r e d she q u i c k l y went on t o the n e x t p a r t , n e v e r p a u s i n g to s t u d y t h e p r o b l e m or s o l u t i o n s p r e s e n t e d . Q u e s t i o n #11 ( t r a p e z o i d ) : She made an i n c o r r e c t e n t r y f o r B l . Then a b r e a k t h r o u g h a t B1+B2/2. She added Bl+B2=12 and 108 t h e n s i g n e d Bl+B2=12, f o r g e t t i n g t o d i v i d e by 2. She a l s o e n t e r e d an i n c o r r e c t v a l u e f o r t h e a r e a . Q u e s t i o n #12 ( t r a p e z o i d ) : She c o r r e c t l y e n t e r e d v a l u e s f o r B l , B2, and H. At B1+B2/2 she added B1+B2 and t h e n d i v i d e d i t by 2, but due t o c o m p u t a t i o n a l p r o b l e m s (15/2=7.1) she e n t e r e d an i n c o r r e c t v a l u e . Then a t t h e a r e a c a l c u l a t i o n she u s e d t h e g i v e n v a l u e of B1+B2/2 and m u l t i p l i e d i t by H, but a g a i n due to c o m p u t a t i o n a l p r o b l e m s she got an i n c o r r e c t a n s w e r . She had f i g u r e d out the c o r r e c t method f o r s o l v i n g b o t h B1+B2/2 and the a r e a , but t h e c o m p u t e r had not been a b l e t o t e l l h e r , b e c a u s e i t was not p r o g r a m e d t o be s e n s a t i v e to t h e s e s i t u a t i o n s . Q u e s t i o n #13 ( t r i a n g l e ) : She p l a c e d t h e a p p r o p r i a t e v a l u e f o r B and H and s u c c e s s f u l l y computed B/2, but t h e n m u l t i p l i e s BxH t o g e t an i n c o r r e c t v a l u e f o r the a r e a . She d i d n ot see t h a t B/2xH gave t h e c o r r e c t a n s w e r . Q u e s t i o n #14 ( t r a p e z o i d ) : She was c o r r e c t on B l , B2, H, and B1+B2/2, b u t g u e s s e d i n c o r r e c t l y a t t h e a r e a i n s t e a d of t r y i n g to work i t o u t . She s i g n e d , " S t u p i d game" s h o w i n g h e r f r u s t r a t i o n a t b e i n g u n s u c c e s s f u l . Q u e s t i o n #15 ( 1 2 t h t r a p e z o i d ) : The s t u d e n t p l a c e d t h e a p p r o p r i a t e v a l u e s f o r B l , B2, H, and s u c c e s f u l l y computed B1+B2/2 and t h e n u s e d t h e c o r r e c t method t o c a l c u l a t e t h e a r e a . She s i g n e d , " I g o t i t ! " The s t u d e n t f o r t h e f i r s t t i m e saw t h a t she was u s i n g t h e c o r r e c t method and s u c c e s s f u l l y a n s w e r e d t h e q u e s t i o n . Q u e s t i o n s #16 , #17 , #18 , #19,#20 ( t r a p e z o i d s ) : The s t u d e n t 109 c o r r e c t l y a n s w e r e d a l l t h e components i n c l u d i n g B1+B2/2 and t h e a r e a , a f t e r g u e s s i n g i n c o r r e c t l y a t t h e i n i t i a l a r e a q u e s t i o n . Q u e s t i o n #21,#22,#23 ( 4 t h , 5 t h , 6 t h t r i a n g l e s ) : The s t u d e n t was s u c c e s s f u l f o r the f i r s t t i m e w i t h t r i a n g l e s . She computed B/2 and t h e n used t h i s v a l u e m u l t i p l i e d by the h e i g h t to g e t t h e a p p r o p r i a t e a n s w e r s . U s i n g t h e d a t a on t h e s c r e e n she had now d i s c o v e r e d t h e c o r r e c t method f o r s o l v i n g a r e a s of t r i a n g l e s . But she was u n a b l e t o c a l c u l a t e the i n i t i a l a r e a q u e s t i o n f o r any of t h e s e t r i a n g l e s . Q u e s t i o n #24 ( t r a p e z o i d s ) : She c o r r e c t l y a n s w e r e d a l l t h e components of t h i s q u e s t i o n a f t e r g u e s s i n g a t the i n i t i a l a r e a q u e s t i o n . Due to the t i m e l i m i t o f a p p r o x i m a t e l y 30 m i n u t e s and the f e e l i n g t h a t t h e s t u d e n t w o u l d not r e a c h t h e e x p e c t e d l e v e l of e f f i c i e n c y , t h e t r e a t m e n t was s t o p p e d a f t e r 30 m i n u t e s . Summary: T h i s s t u d e n t c o u l d i d e n t i f y t h e a p p r o p r i a t e p a r t s needed f o r t h e t r a p e z o i d f o r m u l a a f t e r q u e s t i o n #7, b u t c o u l d not comprehend t h e t a s k a t e i t h e r B1+B2/2 o r a r e a u n t i l q u e s t i o n #15. Some d i a g n o s t i c and r e m e d i a l h e l p h e r e f r o m the p r o g r a m c o u l d have h a s t e n e d h e r u n d e r s t a n d i n g o f t h i s p r o c e s s . The same p r o b l e m e x i s t e d w i t h t h e t r i a n g l e s and the same t y p e of h e l p w o u l d have made t h e p r o g r a m much more h e l p f u l and l e s s f r u s t r a t i n g f o r t h e s t u d e n t . The s t u d e n t c o u l d n e v e r do a l l t h e work i n d e p e n d e n t l y t o a n s w e r t h e i n i t i a l q u e s t i o n , however she c o u l d f o l l o w t h e 110 s t e p by s t e p method and c a l c u l a t e t he a nswer by b e i n g l e a d t h r o u g h the c o r r e c t p r o c e d u r e s by t h e p r o g r a m . The n e x t s t e p f o r h e r was t o use t h e k n o w l e d g e of t h i s p r o c e d u r e and i n d e p e n d e n t of t h e c o m p u t e r , work out t h e answer and e n t e r i t as t h e i n i t i a l a r e a a n s w e r . She n e v e r r e a l i l z e d t h e s i g n i f i g a n c e o r m e a n ing of t h i s i n i t i a l a r e a q u e s t i o n . I f t h e p r o g r a m had been a l i t t l e more s e n s a t i v e t o t h e p r o b l e m s e n c o u n t e r e d by t h e s t u d e n t and a p p l i e d a p p r o p r i a t e r e m e d i a t i o n , t h i s s t u d e n t may have r e a c h e d the 80% e f f i c i e n c y l e v e l . On the p o s t - t e s t she s c o r e d 2/10 g u e s s i n g a t the a r e a of t h e t r a p e z o i d s and u s i n g BxH f o r the a r e a of the t r i a n g l e s . T h e s e were t h e same s t r a t e g i e s she a p p l i e d on the p r e - t e s t . C a s e # 5 S t u d e n t #5 w o u l d be r a n k e d i n t h e t o p 25% of the p a r t i c i p a n t s i n t h i s s t u d y based on o v e r a l l a b i l i l t l y . She has r e c e n t l y been a c c e p t e d i n t o t he f r e s h m a n y e a r at G a l l a u d e t C o l l e g e and i s p r e s e n t l y w o r k i n g a t t h e end of t h e A l g e b r a 11 math c u r r i c u l u m . B e l o w i s a d e t a i l e d o u t l i n e of h e r e x p e r i e n c e w i t h t h e p r a c t i s e p o r t i o n of the s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : She g u e s s e d i n c o r r e c t l y a t t h e i n i t i a l a r e a q u e s t i o n and B l and H. She u n d e r s t o o d the n o t a t i o n B1+B2/2 and c o r r e c t l y c a l c u l a t e d i t . However, she c o u l d not c a l c u l a t e t he a r e a . Q u e s t i o n #2 ( t r i a n g l e ) : She e n t e r e d the c o r r e c t v a l u e s f o r B, H, and B/2 and t h e n w o r k i n g on p a p e r she i n c o r r e c t l y I l l guessed at the area. A f t e r only two t r i a l s the student showed the experimenter that she understood the n o t a t i o n B/2 and B1+B2/2, but she had not yet discovered the use of the formulae to c a l c u l a t e the areas. Question #4,//5 ( t r a p e z o i d s ) : She c a r e f u l l y t r i e d to c a l c u l a t e the i n i t i a l area, but entered a guess each time. Then she s t u d i o u s l y worked through the remediation s e c t i o n s and s u c c e s s f u l l y answered a l l components of both questions. Question #6,#7 ( t r a p e z o i d s ) : On #6, working on paper and usi n g the formula sheet to c a l c u l a t e the i n i t i a l area, she used the app r o p r i a t e d i g i t s 11/2x5, but had problems with 11/2. When working through the step by step breakdown again she had problems with B1+B2/2 (11/2), but she used the c o r r e c t data to c a l c u l a t e the area. The exact same scenario happened with question #7. Both with her attempts at the i n i t i a l area question and the step by step method she was stuck at B1+B2/2 because i t i n v o l v e d 7+6/2=13/2 to which she answered 7.5. Therefore a s i l l y computational e r r o r caused f a i l u r e . However, again she had used the c o r r e c t data to c a l c u l a t e the area. Question #8 ( t r a p e z o i d ) : Working on paper she s u c c e s s f u l l y c a l c u l a t e d the i n i t i a l area on t h i s the 7th t r a p e z o i d . Question #9 ( t r a p e z o i d ) : Again computational problems i n v o l v i n g B1+B2/2 caused f a i l u r e at the i n i t i a l area c a l c u l a t i o n . T h i s problem occured again during the step by step breakdown, but she used the c o r r e c t value f o r B1+B2/2 and m u l t i p l i e d i t by H to get the r i g h t area. 112 Q u e s t i o n #10 ( t r i a n g l e ) : C o m p u t a t i o n a l p r o b l e m s a t B/2 and a r e a made t h e s t u d e n t u n s u c c e s s f u l a t t h i s q u e s t i o n . P r o b l e m s w i t h d i v i s i o n and m u l t i p i c a t i o n w i t h .5 r e s u l t e d i n an i n c o r r e c t a n swer a l t h o u g h she was u s i n g t h e c o r r e c t m e t hod. (She knows t h a t B/2xH=Area f o r a T r i a n g l e . ) Q u e s t i o n #12 ( t r a p e z o i d ) : She c o r r e c t l y c a l c u l a t e d t h e a r e a i n v o l v i n g .5, but e n t e r e d i t as 375 ( i n s t e a d o f f 37.5) f o r g e t t i n g t h e d e c i m a l . She t h e n had t o go t h r o u g h t h e s t e p by s t e p r e m e d i a l method. Q u e s t i o n #13 ( t r i a n g l e ) : She c a l c u l a t e d t h e r i g h t i n i t i a l a r e a f o r t h i s t r i a n g l e . Q u e s t i o n #14 ( t r a p e z o i d ) : W o r k i n g q u i c k l y and c a r e l e s s l y she e n t e r e d an i n c o r r e c t i n i t i a l a r e a and t h e n sped t h r o u g h t h e r e m e d i a l p a r t and c a l c u l a t e d t h e a r e a . Q u e s t i o n #15,#16,#17 ( t r a p e z o i d s ) : U s i n g p a p e r and p e n c i l , s h e q u i c k l y w o r k e d out t h e c o r r e c t i n i t i a l a r e a f o r each of t h e s e t r a p e z o i d s and r e a c h e d t h e 80% e f f i c i e n c y l e v e l . On t h e p r a c t i s e q u e s t i o n s w i t h o u t t h e a i d of the f o r m u l a s h e e t she u s e d t h e c o r r e c t d i g i t s and method but i n the f i n a l p o r t i o n Bl+B2xH o f t h e f i r s t t r a p e z o i d she made a s i l l y c o m p u t a t i o n a l e r r o r . On t h e s e c o n d t r a p e z o i d she c o r r e c t l y c a l c u l a t e d t h e a r e a . Then on t h e f i r s t t r i a n g l e she had no p r o b l e m s c a l c u l a t i n g t h e a r e a . Summary: T h i s s t u d e n t u n d e r s t o o d t h e n o t a t i o n B1+B2/2 and B/2 r i g h t f r o m t h e s t a r t . She a l s o q u i c k l y p i c k e d up on the a p p r o p r i a t e use of t h e f o r m u l a f o r c a l c u l a t i n g t h e a r e a (on 113 t h e s e c o n d t r a p e z o i d and t r i a n g l e p r o b l e m s ) . Her b i g g e s t p r o b l e m i n v o l v e d c o m p u t a t i o n when .5 a p p e a r e d as a q u o t i e n t o r when m u l t i p l y i n g w i t h .5. I f t h e c o m p u t e r had been a b l e t o d e t e c t t h i s p r o b l e m and p r o v i d e r e m e d i a t i o n t o c o r r e c t t h i s m i s u n d e r s t a n d i n g , t h i s s t u d e n t w o u l d have r e a c h e d t h e 80% e f f i c i e n c y l e v e l s o o n e r . She d i d f i n a l l y overcome t h i s c o m p u t a t i o n a l p r o b l e m h e r s e l f . Case #6 T h i s s t u d e n t w o u l d be r a n k e d i n t h e m i d d l e ( 5 0 % ) of t h e p a r t i c i p a n t s i n v o l v e d i n t h i s s t u d y as f a r as o v e r a l l a b i l i t y i s c o n c e r n e d . She i s p r e s e n t l y w o r k i n g a t t h e h a l f w a y p o i n t i n t h e g r a d e 9 math c u r r i c u l u m . On t h e p r e - t e s t she s c o r e d 1/10 g u e s s i n g r a n d o m l y at the a r e a of b o t h t r a p e z o i d s and t r i a n g l e s . B e l o w i s a d e t a i l e d a c c o u n t of h e r e x p e r i e n c e w i t h the p r a c t i s e p o r t i o n of the s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : T h i s s t u d e n t went d i r e c t l y t o p a p e r t o t r y and s o l v e the p r o b l e m s . She g u e s s e d 175 f o r the i n i t i a l a r e a and t h e n l o o k i n g a t t h e f o r m u l a s h e e t c o r r e c t l y i d e n t i f i e d B l , B2, H, and c a l c u l a t e d B1+B2/2. However she d i d n ot know how t o c a l c u l a t e t h e a r e a and e n t e r e d 6. She c o u l d u n d e r s t a n d t h e n o t a t i o n B1+B2/2, but d i d not u n d e r s t a n d t h e a p p r o p r i a t e use of t h e f o r m u l a . Q u e s t i o n #2 ( t r i a n g l e ) : She c o r r e c t l y i d e n t i f i e d B and H and c a l c u l a t e d B/2, but she e n t e r e d BxH=36 f o r the a r e a . Q u e s t i o n //3 ( t r a p e z o i d ) : She l o o k e d a t the f i g u r e f o r a l o n g t i m e and t h e n e n t e r e d a g u e s s f o r t h e i n i t i a l a r e a . She 114 had p r o b l e m s a s s i g n i n g B l and B2, g i v i n g t h e v a l u e f o r H t o b o t h . She c o r r e c t l y a s s i g n e d H and a l s o c a l c u l a t e d B1+B2/2, bu t a g a i n f a i l e d t o c a l c u l a t e t he a r e a , e n t e r i n g a g u e s s . Q u e s t i o n #4 ( t r a p e z o i d ) : She c o r r e c t l y i d e n t i f i e d B l , B2, H, and c a l c u l a t e d B1+B2/2. Then she a l m o s t c a l c u l a t e d the a r e a , m u l t i p l y i n g B l + B 2 x H . However she s h o u l d have d i v i d e d B1+B2/2 and t h e n m u l t i p l i e d by H. Q u e s t i o n #5 ( t r a p e z o i d ) : She had no p r o b l e m w i t h B l , B2, H, and B1+B2/2, but c o u l d not d i s c o v e r t h e method r e q u i r e d to c a l c u l a t e t h e a r e a , and e n t e r e d a g u e s s of 96. Q u e s t i o n #6 ( t r a p e z o i d ) : The s t u d e n t became c o n f u s e d on B1+B2/2 and was a l s o u n a b l e t o c a l c u l a t e t he a r e a . She e n t e r e d w i l d g u e s s e s f o r b o t h a n s w e r s . Q u e s t i o n #7 ( t r a p e z o i d ) : She g o t the i n i t i a l a r e a q u e s t i o n c o r r e c t . She d i d n o t showed her work so the e x p e r i m e n t e r was u n s u r e i f t h i s was s i m p l y a l u c k y g u e s s . Q u e s t i o n #8 ( t r a p e z o i d ) : A t B1+B2/2 she m u l t i p l i e d B l x B 2 and t h e n d i v i d e d by 2 f o r an i n c o r r e c t a n s w e r . However she was a b l e t o use t h e c o r r e c t answer f o r B1+B2/2 and f o r the f i r s t t i m e c o r r e c t l y c a l c u l a t e t h e a r e a o f t h e t r a p e z o i d . She now u n d e r s t o o d how t o c a l c u l a t e t h e a r e a . Q u e s t i o n #9 ( t r a p e z o i d ) : She c o r r e c l y a n s w e r e d the i n i t i a l a r e a q u e s t i o n . Q u e s t i o n #10 ( t r i a n g l e ) : F o r t h e i n i t i a l a r e a q u e s t i o n she m u l t i p l i e d t h e base t i m e s t h e h e i g h t . Then she worked t h r o u g h t h e s t e p by s t e p p r o c e s s w i t h o u t any e r r o r s . Q u e s t i o n #11,#12 ( t r a p e z o i d s ) : D o i n g the c o m p u t a t i o n s i n 115 h e r h e a d , she c a l c u l a t e d b o t h i n i t i a l a r e a q u e s t i o n s . Q u e s t i o n #13 ( t r i a n g l e ) : She c o r r e c t l y c a l c u l a t e d the i n i t i a l a r e a f o r t h i s t r i a n g l e . A f t e r 16 m i n u t e s and 10 s e c o n d s she had r e a c h e d t h e 80% e f f i c i e n c y l e v e l . She t h e n q u i c k l y a n s w e r e d b o t h t h e f i r s t t r a p e z o i d and t r i a n g l e a r e a q u e s t i o n s w i t h o u t t h e a i d of t h e f o r m u l a s h e e t . Summary: T h i s s t u d e n t c o u l d a s s i g n t h e a p p r o p r i a t e v a l u e s t o the i n d i v i d u a l components of the " s o l v i n g p r o c e s s " and u n d e r s t o o d t h e t a s k a t B/2 and B1+B2/2, r i g h t f r o m t h e s t a r t . She q u i c k l y d i s c o v e r e d t h e c o r r e c t use of t h e f o r m u l a e f o r c a l c u l a t i n g t h e a r e a s . She w o r k e d t h r o u g h t h e p r a c t i s e s e c t i o n , s m o o t h l y l e a r n i n g t h e t a s k s and r e a c h e d t h e 80% e f f i c i e n c y l e v e l q u i c k l y . She c o u l d have a t t a i n e d t h i s l e v e l e a r l i e r i f t h e p r o g r a m had some d i a g n o s t i c and r e m e d i a l a b i l i t i e s t o h e l p b r i n g a b o u t a b e t t e r u n d e r s t a n d i n g of t h e p r o p e r f o r m u l a u s a g e . T h i s s t u d e n t i m m e d i a t e l y u n d e r s t o o d and c o u l d c a l c u l a t e t h e c o m p o n e n t s . She s i m p l y needed some a s s i s t a n c e i n p u t t i n g t h e component p a r t s i n t o t h e o v e r a l l f o r m u l a t o s u c c e s s f u l l y a t t a i n t h e a r e a s . On t h e p o s t - t e s t she s c o r e d 3/10, g u e s s i n g a t the a r e a o f t h e t r a p e z o i d s and a d d i n g B+H t o g e t t h e t r i a n g l e a r e a s . Case #7 T h i s s t u d e n t w o u l d be r a n k e d a b o u t t he 5 0 t h p e r c e n t i l e when c o m p a r i n g h e r g e n e r a l a b i l i t i e s t o o t h e r s t u d e n t s i n v o l v e d i n t h i s s t u d y . She i s p r e s e n t l y w o r k i n g a t the 116 m i d - p o i n t of t h e g r a d e 9 math c u r r i c u l u m . On the p r e - t e s t she s c o r e d 1/10 g u e s s i n g a t t h e a r e a of the t r a p e z o i d s and t r i a n g l e s . B e l o w i s a d e t a i l e d a c c o u n t of h e r e x p e r i e n c e w h i l e w o r k i n g t h r o u g h t h e p r a c t i s e p o r t i o n of the s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : A f t e r c a r e f u l l y v i e w i n g t h e p r o b l e m she g u e s s e d a t t h e i n i t i a l a r e a q u e s t i o n . She had d i f f i c u l t y a s s i g n i n g B l and H, but computed B1+B2/2 and a l s o c o r r e c t l y c a l c u l a t e d t h e a r e a . She u n d e r s t o o d t h e n o t a t i o n B1+B2/2 and c o u l d compute i t r i g h t f r o m t h e b e g i n n i n g . She a l s o u n d e r s t o o d t h e s i g n i f i c a n c e o f t h e f o r m u l a and c o u l d use i t t o c a l u l a t e t h e a r e a . Q u e s t i o n //2 ( t r i a n g l e ) : She had no p r o b l e m a f t e r g u e s s i n g a t t h e i n i t i a l a r e a q u e s t i o n . She c o r r e c t l y p l a c e d t h e v a l u e s f o r B and H and c a l c u l a t e d B/2. She was a l s o a b l e to use t h e f o r m u l a and c a l c u l a t e the a r e a f o r the t r i a n g l e . Q u e s t i o n #3 ( t r a p e z o i d ) : She s i g n e d , " I d o n ' t u n d e r s t a n d " what t he f i r s t ( i n i t i a l ) a r e a q u e s t i o n meant and t h e n g u e s s e d i n c o r r e c t l y a t i t . She got t h r o u g h t h e s t e p by s t e p p r o c e s s w i t h o u t m a k i n g an e r r o r and c a l c u l a t e d t h e a r e a . Q u e s t i o n #4,#5,#6 ( t r a p e z o i d s ) : She w o u l d g u e s s a t the i n i t i a l a r e a q u e s t i o n and t h e n c o n t i n u e t h r o u g h t h e r e m e d i a l s e c t i o n of t h e p r a c t i c e w i t h o u t any p r o b l e m s . She had not y e t r e a l i z e d t h a t t h e i n i t i a l a r e a was t h e same as the f i n a l a r e a answer she g o t i n t h e r e m e d i a l s e c t i o n . Q u e s t i o n iH ( t r a p e z o i d ) : The s t u d e n t q u i c k l y g u e s s e d a t the i n i t i a l a r e a , t h e n w o r k e d c o r r e c t l y t h r o u g h t h e s t e p by s t e p b r e a k d o w n of t h e method, but due t o a s i l l y c o m p u t a t i o n a l 117 m i s t a k e she d i d n o t c a l c u l a t e t h e c o r r e c t a r e a . Q u e s t i o n #8 ( t r a p e z o i d ) : A g a i n she made a q u i c k guess at t h e i n i t i a l a r e a , t h e n a m i s t a k e a t H, f o r g e t t i n g t o d i v i d e B1+B2 by 2, and t h e n a c o r r e c t a r e a c a l c u l a t i o n u s i n g the c o r r e c t v a l u e f o r B1+B2/2. Q u e s t i o n #9 ( t r a p e z o i d ) : F o r t h e f i r s t t i m e the s t u d e n t w o r k e d on p a p e r t o t r y and s o l v e the answer but a g a i n she e n t e r e d a g u e ss f o r t h e i n i t i a l a r e a . She had no p r o b l e m s w i t h the r e s t of t h e work e x c e p t f o r a c a r e l e s s c o m p u t a t i o n a l m i s t a k e on t h e a r e a . Q u e s t i o n #10 ( t r i a n g l e ) : She c a l c u l a t e d a wrong i n i t i a l a r e a and t h e n had no d i f f i c u l t i e s w o r k i n g t h r o u g h t h e r e m e d i a l p o r t i o n . Q u e s t i o n #11,#12,(#13 t r i a n g l e ) , # 1 4 , # 1 5 ( t r a p e z o i d s ) : I n e a c h case she w o u l d q u i c k l y guess a t the i n i t i a l a r e a and t h e n q u i c k l y and a c c u r a t e l y work t h r o u g h t h e r e m e d i a l p o r t i o n o f t he p r a c t i c e . She was becomming i n c r e a s i n g l y f r u s t r a t e d w i t h e a c h s u c c e s s i v e f a i l u r e on t h e i n i t i a l a r e a q u e s t i o n . The s t u d e n t was n o t u s i n g t h e f o r m u l a s h e e t o r o t h e r d a t a d i s p l a y e d on t h e m o n i t o r t o h e l p h e r d i s c o v e r t h e s i g n i f i c a n c e of t h e i n i t i a l q u e s t i o n . E v e n t h e d i f f i c u l t c o m p u t a t i o n s i n v o l v i n g .5 were no p r o b l e m f o r h e r . However, t h e i n i t i a l a r e a was a m y s t e r y t o h e r , w h i l e a l l t h e o t h e r c o m p o n e n t s had been s i m p l e s i n c e t h e s t a r t . Q u e s t i o n #16 ( t r a p e z o i d ) : She l o o k e d a t t h e f o r m u l a s h e e t #4 and s i g n e d , " S t u p i d me, I u n d e r s t a n d now." She t h e n q u i c k l y u s e d the c o r r e c t method t o c a l c u l a t e the wrong answer 118 b e c a u s e of a n o t h e r c a r e l e s s c o m p u t a t i o n a l e r r o r . Q u e s t i o n #17,#18,#19 ( t r a p e z o i d s ) : She c o r r e c t l y c a l c u l a t e d t h e i n i t i a l a r e a f o r a l l 3 t r a p e z o i d s . Q u e s t i o n #20 ( t r a p e z o i d ) : She q u i c k l y c a l c u l a t e d and e n t e r e d t h e c o r r e c t answer f o r the i n i t i a l a r e a q u e s t i o n . She had r e a c h e d t h e 80% e f f i c i e n c y l e v e l a f t e r 20 m i n u t e s and 30 s e c o n d s . On t h e two p r a c t i s e q u e s t i o n s done w i t h o u t t h e use of t h e f o r m u l a s h e e t she made a c o m p u t a t i o n a l e r r o r on t h e f i r s t t r a p e z o i d , but t h e n c o r r e c t l y computed t he n e x t t r a p e z o i d and t h e f i r s t t r i a n g l e a r e a . Summary: T h i s s t u d e n t had i n i t i a l d i f f i c u l t y p l a c i n g t h e v a l u e s f o r B l , B2, and H, but had no p r o b l e m on t h e f i r s t a t t e m p t a t B1+B2/2 o r the use of the a r e a f o r m u l a . She had no p r o b l e m a t a l l w i t h t h e f i r s t t r i a n g l e q u e s t i o n . Her o n l y d o w n f a l l was i n u n d e r s t a n d i n g t h e s i g n i f i c a n c e of t h e i n i t i a l a r e a q u e s t i o n . I f t h e p r o g r a m c o u l d have d e t e c t e d t h i s and p r o v i d e d r e m e d i a l h e l p o r c l u e s , she w o u l d have r e a c h e d t h e 80% e f f i c i e n c y l e v e l a f t e r 4 o r 5 q u e s t i o n s . The o n l y t h i n g h o l d i n g h e r back was h e r i n a b i l i t y t o u n d e r s t a n d t h a t t h e i n i t i a l a r e a q u e s t i o n was t h e same as t h e l a s t a r e a c a l c u l a t i o n i n t h e r e m e d i a l p o r t i o n of e a c h p r a c t i s e q u e s t i o n . Once she d i s c o v e r e d t h i s she e x p r e s s e d h e r f e e l i n g s o f s t u p i d i t y o v e r h e r i n e p t n e s s . T h i s s o f t w a r e gave no h e l p i n h e r o n l y a r e a of m i s u n d e r s t a n d i n g and she became f r u s t r a t e d and was on t h e v e r g e of q u i t t i n g when she f i n a l l y u n r a v e l l e d t h e m y s t e r y h e r s e l f . 119 On the p o s t - t e s t she s c o r e d A/10, q u i c k l y and r a n d o m l y g u e s s i n g a t b o t h t r a p e z o i d and t r i a n g l e a r e a s . C a s e #8 S t u d e n t #8 w o u l d be r a n k e d i n t h e t o p 10% when c o m p a r i n g h e r g e n e r a l a b i l i t i e s t o t h o s e of t h e o t h e r p a r t i c i p a n t s i n t h i s s t u d y . She was r e c e n t l y a c c e p t e d i n t o t h e f r e s h m a n y e a r a t G a l l a u d e t c o l l e g e and i s p r e s e n t l y w o r k i n g at the b e g i n n i n g of the g r a d e 11 A l g e b r a c u r r i c u l u m . T h i s s t u d e n t s c o r e d 2/10 on the p r e - t e s t , a n s w e r i n g b o t h of t h e t r i a n g l e a r e a q u e s t i o n s c o r r e c t l y and g u e s s i n g a t the a r e a of t h e t r a p e z o i d s . B e l o w i s a d e t a i l e d d e s c r i p t i o n of h e r i n t e r a c t i o n w i t h t h e p r a c t i s e p o r t i o n of the s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : The s t u d e n t s i g n e d , " T h i s was a d i f f e r e n t f o r m u l a s h e e t t h e n what I n e e d . " She e n t e r e d a g u e s s f o r t h e i n i t i a l a r e a and t h e n e n t e r e d B l = 1 0 when t h e r e was no 10 i n s i g h t . F o r B2 she e n t e r e d t h e v a l u e the compute a s s i g n e d t o B l . Then she c o r r e c t l y c a l c u l a t e d b o t h B1+B2/2 and t h e a r e a . She u n d e r s t o o d t h e n o t a t i o n B1+B2/2 and c o u l d u s e t h e a r e a f o r m u l a r i g h t f r o m t h e s t a r t . Q u e s t i o n #2 ( t r i a n g l e ) : She t r i e d t o work out the i n i t i a l a r e a on p a p e r but was n o t s u c c e s s f u l . Then f o r B, she t r i e d t o e n t e r t h e B/2 v a l u e . She c o r r e c t l y i d e n t i f i e d H and B/2 and a l s o u s e d t h e f o r m u l a t o c a l c u l a t e t h e a r e a . She had no p r o b l e m s w i t h e i t h e r t h e n o t a t i o n ( B / 2 ) o r the c a l c u l a t i o n s i n v o l v e d w i t h t h e t r i a n g l e f o r m u l a . Q u e s t i o n #3 , #4 , #5 , #6 , #7 , #8 , #9 ( t r a p e z o i d s ) : I n each case 120 she w o u l d l o o k a t t h e f o r m u l a and t h e n q u i c k l y g u e s s a t the i n i t i a l a r e a . Then she w o u l d q u i c k l y but c a r e f u l l y f o l l o w t h e s t e p by s t e p r e m e d i a t i o n p r o v i d e d and p e r f o r m t h e c o r r e c t a r e a c a l u l a t i o n . A t q u e s t i o n #6 she a s k e d i f t h e f i r s t a r e a meant t h e a r e a of ' t h i s ' ( s h e p o i n t e d a t t h e t r a p e z o i d ) . She d i d n ot see t h e r e l a t i o n s h i p b etween t h e f i r s t AREA= and t h e a r e a of t h e f i g u r e . A t q u e s t i o n #6 she a s k e d how to e n t e r a d e c i m a l f o r h e r answer 27.5 . Q u e s t i o n #10 ( t r i a n g l e ) : She was not u s i n g the f o r m u l a . I n s t e a d she t r i e d t o measure u s i n g h e r p e n c i l on t h e s c r e e n . She e n t e r e d an i n c o r r e c t g u e s s . T h e n , w r i t i n g h e r c o m p u t a t i o n s on p a p e r she s m o o t h l y w o rked t h r o u g h the component p a r t s of t h e p r a c t i c e w i t h o u t m a k i n g a m i s t a k e . Q u e s t i o n #11 ( t r a p e z o i d ) : She l o o k e d a t t h e f i g u r e f o r a l o n g t i m e and t h e n e n t e r e d an i n c o r r e c t g u e s s . A s e l f c o n f e s s e d " s t u p i d " m i s t a k e a t B l was t h e onl^y p r o b l e m i n s o l v i n g t h e q u e s t i o n v i a the s t e p by s t e p p r o c e s s . Q u e s t i o n #12 ( t r a p e z o i d ) : The s t u d e n t ' s f r u s t r a t i o n w i t h t h e i n i t i a l a r e a q u e s t i o n became a p p a r e n t a t t h i s q u e s t i o n . " I c a n ' t do t h i s p a r t . " " I d o n ' t know what t o do." The e x p e r i m e n t e r a n s w e r e d h e r p l e a s f o r h e l p by s i g n i n g , " I c a n ' t h e l p y o u , remember you have t h i s s h e e t ( f o r m u l a ) t o h e l p y o u . " She e n t e r e d an i n c r e d i b l e g u e s s of 135 f o r t h i s i n i t i a l a r e a and t h e n c o m p l e t e d t h e s t e p by s t e p r e m e d i a t i o n w i t h o u t a p r o b l e m . She c o u l d do a l l t h e s t e p s , but she d i d n o t u n d e r s t a n d t h e s i g n i f i c a n c e of t h e i n i t i a l a r e a q u e s t i o n . She d i d n o t know t h a t the i n i t i a l a r e a was t h e same as the 121 f i n a l a r e a she c a l c u l a t e d a f t e r g o i n g t h r o u g h t h e p r o p e r p r o c e d u r e . She a p p e a r e d to t h i n k t h a t t h i s i n i t i a l a r e a was somehow u n r e l a t e d t o t h e answer she g o t a t t h e end. Q u e s t i o n #13 ( t r i a n g l e ) : She s t a r t e d o f f i n c o r r e c t l y by d i v i d i n g 2 i n t o t h e p r o d u c t of BxH, but t h e n changed h e r method and g o t t h e r i g h t i n i t i a l a r e a f o r t h e f i r s t t i m e . Q u e s t i o n #14, #15 ( t r a p e z o i d s ) : A g a i n a q u i c k g u e ss a t the m y s t e r i o u s i n i t i a l a r e a q u e s t i o n f o l l o w e d by a f a u l t l e s s c o m p u t a t i o n t h r o u g h t h e g u i d e d method. A t t h i s p o i n t she c o u l d n o t u n d e r s t a n d t h e s i g n i f i c a n c e of t h e i n i t i a l a r e a q u e s t i o n . Q u e s t i o n #16 ( t r a p e z o i d ) : She l o o k e d a t the f i g u r e on the s c r e e n and e n t e r e d 66 as t h e i n i t i a l a r e a . She wanted to g i v e up and was e m b a r r a s s e d by h e r i n a b i l i t y to d e c i p h e r the m e a n i n g of t h i s i n i t i a l q u e s t i o n . She q u i c k l y c a l c u l a t e d the c o r r e c t a n swer s t e p by s t e p . Q u e s t i o n s #17,#18 ( t r a p e z o i d s ) : A g a i n she was not l o o k i n g a t t h e f o r m u l a s h e e t , but i n s t e a d at t h e numbers on the f i g u r e , t r y i n g t o g e t o v e r t h i s h u r d l e of t h e i n i t i a l a r e a . I n b o t h c a s e s she e n t e r e d an u n c a l c u l a t e d g u e s s and t h e n p r o c e e d e d t o q u i c k l y answer t h e r e m e d i a l p o r t i o n s t e p by s t e p . Q u e s t i o n #19 ( t r a p e z o i d ) : She l o o k e d a t t h e f i g u r e f o r a l o n g t i m e , p o i n t i n g t o t h e b a s e s and s i g n i n g , "base 1, base 2." Then a g a i n a f t e r p e r f o r m i n g a s t r a n g e s e q u e n c e of c o m p u t a t i o n ( 1 2x6=72, 7 2 / 2 = 3 6 ) , she e n t e r e d 36 as h e r a n s w e r . T h e n , as u s u a l , she went on t o e a s i l y o b t a i n t h e c o r r e c t 122 s o l u t i o n by w o r k i n g t h r o u g h t h e r e m e d i a l s e c t i o n . Due to the a p p r o x i m a t e t i m e l i m i t of 30 m i n u t e s , t h e s t u d e n t ' s f r u s t r a t i o n w i t h t h e t a s k , and t h e f e e l i n g t h a t t h e s t u d e n t w o u l d n o t r e a c h t h e e x p e c t e d l e v e l o f e f f i c i e n c y , t h e t r e a t m e n t was s t o p p e d a f t e r 30 m i n u t e s . Summary: From t h e v e r y s t a r t t h i s s t u d e n t c o u l d a s s i g n t h e. a p p r o p r i a t e v a l u e s f o r B, H, or B l , B2, H, and c o u l d u n d e r s t a n d t h e n o t a t i o n and c o m p l e t e B/2 and B1+B2/2. She c o u l d a l s o use t h e f o r m u l a t o c a l c u l a t e t h e a p p r o p r i a t e a r e a s . Some of t h e more d i f f i c u l t c o m p u t a t i o n s i n v o l v i n g .5 gave h e r no p r o b l e m s . She s h o u l d have q u i c k l y gone t h r o u g h t h i s t r e a t m e n t and e a s i l y r e a c h e d t h e 80% e f f i c i e n c y l e v e l . H o w e v e r , she c o u l d n o t d u r i n g t h i s t r e a t m e n t d i s c o v e r the m e a n i n g of t h e i n i t i a l q u e s t i o n AREA= . I f t h i s s o f t w a r e had t h e d i a g n o s t i c c a p a b i l i t i e s t o d e t e c t t h i s p r o b l e m and g i v e t h e s t u d e n t h e l p i n u n d e r s t a n d i n g t h e s i g n i f i c a n c e of t h i s i n i t i a l q u e s t i o n , t h e n t h i s s t u d e n t w o u l d have s u c c e s s f u l l y a t t a i n e d t h e 80% e f f i c i e n c y i n a v e r y s h o r t t i m e . On t h e p o s t - t e s t she s c o r e d 2/10, g e t t i n g t h e t r i a n g l e a r e a s c o r r e c t as she had done on t h e p r e - t e s t and g u e s s i n g a t two of t h e t r a p e z o i d q u e s t i o n s , w h i l e u s i n g a summation method (a+b+c) f o r t h e a r e a s of t h e o t h e r s i x t r a p e z o i d s . She s i g n e d " I f o r g o t how t o do t h e s e . " 123 C a s e #9 T h i s s t u d e n t w o u l d be r a n k e d a t or below t he 9 0 t h p e r c e n t i l e when c o m p a r i n g h i s o v e r a l l a b i l i t i e s to t h e o t h e r p a r t i c i p a n t s i n v o l v e d i n t h i s s t u d y . He had been r e c e n t l y a c c e p t e d i n t o t h e p r e p a r a t o r y y e a r a t G a l l a u d e t C o l l e g e and i s p r e s e n t l y w o r k i n g a t t h e m i d - p o i n t of t h e A l g e b r a 11 c u r r i c u l u m . T h i s s t u d e n t s u r p r i s e d t h e e x p e r i m e n t e r by s c o r i n g 9/10 on t h e p r e - t e s t . The e x p e r i m e n t e r i n t e r v i e w e d t h e s t u d e n t a f t e r t h e p r e - t e s t t o d i s c o v e r how he was a b l e to compute t h e c o r r e c t a n s w e r s . He s t a t e d t h a t he remembered how t o do t h e t r i a n g l e s f r o m p r e v i o u s math e x p e r i e n c e . W i t h t h e t r a p e z o i d s he l o g i c a l l y d e v i s e d a u n i q u e method w h i c h was s i m i l a r i n p u r p o s e but not i d e n t i c a l t o the a p p r o p r i a t e f o r m u l a f o r t r a p e z o i d s . He saw t h a t he c o u l d make a r e c t a n g l e o ut of t h e t r a p e z o i d by moving one c o r n e r ( t r i a n g l e ) of t h e t r a p e z o i d o v e r and f l i p p i n g i t up o n t o t h e o t h e r s i d e . He s u b t r a c t e d h a l f t h e d i f f e r e n c e between t he s m a l l e r and l a r g e r b a s e , f r o m t h e l a r g e r base and m u l t i p l i e d t h i s by t h e h e i g h t t o c a l c u l a t e t h e a r e a . I t w o r k e d and he s c o r e d 9/10, m a k i n g one c o m p u t a t i o n a l m i s t a k e w h i c h r e s u l t e d i n an i n c o r r e c t a n s w e r . By s u b t r a c t i n g h a l f t h e d i f f e r e n c e b e t w e e n t he l a r g e r and s m a l l e r b a s e s on t h e t r a p e z o i d f r o m t h e l a r g e r base he was a c t u a l l y c a l c u l a t i n g t h e a v e r a g e of t h e two b a s e s (B1+B2/2) and t h e n m u l t i p l y i n g t h i s by t h e h e i g h t t o a r r i v e a t t h e c o r r e c t a n s w e r . He was m a k i n g a r e c t a n g l e o ut of t h e t r a p e z o i d by moving a p a r t ( t r i a n g l e ) o v e r as was done i n t h e a n i m a t i o n of frame #11 i n the 124 t u t o r i a l , and t h e n u s i n g t h e r e c t a n g l e f o r m u l a BxH t o c a l c u l a t e t h e a r e a . B e l o w i s a d e t a i l e d o u t l i n e of h i s i n t e r a c t i o n w i t h t h e p r a c t i s e p o r t i o n of t h i s s o f t w a r e . Q u e s t i o n #1 ( t r a p e z o i d ) : He l o o k e d at i t and s i g n e d , " I f o r g e t . " He d i d n o t l o o k a t t h e f o r m u l a s h e e t but i n h i s h e a d c a l c u l a t e d t h e c o r r e c t i n i t i a l a r e a . Q u e s t i o n #2 ( t r i a n g l e ) : He a n s w e r e d t h i s p a r t c o r r e c t l y on t h e p r e - t e s t , b u t g u e s s e d a t t h e i n i t i a l a r e a h e r e and t h e n q u i c k l y w o r k e d t h r o u g h the r e m e d i a t i o n w i t h o u t any p r o b l e m s . Q u e s t i o n #3,//4 ( t r a p e z o i d s ) : He c a l c u l a t e d t h e i n i t i a l a r e a f o r t h e s e q u e s t i o n s i n h i s head w i t h o u t any e r r o r s . Q u e s t i o n #5 ( t r i a n g l e ) : The e x p e r i m e n t e r moved ahead to the n e x t t r i a n g l e b e c a u s e i f t h e s t u d e n t c o r r e c t l y a n s w e r e d i t he w o u l d have r e a c h e d t h e 80% e f f i c i e n c y l e v e l . He q u i c k l y c a l c u l a t e d t he c o r r e c t i n i t i a l a r e a and was f i n i s h e d . On the two q u e s t i o n s done w i t h o u t t h e a i d of the f o r m u l a s h e e t t h i s s t u d e n t e n c o u n t e r e d no d i f f i c u l t i e s . Summary: S t u d e n t #9 had d e v i s e d h i s own method f o r s o l v i n g t h e a r e a and u s e d i t s u c c e s s f u l l y on b o t h the p r e and p o s t - t e s t s . On t h e p o s t - t e s t he s c o r e d 10/10. 125 5.4 Q u a n t a t a t i v e D a t a f o r T u t o r i a l and N o n - t u t o r i a l G r o u p s The d a t a d e s c r i b e d i n t h e f o l l o w i n g t a b l e s were c o l l e c t e d f r o m t h e T u t o r i a l and N o n - t u t o r i a l g r o u p s b e f o r e , d u r i n g , and a f t e r t h e i r e x p o s u r e t o t h e c omputer s o f t w a r e . The s t u d e n t s were g i v e n a p r e - t e s t one t o t h r e e weeks b e f o r e b e i n g e x p o s e d t o t h e s o f t w a r e . D u r i n g t h e i r i n t e r a c t i o n w i t h t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e d a t a were c o l l e c t e d on t h e number of t r i a l s ( p r a c t i s e q u e s t i o n s c o m p l e t e d ) , the l e n g t h of t i m e s p e n t i n t e r a c t i n g w i t h t h e c o m p u t e r , and w h e t h e r t h e y r e a c h e d t h e 80% e f f i c i e n c y l e v e l on the i n i t i a l a r e a q u e s t i o n s . T h e s e d a t a and t h e s c o r e s f r o m the p o s t - t e s t s t a k e n one week a f t e r t h e i r e x p o s u r e t o the s o f t w a r e , a r e d i s p l a y e d i n t a b l e s 2 and 3. A more d e t a i l e d a n a l y s i s of t h e i r e x p e r i e n c e w i t h t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e i s g i v e n i n t a b l e s 4 and 5. The i n f o r m a t i o n f o r t h e s e t a b l e s was o b t a i n e d by c a r e f u l l y a n a l y s i n g the o b s e r v a t i o n s c o l l e c t e d by t h e e x p e r i m e n t e r as e ach s t u d e n t w o r k e d t h r o u g h t h e p r a c t i s e s e c t i o n of the s o f t w a r e . A h e a d i n g d i s p l a y s a l l t h e i n d i v i d u a l component p a r t s w h i c h made up t h e r e m e d i a l s e c t i o n , a l o n g w i t h o t h e r d a t a t h a t t o g e t h e r l i s t a l l t h e r e s p o n s e s r e q u i r e d f o r the two d i f f e r e n t t y p e s of q u e s t i o n s ( t r a p e z o i d or t r i a n g l e ) . The d a t a show t h e number ( l = f i r s t , 2 = s e c o n d , e t c . ) of t h e t r i a n g l e o r t r a p z o i d at w h i c h t h e s t u d e n t f i r s t e n t e r e d a c o r r e c t r e s p o n s e f o r e a c h of t h e component p a r t s . 126 T a b l e 2 R e s u l t s f r o m the T u t o r i a l G r oup S t u d e n t Number P r e - t e s t S c o r e 80% E f f i c i e n c y Yes/No It o f Reached ( i n ) : T r i a l s Time P o s t - t e s t S c o r e it I 0/10 Yes 13 10:00 10/10 it 2 2/10 No 14 20 : 00 1/10 #3 0/10 No 15 20:00 0/10 #4 5/10 Yes 4 1 :55 10/10 1t5 • 1/10 Yes 16 20 : 10 0/10 #6 0/10 No 14 20: 00 1/10 in 2/10 Yes 4 2:25 0/10 11 & 0/10 Yes 16 21 :00 3/10 #9 0/10 Yes 14 15 : 10 4/10 T a b l e 3 R e s u l t s f r o m the N o n - t u t o r i a l G r oup S t u d e n t P r e - t e s t 80% E f f i c i e n c y Reached ( i n ) : P o s t - t e s t Number S c o r e Yes/No It o f T r i a l s Time S c o r e #1 1/10 No 19 31 :30 1/10 #2 3/10 - No 19 32 :00 0/10 #3 2/10 Yes 25 22 : 05 1/10 #4 1/10 No 24 30 : 00 2/10 #5 1/10 Yes 17 14:20 3/10 #6 1/10 Yes 13 16:10 3/10 in 1/10 Yes 20 20: 30 4/10 #8 2/10 No 19 30:30 2/10 It 9 9/10 Yes 5 3 :00 10/10 The two t a b l e s above d i s p l a y d a t a c o l l e c t e d f r o m the t u t o r i a l and non- t u t o r i a l g r o u p s i n t h i s s t u d y . These r e s u l t s show t h e s t u d e n t 1 s number , s c o r e on t h e p r e - t e s t , w h e t h e r she/he s u c e s s f u l l y r e a c h e d t h e 80% e f f i c i e n c y r a t e d u r i n g t h e p r a c t i s e p o r t i o n ( Y e s / N o ) , t h e number of t r i a l s ( p r a c t i s e q u e s t i o n s ) t h e s t u d e n t w o rked t h r o u g h , the t i m e s p e n t on t h e p r a c t i s e s e c t i o n , and h i s / h e r s c o r e on the 127 post-test. On a l l s t a t i s t i c a l analysis the null hypothesis was that the difference between the means of the two populations (TG and NTG) is equal to zero, while the alternative hypothesis was that i t is different from zero. S t a t i s t i c a l tests were performed using an alpha (level of significance) of .05. Ho : ul - u2 = 0 HI : ul - u2 <> 0 S t a t i s t i c a l A n a l y s i s Pre-test data showed that the TG had a mean of 1.1 and the NTG had a mean of 2.3. Using a t-test for independent samples this difference was found to be i n s i g n i f i c a n t (t=1.063, df=16, p>.05). Ho is accepted, there is no si g n i f i c a n t difference between the groups with regard to the pre-test. The next set of data shows that 5 members of the NTG and 6 members of the TG reached 80% e f f i c i e n c y (Yes/No) while interacting with the practise portion of the software. A Chi square test showed that there was no s i g n i f i c a n t difference 2 between the two populations (X =1.11, v=l, p>.05). Ho is accepted, there is no s i g n i f i c a n t difference between the groups on reaching 80% e f f i c i e n c y . Data from these 11 people (5 from the NTG and 6 from the TG) who sucessfully reached 80% e f f i c i e n c y on the practise portion, were used in the next two s t a t i s t i c a l analysis. The mean number of t r i a l s required to reach 80% ef f i c i e n c y for the TG was 11.17 and for the NTG was 16.4. 128 This difference proved to be non-s igni f icant using a t - test for dependent samples (t=1.329, df = 9, p>.05). The n u l l hypothesis is accepted again. The mean time required to reach 80% ef f i c iency for the TG was 13.28 minutes and for the NTG was 15.67 minutes. This proved to be a non-s igni f icant difference when the t-test for dependent samples was used (t=.561, df=9, p>.05). Again the n u l l hypothesis is accepted. There is no s ign i f i cant difference between the two populations with regard to the time required to reach 80% e f f i c i e n c y . Data col lected showed that the TG had a mean of 3.111 while the NTG had a mean of .2 .888 on the post - test . This difference again proved to be non-s igni f icant when tested using a t - test for dependent samples (t=.262, df=16, p>.05). No s ign i f i cant difference was found between the two groups with regard to the post - tes t . Analysis of these data reveals that there was no s i g n i f i c a n t difference between the TG and the NTG on any of th is co l lected information. 129 T a b l e 4 R e s u l t s f r o m t h e T u t o r i a l G roup S t u d e n t [ t r i a n g l e ] [ t r a p e z o i d ] Numbe r B H B/2 A AA B l B2 H B1+B2/2 A AA 80% #1 1 1 1 1 2 1 1 1 1 1 9 13 it 2 1 1 1 2 N 2 2 2 N 4 N N it 3 2 2 N N N 2 1 2 N N N N #4 1 1 1 1 1 1 1 1 1 1 1 4 it 5 1 1 1 3 4 1 1 1 2 3 7 16 it 6 1 1 6 N N , 1 1 N N N N it 7 1 1 1 1 1 1 1 1 1 1 1 4 its 1 1 1 1 1 1 3 1 1 1 7 16 it 9 1 1 1 1 3 1 1 1 2 1 3 14 T a b l e 5 R e s u l t s f r o m t h e N o n - t u t o r i a l G roup S t u d e n t [ t r i a n g l e ] [ t r a p e z o i d ] Number B H B/2 A AA : B l B2 H B1+B2/2 A AA 80% #1 3 1 N 1 N 1 2 1 11 9 N N itl 1 1 N N N 3 1 1 4 6 N N it 3 1 1 1 1 5 2 1 1 1 1 18 25 #4 3 1 1 4 N 3 1 1 11 12 N N #5 1 1 1 3 3 3 1 2 1 2 7 17 itb 1 1 1 2 3 1 1 1 1 7 7 15 it 7 1 1 1 1 4 2 1 2 1 1 14 20 it 8 2 1 1 1 3 2 3 1 1 1 N N it 9 1 1 1 2 2 1 1 1 1 1 1 5 The two t a b l e s above d i s p l a y mo r e d e t a i l e d d a t a a b o u t t h e a c h i e v e m e n t of b o t h t h e TG and NTG on t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e . These d a t a show t h e r e s u l t s on t h e i n d i v i d u a l component p a r t s o f t h e p r a c t i s e e x e r c i s e . The i d i g i t s d e s i g n a t e t h e number of t h e t r i a n g l e o r t r a p e z o i d ( i e 1 s t , 2 n d , 3 r d , 4 t h , e t c . ) where t h e s t u d e n t f i r s t s u c c e s s f u l l y a n s w e r e d t h e l a b e l l e d component ( i e . B=Base, 130 H = H e i g h t ) . The l a b e l l e d components f o u n d i n t h e f i r s t row u n d e r the t r i a n g l e i n f o r m a t i o n a r e : B ( b a s e ) , H ( h e i g h t ) , B/2, A ( a r e a q u e s t i o n f o u n d at the end of the r e m e d i a l s e c t i o n ) , AA ( t h e f i r s t t i m e the s t u d e n t got the i n i t i a l t r i a n g l e a r e a q u e s t i o n r i g h t ) , and 80% ( t h e number of the q u e s t i o n at w h i c h t h e s t u d e n t r e a c h e d t h e 80% e f f i c i e n c y l e v e l ) . The l a b e l l e d components u n d e r t h e t r a p e z o i d i n f o r m a t i o n a r e : B l ( b a s e l ) , B2 ( b a s e 2 ) , H ( h e i g h t ) , B1+B2/2, A ( a r e a q u e s t i o n f o u n d a t t h e end of t h e r e m e d i a l s e c t i o n ) , AA ( t h e number of the t r a p e z o i d q u e s t i o n where the s t u d e n t f i r s t s u c c e s s f u l l y a n s w e r e d the i n i t i a l a r e a q u e s t i o n ) , and 80% ( t h e number of t h e q u e s t i o n a t w h i c h t h e s t u d e n t r e a c h e d t h e 80% e f f i c i e n c y l e v e l ) . The c a p i t a l (N) s i g n i f i e s t h a t t h e s t u d e n t n e v e r s u c c e s s f u l l y a n s w e r e d t h i s component of t h e p r a c t i c e or f a i l e d to r e a c h t h e 80% e f f i c i e n c y l e v e l . S t a t i s t i c a l t e s t s were p e r f o r m e d on t h i s d a t a to see i f t h e r e were any s i g n i f i c a n t d i f f e r e n c e s between the p e r f o r m a n c e of t h e TG and t h e NTG. T - t e s t s f o r dependent s a m p l e s were u s e d w i t h an a l p h a of .05. The TG had a mean of 2 f o r t h e f i r s t s u c c e s s on t h e i n i t i a l a r e a q u e s t i o n f o r t r i a n g l e s , w h i l e the NTG had a mean of 3.33. T h i s means t h a t on a v e r a g e TG i n d i v i d u a l s were s u c c e s s f u l on the i n i t i a l t r i a n g l e q u e s t i o n s on t h e i r s e c o n d a t t e m p t , w h i l e NTG i n d i v i d u a l s were f i r s t s u c c e s s f u l on t h e i r 3.33 a t t e m p t . The t - t e s t p e r f o r m e d on t h i s d a t a gave s i g n i f i c a n c e at the .05 l e v e l ( t = 1 . 9 5 0 , d f = 1 0 , p>.05). T h e r e was a s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e between t h e TG and the NTG i n t h e i r 131 f i r s t s u c c e s s on t h e i n i t i a l a r e a q u e s t i o n s f o r t r i a n g l e s . A t - t e s t was a l s o p e r f o r m e d on t h e d i f f e r e n c e between t h e two g r o u p s i n s u c c e s s f u l l y c a l c u l a t i n g t h e i n i t i a l a r e a q u e s t i o n f o r t r a p e z o i d s . The TG had a mean of 4.66 and t h e NTG had a mean of 9.4. But t h i s p r o v e d t o be i n s i g n i f i c a n t ( t - 1 . 5 2 4 , d f = 9 , p>.05). A f t e r t h e c o m p l e t i o n of s t a t i s t i c a l t e s t s on t h e s e d a t a t h e o n l y s i g n i f i c a n t r e s u l t o c c u r r e d when t h e TG and NTG were compared on t h e i r i n i t i a l t r i a n g l e a r e a success. In a l l o t h e r a s p e c t s of t h i s s t u d y t h e r e were no s t a t i s t i c a l l y s i g n i f i c a n t d i f f e r e n c e s between t h e two g r o u p s . 132 C h a p t e r 6 : Summary and C o n c l u s i o n s 6.1 T u t o r i a l S o f t w a r e : S u g g e s t e d I m p r o v e m e n t s As documented i n the t u t o r i a l g r o up case s t u d i e s t h e r e w ere many d i f f e r e n t p r o b l e m s e n c o u n t e r e d by the s t u d e n t s who w o r k e d t h r o u g h t h e t u t o r i a l p r o g r a m . S e v e r a l of t h e s e p r o b l e m s were common t o most or a l l of the p a r t i c i p a n t s and a r e u s e d as a b a s i s t o make r e c o m m e n d a t i o n s t o i m p r o v e t h i s s o f t w a r e and s e t some g u i d e l i n e s f o r t h e d e v e l o p m e n t of f u t u r e t u t o r i a l s o f t w a r e f o r use w i t h t h e h e a r i n g i m p a i r e d . The main p r o b l e m w h i c h a l l s t u d e n t s e n c o u n t e r e d i n v a r y i n g d e g r e e s , was w i t h t h e s y n t a x i n v o l v e d i n the t u t o r i a l p r o g r a m . A l t h o u g h the math c o n c e p t s were a t or below the a p p r o p r i a t e g r a d e l e v e l f o r t h e s e h e a r i n g i m p a i r e d s t u d e n t s , t h e s y n t a x used d u r i n g most of t h i s p r o g r a m was f a r beyond t h e r e a d i n g a b i l i t y f o r t h e m a j o r i t y of them. The i n d i v i d u a l s i n t h e t u t o r i a l g r o u p d i s p l a y e d v a r y i n g d e g r e e s of d i f f i c u l t y u n d e r s t a n d i n g i n s t r u c t i o n s and t e x t f o u n d i n t h e p r o g r a m . On a number of o c c a s i o n s t h e y c o u l d comprehend t h e i n d i v i d u a l words but were c o n f u s e d by t h e s y n t a x and u n a b l e t o u n d e r s t a n d t h e t a s k o r c o n c e p t . F o r example the f o l l o w i n g s e n t e n c e s were not u n d e r s t o o d by most s t u d e n t s as i n d i c a t e d by t h e i r b e h a v i o r : " U n l i k e p a r a l l e l o g r a m s , t h e p a r a l l e l s i d e s of a t r a p e z o i d have d i f f e r e n t l e n g t h s . " "Compare t h e t r a p e z o i d w i t h t h e r e c t a n g l e whose w i d t h I s 3 cm and l e n g t h 8 cm t h e same as t h e t r a p e z o i d s l o n g e r b a s e . " " I n s t e a d of c a l l i n g t h e t o p a base of l e n g t h 0 j u s t t a k e the b a s e t h a t r e m a i n s and d i v i d e by 2." T h i s i s a p r o b l e m w h i c h 133 t e a c h e r s of the h e a r i n g i m p a i r e d have d e a l t w i t h i n the p a s t , and i t w i l l s e v e r e l y l i m i t the amount of p o t e n t i a l l y u s e f u l s o f t w a r e a v a i l a b l e i n the f u t u r e , u n l e s s s o f t w a r e can be p r o d u c e d s p e c i f i c a l l y w i t h the h e a r i n g i m p a i r e d and o t h e r " l a n g u a g e l i m i t e d " p o p u l a t i o n s i n mind. The s y n t a x i n v o l v e d i n most s o f t w a r e p r o g r a m s p r e c l u d e s t h e i r s u c c e s s f u l use by g r o u p s l i k e the h e a r i n g i m p a i r e d b e c a u s e t h e y f i n d the t e x t o r i n s t r u c t i o n s t o be l a n g u a g e bound. S o f t w a r e c r e a t e d f o r t h e h e a r i n g i m p a i r e d s h o u l d be c a r e f u l l y s c r i p t e d and the s y n t a x s t r i n g e n t l y m o n i t o r e d t o e n s u r e the d e v e l o p m e n t of h i g h q u a l i t y , e d u c a t i o n a l l y u s e f u l s o f t w a r e . The c omputer w i l l not be a u s e f u l t o o l i n t h e c l a s s r o o m i f i t s use r e q u i r e s the c o n s t a n t s u p e r v i s i o n and a i d of a t e a c h e r . T h e r e i s an enormous need f o r s y n t a t i c a l l y s i m p l e s o f t w a r e w h i c h a l s o h a n d l e s a d v a n c e d c o n c e p t s . P r o g r a m s l i k e the one i n v e s t i g a t e d i n t h i s s t u d y w o u l d be more e d u c a t i o n a l l y b e n e f i c i a l t o g r o u p s l i k e the h e a r i n g i m p a i r e d , i f the s y n t a x were s i m p l i f i e d . A n o t h e r m a j o r p r o b l e m w i t h t h e t u t o r i a l p r o g r a m i s t h a t i t was u n s u c c e s s f u l i n t e a c h i n g one of i t s main c o n c e p t s . A l a r g e p o r t i o n (9 o u t of 2 5 f r a m e s ) of the t u t o r i a l p rogram was c o n c e r n e d w i t h d e m o n s t r a t i n g how t h e f o r m u l a f o r t r a p e z o i d s was d e r i v e d , but n o t one of t h e s t u d e n t s i n the t u t o r i a l g r o up u n d e r s t o o d t h i s c o n c e p t a f t e r e x p o s u r e to the s o f t w a r e . The s t u d e n t was r e q u i r e d t o compare a s e t of t h r e e d i f f e r e n t r e c t a n g l e s to a t r a p e z o i d w i t h o u t any e x p l a n a t i o n as t o why t h i s had been done and was e x p e c t e d t o see t h a t 134 t h i s e x p l a i n s t h e d e r i v a t i o n of t h e t r a p e z o i d f o r m u l a . I f t h i s c o n c e p t i s deemed t o be i m p o r t a n t t h e n i t s h o u l d be t a u g h t more t h o r o u g h l y w i t h a d e t a i l e d but c l e a r e x p l a n a t i o n o u t l i n i n g t h e r e a s o n f o r e a c h s t e p of the p r o o f . T h i s w o u l d r e q u i r e a g r e a t d e a l more d i s c u s s i o n and g u i d a n c e t h a n i s p r e s e n t l y o f f e r e d . F o r h e a r i n g i m p a i r e d s t u d e n t s who have d i f f i c u l t y r e a d i n g and c o m p r e h e n d i n g a s t r a i g h t f o r w a r d e x p l a n a t i o n , t h i s s e c t i o n w i t h a l l of i t s i n f e r e n c e s and l a c k o f d e t a i l w o u l d be v e r y d i f f i c u l t t o u n d e r s t a n d . H owever, t h e f a c t t h a t t h i s p o r t i o n of t h e t u t o r i a l was n o t u n d e r s t o o d seemed t o have no a p p a r e n t e f f e c t on the s t u d e n t s a b i l i t y t o l e a r n the c o r r e c t a p p l i c a t i o n of t h e t r a p e z o i d f o r m u l a . S o f t w a r e f o r the h e a r i n g i m p a i r e d s h o u l d be d e t a i l e d to e x p l a i n t h e c o n c e p t s put f o r t h , y e t i n s i m p l e l a n g u a g e so t h a t i t can be u n d e r s t o o d . T h i s p a r t i c u l a r s o f t w a r e w o u l d need t o be b r o k e n down i n t o more s t e p s ( f r a m e s ) so the c o n c e p t s c o u l d be p r e s e n t e d i n a more c l e a r , d e t a i l e d , and u n d e r s t a n d a b l e f a s h i o n . T h e r e were t h r e e p r o b l e m s w i t h t h i s t u t o r i a l p r o g r a m t h a t p r o b a b l y were not n o t i c e d by t h e s t u d e n t s , but showed i n c o n s i s t e n c y and poor p l a n n i n g by t h e p r o g r a m m e r s . The f i r s t c o n c e r n s h a n d o u t #4. On h a n d o u t #4 t h e d i a g r a m of the t r a p e z o i d and t r i a n g l e was a c c o m p a n i e d by a s p e c i f i c p l a c e f o r t h e s t u d e n t t o copy t h e f o r m u l a . The p r o b l e m was t h a t on t h e s h e e t t h e p l a c e f o r t h e f o r m u l a was w r i t t e n l i k e t h i s ; A= _. W h i l e on t h e c o m p u t e r t he f o r m u l a i n s i d e t h e box t h a t t h e y were t o copy was w r i t t e n as f o l l o w s : 1 3 5 Bl+B2/2xH=AREA. A l l of t h e t u t o r i a l s t u d e n t s e x c e p t one ended up c o p y i n g the f o r m u l a t o r e a d A= B1+B2/2xH=AREA . T h i s c a u s e d some c o n f u s i o n f o r t he s t u d e n t s and i n t e r f e r e d w i t h t h e i r l e a r n i n g of the c o n c e p t . The s e c o n d p r o b l e m o c c u r r e d d u r i n g t h e t r i a n g l e a r e a c a l c u l a t i o n . D u r i n g t h e t u t o r i a l p r a c t i c e t h e B/2 s t e p was l e f t out of the s t e p by s t e p t e a c h i n g of the c a l c u l a t i o n . W h i l e i n t h e p r a c t i s e p o r t i o n o f t h e s o f t w a r e i t was u s e d i n e v e r y c a s e d u r i n g t h e r e m e d i a t i o n p r o c e d u r e . F o r the sak e of c o n s i s t e n c y t h e B/2 s t e p s h o u l d have a l s o a p p e a r e d i n t h e one p r a c t i s e q u e s t i o n i n t h e t u t o r i a l . T h i s w o u l d have h e l p e d s t u d e n t s u n d e r s t a n d t h e t a s k b e t t e r once t h e y s t a r t e d t h e p r a c t i s e s e c t i o n . The t h i r d p r o b l e m i n v o l v e d a m i s s i n g t i t l e f o r the t r a p e z o i d f o r m u l a . I n f r a m e s #21 and #22 t h e t r i a n g l e f o r m u l a a p p e a r s i n a r e c t a n g u l a r box c l e a r l y t i t l e d "TRIANGLE FORMULA" so t h e s t u d e n t s u n d e r s t a n d i t s u s e . B u t i n fr a m e s #11 and #12 t h e t r a p e z o i d f o r m u l a a p p e a r s i n a r e c t a n g u l a r box w i t h o u t a c l e a r t i t l e t o i n d i c a t e what i t was. T h i s a p p e a r e d to be a s o u r c e of c o n f u s i o n and m i s u n d e r s t a n d i n g f o r some of t h e t u t o r i a l g r o u p s t u d e n t s . I t was c l e a r f r o m o b s e r v i n g s e v e r a l of t h e t u t o r i a l s t u d e n t s t h a t t h e y d i d not need t o u n d e r s t a n d a l l f a c e t s of t h e t u t o r i a l p r o g r a m i n o r d e r t o a q u i r e enough i n s i g h t and i n f o r m a t i o n t o f a c i l i t a t e t h e l e a r n i n g of the c o r r e c t f o r m u l a e a p p l i c a t i o n . S e v e r a l of t h e s t u d e n t s a l t h o u g h c l e a r l y not u n d e r s t a n d i n g i n f o r m a t i o n i n t h e t u t o r i a l , 136 r e a d i l y a s s i g n e d t h e a p p r o p r i a t e d i g i t s and c o u l d a p p l y t h e f o r m u l a e c o r r e c t l y t o c a l c u l a t e t he i n i t i a l a r e a q u e s t i o n s i n t h e p r a c t i s e p o r t i o n . O t h e r s f o u n d i t e a s y t o a s s i g n the d i g i t s to the c o r r e s p o n d i n g p a r t s but had a h a r d e r t i m e u s i n g t h e f o r m u l a e . Even t h o u g h t h e s e s t u d e n t s d i d not u n d e r s t a n d t h e d e r i v a t i o n of t h e t r a p e z o i d or t r i a n g l e f o r m u l a e t h e y d i d g e t some u s e f u l i n f o r m a t i o n f r o m t h e t u t o r i a l t h a t made i t e a s i e r f o r them t o do t h e p r a c t i s e p r o b l e m s . One of the f r a m e s t h a t t h e e x p e r i m e n t e r f e l t was p a r t i c u l a r l y h e l p f u l was frame //4. I n t h i s f rame a t r a p e z o i d i s d i s p l a y e d g r a p h i c a l l y and t h e n as the components B a s e l , B a s e 2 , and H e i g h t a r e g i v e n n u m e r i c a l v a l u e s t h e s e same v a l u e s a p p e a r on t h e g r a p h i c , s h o w i n g t h e s t u d e n t where t h e p a r t s a r e l o c a t e d on the t r a p e z o i d . T h i s was an e x c e l l e n t example of the p o t e n t i a l power of the c o m p u t e r as a t e a c h i n g a i d . But u n f o r t u n a t e l y t h e r e s t of t h e p r o g r a m was not q u i t e so i l l u m i n a t i n g or c l e a r . One of t h e i n t e r e s t i n g o b s e r v a t i o n s made d u r i n g the t u t o r i a l was t h a t some s t u d e n t s d i d not u n d e r s t a n d the s i g n i f i c a n c e of an i m p o r t a n t frame and q u i c k l y moved on w i t h o u t c a r e f u l l y r e a d i n g i t . The s o f t w a r e s h o u l d be w r i t t e n so t h a t t h e c o m p u t e r i s more s e n s i t i v e t o e r r o r s made by t h e s t u d e n t . The p r o g r a m s h o u l d g i v e t h e c o m p u t e r the c a p a b i l i t y t o p o i n t out i m p o r t a n t i n f o r m a t i o n c o n t a i n e d i n a s p e c i f i c f r a m e where the s t u d e n t has made an e r r o r i n the p a s t . A p r o b l e m w i t h t h i s and o t h e r s o f t w a r e i s the f a i l u r e t o c h e c k t h e u s e r ' s c o m p r e h e n s i o n of t h e p r o g r a m ' s c o n t e n t and 1 3 7 p r o v i d e r e m e d i a t i o n i f r e q u i r e d . T h i s p r o g r a m had no q u e s t i o n s w h i c h d i r e c t l y c h e c k e d the s t u d e n t ' s u n d e r s t a n d i n g of t h e i d e a s d i s c u s s e d . T h e r e were o n l y a few q u e s t i o n s ( f o u r ) a s k i n g him to e n t e r a n s w e r s o t h e r t h a n t h e two p r a c t i s e q u e s t i o n s . And none of t h e s e f o u r q u e s t i o n s t e s t e d h i s u n d e r s t a n d i n g of the c o n t e n t of t h e t e x t . I t has been t h e e x p e r i m e n t e r ' s e x p e r i e n c e t h a t i f a h e a r i n g i m p a i r e d s t u d e n t " r e a d s " s o m e t h i n g t h a t h e / s h e does not u n d e r s t a n d h e / s h e s i m p l y i g n o r e s i t and c o n t i n u e s . T h i s a c t u a l l y h a p p e n e d i n e v e r y c a s e d u r i n g t h e t u t o r i a l o b s e r v a t i o n s . The e x p e r i m e n t e r added a few c o m p r e h e n s i o n t e s t i n g q u e s t i o n s of h i s own t o t h i s s o f t w a r e t o t r y to make i t more i n q u i s i t i v e . F o r t h e h e a r i n g i m p a i r e d and o t h e r s , s o f t w a r e needs to be w r i t t e n t h a t c o n t a i n s more q u e s t i o n s r e q u i r i n g i n p u t to t e s t c o m p r e h e n s i o n of t h e t e x t . I f t h e s t u d e n t makes a m i s t a k e o r m i s u n d e r s t a n d s a s e c t i o n t h e n r e m e d i a t i o n can t a k e p l a c e t o h e l p the s t u d e n t comprehend and l e a r n . F o r t h i s k i n d of s o p h i s t i c a t e d and i n v o l v e d s o f t w a r e more t i m e and p l a n n i n g w i l l be r e q u i r e d to p r o d u c e i t . T h i s w i l l mean more e x p e n s e , b u t t h e s o f t w a r e w i l l be f a r s u p e r i o r . The s o f t w a r e u s e d i n t h i s s t u d y i s f a i r l y t y p i c a l i n t h a t i t c o n t a i n s l i t t l e i n t h e way of d i a g n o s t i c o r r e m e d i a t i o n c a p a b i l i t i e s . A n o t h e r weakness of t h i s t u t o r i a l p r o g r a m was t h a t i t o n l y gave t h e s t u d e n t one o p p o r t u n i t y t o p r a c t i s e e a ch s k i l l i t was a t t e m p t i n g t o t e a c h . O n l y 9 o f t h e 25 f r a m e s d e a l t w i t h p r a c t i c e u s i n g t h e f o r m u l a e t o s o l v e q u e s t i o n s . Y e t t h i s was t h e o n l y c o n c e p t t e s t e d i n the p r a c t i s e s e c t i o n of 138 t h e s o f t w a r e . I t w o u l d be d i f f i c u l t f o r any s t u d e n t to l e a r n a c o n c e p t w i t h o n l y one p r a c t i c e . T e a c h e r s of the h e a r i n g i m p a i r e d know a b o u t t he r e p e t i t i o n r e q u i r e d when t e a c h i n g any new c o n c e p t . One p r a c t i c e i s not enough. Many of the s t u d e n t s i n t h e t u t o r i a l g r o u p c o u l d have r e a c h e d the 80% e f f i c i e n c y s o o n e r i f t h e t r e a t m e n t i n t h e t u t o r i a l s o f t w a r e had been more p o w e r f u l . By g i v i n g t h e s t u d e n t s more p r a c t i c e d u r i n g t h e t u t o r i a l t h e y w o u l d e n t e r t h e p r a c t i s e p o r t i o n of t h e s o f t w a r e b e t t e r p r e p a r e d to answer the q u e s t i o n s . F o r many s t u d e n t s i t i s u n f a i r t o p r o v i d e o n l y one a t t e m p t a t t h e p r o c e d u r e and t h e n t h r o w them i n t o t h e p r a c t i c e . I n any t u t o r i a l s o f t w a r e f o r the h e a r i n g i m p a i r e d t h e r e s h o u l d be ample o p p o u r t u n i t y t o p r a c t i s e t h e i m p o r t a n t s k i l l s b e i n g t a u g h t b e f o r e t h e s t u d e n t i s l e f t t o p r a c t i s e the c o n c e p t on h i s own. By p r o v i d i n g more p r a c t i c e i n a more s o p h i s t i c a t e d ( d i a g n o s t i c and r e m e d i a l ) t u t o r i a l t h e t r e a t m e n t can be made more p o w e r f u l and the p r a c t i s e p o r t i o n w o u l d not need to be so i n v o l v e d . 6.2 P r a c t i s e S o f t w a r e : S u g g e s t e d I m p r o v e m e n t s As o u t l i n e d i n t h e t u t o r i a l and n o n - t u t o r i a l case s t u d i e s t h e r e were many d i f f e r e n t p r o b l e m s t h a t o c u r r e d w h i l e t h e s t u d e n t s w o r k e d t h r o u g h t h e p r a c t i s e p o r t i o n of the s o f t w a r e . As w i t h t h e p r o b l e m s e n c o u n t e r e d i n t h e t u t o r i a l p r o g r a m s e v e r a l o f t h e s e were common t o many of t h e s t u d e n t s . T h e s e p r o b l e m s a r e used as a b a s i s f o r r e c o m m e n d a t i o n s t o i m p r o v e t h i s s o f t w a r e and p r o v i d e g u i d e l i n e s f o r the f u t u r e d e v e l o p m e n t of d r i l l and p r a c t i s e s o f t w a r e f o r t h e h e a r i n g 139 i m p a i r e d . U n l i k e t u t o r i a l s o f t w a r e , d r i l l and p r a c t i s e s o f t w a r e i s n o t d e s i g n e d to t e a c h new c o n c e p t s . I t was used i n t h i s s t u d y t o t e a c h t h e use of t h e f o r m u l a e so t h a t the e f f e c t i v e n e s s o f t h e t u t o r i a l s o f t w a r e c o u l d be measured. By d o i n g t h i s t h e e x p e r i m e n t e r d i s c o v e r e d some v e r y i n t e r e s t i n g t h i n g s a b o u t how t h i s p r a c t i s e s o f t w a r e c o u l d be i m p r o v e d f o r i t s use w i t h h e a r i n g i m p a i r e d s t u d e n t s . Many of t h e s t u d e n t s i n t h e t u t o r i a l g r o u p depended on t h e p r a c t i s e p o r t i o n t o t e a c h them t h e s k i l l s d i s c u s s e d i n t h e t u t o r i a l b e c a u s e t h e y d i d not g e t enough p r a c t i c e u s i n g t h e f o r m u l a e d u r i n g t h e t u t o r i a l t o l e a r n i t s a p p l i c a t i o n o r t h e y d i d not comprehend t h e t u t o r i a l i n f o r m a t i o n . So t h e s e t u t o r i a l s t u d e n t s were s i m i l i a r t o t h e p r a c t i s e s t u d e n t s b e c a u s e t h e y t o o were l e a r n i n g t h e a p p r o p r i a t e a p p l i c a t i o n s o f t h e f o r m u l a e d u r i n g t h e i r e x p o s u r e t o t h e p r a c t i s e s o f t w a r e . The main p r o b l e m w i t h t h e p r a c t i s e p o r t i o n of the s o f t w a r e was i d e n t i c a l t o a p r o b l e m t h a t o c c u r r e d d u r i n g t h e t u t o r i a l p o r t i o n , t h e l a c k of d i a g n o s t i c and r e m e d i a l c a p a b i l i t i e s . S t u d e n t s w o u l d make t h e same e r r o r s or get s t u c k a t t h e same j u n c t i o n i n t h e p r o g r a m w h i c h d i d not have t h e d i a g n o s t i c a b i l i t y t o n o t i c e t h e p r o b l e m or a p p l y r e m e d i a t i o n t o c o r r e c t i t . None o f t h e s t u d e n t s had d i f f i c u l t y a s s i g n i n g the a p p r o p r i a t e d i g i t s t o t h e component p a r t s of t h e p r a c t i c e ( B l , B 2 , H o r B, H ) . W i t h i n a few t r i a l s e v e r y o n e had 140 l e a r n e d t h i s p a r t of t h e c o n c e p t t h r o u g h r e p e t i t i o n and p r a c t i c e . The p r o b l e m s s t a r t e d a t t h e n e x t p a r t of the p r o g r a m when the v a l u e s f o r B / 2 o r B1+B2/2 were demanded. Many s t u d e n t s had d i f f i c u l t y u n d e r s t a n d i n g t h e n o t a t i o n and task, a t t h i s s t e p of the p r o g r a m . Some c o n t i n u e d to guess e a c h t i m e t h e y a r r i v e d a t t h i s p o r t i o n of the s t e p by s t e p b r e a k d o w n of the p r o b l e m w i t h o u t g e t t i n g any c l o s e r to c o m p r e h e n d i n g i t s s o l u t i o n . O t h e r s e v e n t u a l l y g r a s p e d t h e c o n c e p t t h r o u g h s i m p l e r e p e t i t i o n of t h e t a s k . I f the p r o g r a m c o u l d have d e t e c t e d t h i s p r o b l e m and a p p l i e d r e m e d i a t i o n t o t e a c h t h e c o r r e c t method of c a l c u l a t i o n t h e s t u d e n t c o u l d have r e a d i l y l e a r n e d t h i s and c o n t i n u e d o n t o t h e n e x t s e c t i o n w i t h o u t b e c o m i n g f r u s t r a t e d and b o r e d w i t h t h e t a s k . O t h e r s t u d e n t s c o u l d u n d e r s t a n d t h e t a s k s a t B /2 and B1+B2/2 b u t d i d n o t see how to use the f o r m u l a e t o c a l c u l a t e t h e a r e a . A g a i n , some w o u l d c o n t i n u e t o guess each ti m e t h e y a r r i v e d a t t h i s p o i n t , w h i l e o t h e r s s u c c e s s f u l l y m a s t e r e d t h e t a s k a f t e r s e v e r a l p r a c t i c e s . The p r o g r a m s h o u l d have a way t o d e t e c t t h i s p r o b l e m and show t h e s t u d e n t s how to c a l c u l a t e t h e a r e a once t h e y have e n t e r e d t h e i r i n c o r r e c t guess o r a n s w e r . T h i s p r o g r a m s i m p l y t o l d them t h a t t h e y were wrong and s u p p l i e d them w i t h t h e c o r r e c t a n s w e r . One o f t h e most s u r p r i s i n g p r o b l e m s e n c o u n t e r e d by s t u d e n t s i n v o l v e d t h e i n i t i a l a r e a q u e s t i o n . Some s t u d e n t s s t a r t e d t h e p r a c t i s e q u e s t i o n s and had no p r o b l e m w o r k i n g t h r o u g h t h e r e m e d i a l p o r t i o n s t a r t i n g w i t h q u e s t i o n #1. They 141 c o u l d s u c c e s s f u l l y answer a l l t h e component p a r t s i n c l u d i n g t h e a r e a c a l c u l a t i o n w i t h o u t any d i f f i c u l t y . O t h e r s had i n i t i a l d i f f i c u l t i e s but soon became s k i l l e d a t a n s w e r i n g a l l o f t h e q u e s t i o n s i n c l u d i n g t he a r e a q u e s t i o n . Then t h e s e same s t u d e n t s were not a b l e t o comprehend the s i g n i f i c a n c e of t h e i n i t i a l a r e a q u e s t i o n . They c o u l d r e a d i l y s o l v e the a r e a p r o b l e m s but t h e y c o u l d not u n d e r s t a n d t h e t a s k when p r e s e n t e d w i t h t h e i n i t i a l a r e a q u e s t i o n a t t h e b e g i n i n g of e a c h p r a c t i s e q u e s t i o n . I f t h i s p r o g r a m had been a b l e t o d e t e c t t h i s d i f f i c u l t y and e x p l a i n t o the s t u d e n t s what t h i s i n i t i a l q u e s t i o n r e p r e s e n t e d , many more w o u l d have r e a c h e d t h e 80% e f f i c i e n c y l e v e l . And o t h e r s w o u l d not have become so f r u s t r a t e d t r y i n g r e p e a t e d l y t o d i s c o v e r i t s s i g n i f i c a n c e , o n l y t o e v e n t u a l l y s o l v e the a n n o y i n g m y s t e r y and e x p r e s s t h e i r shame at i t s s i m p l i c i t y . A n o t h e r d i f f i c u l t y w h i c h many of the s t u d e n t s had was t h e r e s u l t of the c o m p u t a t i o n s r e q u i r e d t o s o l v e the p r o b l e m s . I n d i v i d u a l s i n b o t h g r o u p s f o r g o t how to d i v i d e 2 i n t o an odd number t o g e t a q u o t i e n t i n v o l v i n g .5, and t h e y a l s o had f o r g o t t e n how t o m u l t i p l y u s i n g t h i s .5 number. A g a i n d e t e c t i o n and r e m e d i a t i o n of t h i s p r o b l e m by the c o m p u t e r w o u l d have s a v e d a g r e a t d e a l of t i m e and f r u s t r a t i o n and h e l p e d some s t u d e n t s a c h i e v e more s u c c e s s . I d e a l l y d r i l l and p r a c t i s e s o f t w a r e f o r t h e h e a r i n g i m p a i r e d s h o u l d have t h e c a p a b i l i t y t o d e t e c t and r e m e d i a t e p r o b l e m s t h a t the u s e r e n c o u n t e r s i n h i s q u e s t to become s u c c e s s f u l . T h i s w i l l r e q u i r e more com p l e x and d e t a i l e d 142 b r a n c h i n g p r o g r a m s t o be w r i t t e n i n o r d e r to g i v e the computer t h e s e c a p a b i l i t i e s , but t h e e f f o r t and e x p e n s e w i l l be w o r t h i t . 6.3 T u t o r i a l vs N o n - t u t o r i a l A c h e i v e m e n t I t was c l e a r i n the s t a t i s t i c a l a n a l y s i s of the r e s u l t s t h a t t h e t u t o r i a l g r o u p d i d not have a s i g n i f i c a n t a d v a n t a g e o v e r t h e n o n - t u t o r i a l g r o u p i n a c h e i v e m e n t on t h e p r a c t i s e s e c t i o n o f t h e p r o g r a m . S t u d e n t s who v i e w e d t h e t u t o r i a l w ere n o t a b l e t o u n d e r s t a n d t h e d e r i v a t i o n of t h e t r a p e z o i d f o r m u l a , and many u n d e r s t o o d o n l y s m a l l p a r t s of i t s c o n t e n t s . T u t o r i a l s t u d e n t s were n o t s i g n i f i c a n t l y f a s t e r a t a c h e i v i n g 80% e f f i c i e n c y . Two of t h e s i x t u t o r i a l s t u d e n t s who a c h e i v e d 80% e f f i c i e n c y remembered t h e c o n c e p t on the p o s t t e s t compared to z e r o out of f i v e f o r t h e n o n - t u t o r i a l g r o u p . The d a t a r e v e a l t h a t t h e t u t o r i a l was n o t s i g n i f i c a n t l y e f f e c t i v e i n p r o v i d i n g t h e s t u d e n t s who v i e w e d i t an a d v a n t a g e i n l e a r n i n g t h e c o n c e p t s of a r e a c a l c u l a t i o n f o r t r i a n g l e s and t r a p e z o i d s . I n o t h e r w o r d s , t h e t u t o r i a l was n o t s i g n i f i c a n t l y e f f e c t i v e i n t e a c h i n g t h e s k i l l s w h i c h w e re r e q u i r e d t o m a s t e r t he a r e a p r o b l e m s . T h i s was l i k e l y due t o s e v e r a l d i f f e r e n t f a c t o r s p r e v i o u s l y d i s c u s s e d . The t u t o r i a l d i d p r o v i d e some s t u d e n t s w i t h s k i l l s o r u n d e r s t a n d i n g s t h a t f a c i l i t a t e d t h e i r p r o g r e s s and a c h i e v e m e n t on t h e p r a c t i c e . B u t o v e r a l l i t a p p e a r e d to be a weak t r e a t m e n t u n a b l e t o s i g n i f i c a n t l y i m p r o v e p r a c t i s e a c h e i v e m e n t . 143 6.4 I m p l i c a t i o n s and S u g g e s t i o n s f o r F u t u r e R e s e a r c h The i n f o r m a t i o n c o m p i l e d i n t h i s s t u d y l e a v e s the e x p e r i m e n t e r as a t e a c h e r of t h e h e a r i n g i m p a i r e d i n t e r e s t e d i n C A I , c u r i o u s a b o u t t h e s u c c e s s of a p r o g r a m w h i c h w o u l d c o n t a i n t h e recommended i m p r o v e m e n t s i n s o f t w a r e made i n t h i s s t u d y . Would t h i s t y p e of s o f t w a r e w i t h i t s c o n t r o l l e d s y n t a x , more a d v a n c e d d i a g n o s t i c and r e m e d i a l c a p a b i l i t i e s , and s i m p l e r y e t d e t a i l e d p r e s e n t a t i o n be more e d u c a t i o n a l l y e f f e c t i v e w i t h h e a r i n g i m p a i r e d s t u d e n t s t h a n t h e s o f t w a r e u s e d i n t h i s p r o j e c t . O t h e r a r e a s f o r f u t u r e i n f o r m a t i o n g a t h e r i n g s h o u l d i n v o l v e : ( a ) R e s e a r c h i n t o t he a d v a n t a g e s of v i s u a l vs a u d i t o r y r e w a r d s t r a t e g i e s u s e d i n CAI w i t h h e a r i n g i m p a i r e d s t u d e n t s . ( b ) How do h e a r i n g i m p a i r e d s t u d e n t s b e s t l e a r n f r o m CAI? ( c ) What t y p e s of CAI t e a c h i n g s t r a t e g i e s work b e s t w i t h h e a r i n g i m p a i r e d s t u d e n t s ? More r e s e a r c h i s r e q u i r e d i n a r e a s i n v o l v i n g t h e measurement of changes t h a t o c c u r due t o m i c r o c o m p u t e r ( C A I ) a p p l i c a t i o n s , so t h a t i m p o r t a n t f a c t o r s w h i c h c o n t r i b u t e to b e t t e r s o f t w a r e f o r h e a r i n g i m p a i r e d s t u d e n t s can be i d e n t i f i e d and programmed i n t o s o f t w a r e f o r t h e h e a r i n g i m p a i r e d . Computer A s s i s t e d I n s t r u c t i o n w i l l l i k e l y become a v e r y e f f e c t i v e t o o l f o r t e a c h e r s of t h e d e a f . I t w i l l be the t e a c h e r ' s r e s p o n s i b i l i t y t o h e l p e d u c a t e s o f t w a r e p r o d u c i n g c o r p o r a t i o n s , so t h a t u s e f u l s o f t w a r e can be d e v e l o p e d t o e n h a n c e the l e a r n i n g of h e a r i n g i m p a i r e d s t u d e n t s . Once an a b u n d a n t s u p p l y of s o f t w a r e s u i t a b l e t o t h e e d u c a t i o n a l needs 144 of h e a r i n g i m p a i r e d s t u d e n t s i s d e v e l o p e d , t h e computer a r e a w i l l h o p e f u l l y become a v e r y busy and p r o d u c t i v e c o r n e r of t h e t e a c h e r ' s c l a s s r o o m . 145 REFERENCES A r c a n i n , J . ( 1 9 7 9 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n a t the C a l i f o r n i a s c h o o l f o r t h e d e a f p a s t , p r e s e n t , and f u t u r e : an a d m i n i s t r a t o r ' s v i e w . A m e r i c a n A n n a l s o f  t h e D e af , 124 , 573 - 7 7 . B a r d e n s t e i n , L. ( 1 9 8 2 ) . M e l b o r p (math d r i l l and p r a c t i c e ) . A m e r i c a n A n n a l s of t h e Deaf , 12 7 , 659-64. C a s t l e , D. J . ( 1 9 8 2 ) . M a t h e m a t i c s s o f t w a r e , a computer l a b , and t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s o f t h e Deaf , 1_27_ , 4 9 5 - 5 0 4 . D a n e l i u k , C. ( 1 9 8 5 ) . A s s i s t a n t D e p u t y M i n i s t e r , M i n i s t r y of E d u c a t i o n . S p e e c h g i v e n a t V a n c o u v e r S e c o n d a r y T e a c h e r s d i s t r i c t w i d e p r o f e s s i o n a l day a t E r i c Hamber S e c o n d a r y S c h o o l , M a r c h 4 1985. D i l l i n g h a m , L.M. and o t h e r s . ( 1 9 8 2 ) . S e l e c t e d a p p l i c a t i o n s o f c o m p u t e r a s s i s t e d v i d e o i n s t r u c t i o n i n the e d u c a t i o n of h e a r i n g - i m p a i r e d s t u d e n t s . A m e r i c a n A n n a l s o f t h e  Deaf , 1_27_ , 652-58. F l e m i n g , R. E. ( 1 9 8 3 ) . R e c e n t changes i n CAI a t CSDF. A m e r i c a n A n n a l s o f t h e Deaf , 128 , 707-09. F l e t c h e r , J.D. and S u p p e s , P. ( 1 9 7 3 ) . Computer a s s i s t e d i n s t r u c t i o n i n m a t h e m a t i c s and l a n g u a g e a r t s f o r the d e a f . F i n a l R e p o r t . F l e t c h e r , J.D. ( 1 9 7 4 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n f o r t h e d e a f . P a p e r p r e s e n t e d a t t h e A m e r i c a n E d u c a t i o n a l R e s e a r c h A s s o c i a t i o n a n n u a l m e e t i n g i n C h i c a g o , I l l i n o i s . F r i s i n a , R. ( 1 9 7 5 ) . R e p o r t on t h e ad hoc c o m m i t t e e to d e f i n e d e a f and h a r d of h e a r i n g f o r e d u c a t i o n a l p u r p o s e s [Summary]. A m e r i c a n A n n a l s o f t h e Deaf , 120 , 509-512. F u l t o n , R. T. ( 1 9 8 3 ) . The use of m i c r o c o m p u t e r t e c h n o l o g y i n a s s e s s i n g and t r a i n i n g c o m m u n i c a t i o n s k i l l s of young h e a r i n g i m p a i r e d c h i l d r e n . A m e r i c a n A n n a l s o f t h e Deaf , 1_28. , 570-76. G r o s m a n , K. E. , S i d e r s , J . and G a r r a w a y , H. ( 1 9 8 3 ) S i g n t e a c h e r : a m i c r o c o m p u t e r a p p l i c a t i o n f o r t h e t e a c h i n g o f s i g n l a n g u a g e . A m e r i c a n A n n a l s o f t h e Deaf , 128 , 577-84. 146 H i g h t , R.L. ( 1 9 8 2 ) . L i p - r e a d e r t r a i n e r : t e a c h i n g a i d f o r t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 564-68. I r w i n , M. G. ( 1 9 8 2 ) . CAI a t CSDF : O r g a n i z a t i o n a l s t r a t e g i e s . A m e r i c a n A n n a l s o f t h e Deaf , 127 , 487-494. J o h n s t o n , D. K. ( 1 9 8 2 ) . D e a f s i g n : a s e r i e s of c o m p u t e r i z e d i n s t r u c t i o n a l p r o g r a m s f o r t h e t e a c h i n g of s i g n l a n g u a g e . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 556-58. J o n e s , B. W. and G r y g a r , J . ( 1 9 8 2 ) . The t e s t of s y n t a c t i c a b i l i t i e s and m i c r o c o m p u t e r s . A m e r i c a n A n n a l s of t h e  Deaf , JL27_ , 638-44. . M c R i t c h i e , M. ( 1 9 8 2 ) . P r o g r a m i n g i n b a s i c : A c o m p l e t e c o u r s e . T o r o n t o , Canada : H o l t , R i n e h a r t and W i n s t o n of Canada L t d . M o r g a n , J . M . ( 1 9 7 5 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n f o r the b l i n d and d e a f . P a p e r p r e s e n t e d a t t h e a n n u a l m e e t i n g o f the A m e r i c a n E d u c a t i o n a l R e s e a r c h A s s o c i a t i o n i n W a s h i n g t o n D. C. N e w e l l , W. J . , S i m s , D. and M y e r s , T. ( 1 9 8 3 ) . P r i n c i p a l s and r e q u i s i t e s of computer a s s i s t e d i n t e r a c t i v e v i d e o i n s t r u c t i o n : A s i g n l a n g u a g e l e s s o n . A m e r i c a n A n n a l s  of t h e Deaf , 128 , 662-72. N i c o l a y , W. L. ( 1 9 8 3 ) . Group l e a r n i n g and the computer : The t e a c h e r b r i n g s an a p p l e f o r t h e s t u d e n t s . A m e r i c a n  A n n a l s o f t h e Deaf , 128 , 521-24. PEMC M i c r o w a r e . ( 1 9 8 5 ) . E v a l u a t o r ' s g u i d e f o r m i c r o c o m p u t e r - b a s e d i n s t r u c t i o n a l p a c k a g e s . P r o v i n c i a l E d u c a t i o n a l M e d i a C e n t e r , R i c h m o n d , B r i t i s h C o l u m b i a . R i l e y , D. C. ( 1 9 8 3 ) . Computer a s s i s t e d e v a l u a t i o n at the C a l i f o r n i a s c h o o l f o r t h e d e a f - F r e m o n t . A m e r i c a n  A n n a l s o f t h e D e a f , 128 , 585-594. S l o v i c k , L. ( 1 9 8 2 ) . CAI a t CSDF : M i c r o c o m p u t e r - b a s e d a u t h o r i n g s y s t e m s . A m e r i c a n A n n a l s o f t h e Deaf , 127 , 5 3 6 - 4 5 . S m a l d i n o , S. E., S c h l o s s , P. J . and G o l d s m i t h , L . ( 1 9 8 3 ) . A n a l y s i s o f t h e r e l a t i v e i n s t r u c t i o n a l e f f i c i e n c y of m i c o c o m p u t e r b a s e d i n s t r u c t i o n and t e a c h e r d i r e c t e d i n s t r u c t i o n f o r h e a r i n g i m p a i r e d and n o r m a l h e a r i n g y o u t h . A m e r i c a n A n n a l s o f t h e Deaf , 12 8 , 642-47. 147 S t a c y , E.M. ( 1 9 8 2 ) . S t u d e n t s : h a n d l e w i t h C.A.R.E. ( c o m p u t e r a s s i s t e d r e m e d i a t i o n and e n r i c h m e n t ) . A m e r i c a n A n n a l s  of t h e Deaf , 127 , 6 17-24. S t o k e r , R. G. ( 1 9 8 3 a ) . A c o m p u t e r a s s i s t e d d i a g n o s t i c and p r e s c r i p t i v e t o o l f o r t e a c h i n g s p e e c h t o t h e d e a f . A m e r i c a n A n n a l s of t h e Deaf , 12 8 , 6 25-30. S t o k e r , R. G . ( 1 9 8 3 b ) . On c o m p u t e r s and t h e h e a r i n g i m p a i r e d . V o l t a R e v i e w , 8_5 , 3 6 4 - 6 5 . S t u c k l e s s , E. R. ( 1 9 8 3 ) . The m i c r o c o m p u t e r i n t h e i n s t r u c t i o n of h e a r i n g i m p a i r e d s t u d e n t s : T o o l o r d i s t r a c t i o n . A m e r i c a n A n n a l s of t h e D eaf , 128 , 5 1 5-20. S u p p e s , P. ( 1 9 7 3 ) . E v a l u a t i o n of c o m p u t e r - a s s i s t e d i n s t r u c t i o n i n e l e m e n t a r y m a t h e m a t i c s f o r h e a r i n g - i m p a i r e d s t u d e n t s . P s y c h o l o g y and e d u c a t i o n s e r i e s . W r i g h t , A. ( 1 9 8 1 ) I n s t r u c t i o n a l t e c h n o l o g y f o r s p e c i a l n e e d s . D i s c u s s i o n p a p e r . B. C. D e p a r t m e n t of E d u c a t i o n , V i c t o r i a , C a nada. 148 A p p e n d i x A R e s e a r c h A r t i c l e s on CAI w i t h t h e Deaf 1. A r c a n i n , J . ( 1 9 7 9 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n a t t h e C a l i f o r n i a s c h o o l f o r t h e d e a f p a s t , p r e s e n t , and f u t u r e : an a d m i n i s t r a t o r ' s v i e w . A m e r i c a n A n n a l s  of t h e Deaf , 124 , 573 - 7 7 . 2. B a r d e n s t e i n , L. ( 1 9 8 2 ) . M e l b o r p (math d r i l l and p r a c t i c e ) . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 659-64. 3. B i l l i n g s , K a r e n and M o u r s u n d , D a v i d . ( 1 9 7 6 ) . A r e you  c o m p u t e r l i t e r a t e ? B e v e r t o n , O r e g o n : D e l i t h i u m P r e s s 4. B l i t z e r , D. ( 1 9 7 9 ) . Uses of CBE f o r t h e h a n d i c a p p e d . A m e r i c a n A n n a l s of t h e Deaf , 124 , 553 - 5 8 . 5. B r a w l e y , R. J . and P e t e r s o n , B. A. ( 1 9 8 3 ) . I n t e r a c t i v e v i d e o d i s c : ah i n n o v a t i v e i n s t r u c t i o n a l s y s t e m . A m e r i c a n A n n a l s o f t h e Deaf , 128 , 6 8 5 - 7 0 0 . 6. C a s e y , K. B. ( 1 9 8 1 ) . Computer a p p l i c a t i o n s f o r the d e a f and d e a f b l i n d . D i r e c t i o n s , 1_ , 6 9 - 7 1 . 7. C a s t l e , D. J . ( 1 9 8 2 ) . M a t h e m a t i c s s o f t w a r e , a co m p u t e r l a b , and t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s of t h e  Deaf , 127 , 495-504. 8. C r o n i n , B. ( 1 9 7 9 ) . The DAVID s y s t e m : t h e d e v e l o p m e n t of an i n t e r a c t i v e v i d e o s y s t e m a t t h e n a t i o n a l t e c h n i c a l i n s t i t u t e f o r the d e a f . A m e r i c a n A n n a l s o f t h e Deaf , 124 , 616 - 1 8 . 9. Dam, L. and o t h e r s . ( 1 9 7 9 ) . C o n f e r e n c e summary. A m e r i c a n A n n a l s o f t h e Deaf , 124 , 6 9 6 - 9 9 . 10. D i l l i n g h a m , L.M. and o t h e r s . ( 1 9 8 2 ) . S e l e c t e d a p p l i c a t i o n s of c o m p u t e r a s s i s t e d v i d e o i n s t r u c t i o n i n t h e e d u c a t i o n of h e a r i n g - i m p a i r e d s t u d e n t s . A m e r i c a n  A n n a l s o f t h e Deaf , 127 , 6 5 2 - 5 8 . 11. D u g d a l e , S. V o g e l , P. ( 1 9 7 8 ) . C o m p u t e r - b a s e d i n s t r u c t i o n f o r h e a r i n g - i m p a i r e d c h i l d r e n i n the c l a s s r o o m . A m e r i c a n A n n a l s o f t h e Deaf , 123 , 730-43. 149 12. F l e h a r t y , J . and Norwood, C. ( 1 9 8 2 ) . P e r s o n a l i z i n g t he p e r s o n a l c o m p u t e r f o r y o u r s c h o o l . A m e r i c a n A n n a l s of  t h e Deaf , 127 , 6 09-12. 13. F l e m i n g , R. E. ( 1 9 8 3 ) . R e c e n t changes i n CAI a t CSDF. A m e r i c a n A n n a l s of t h e Deaf , 128 , 707-09. 14. F l e t c h e r , J.D. S u p p e s , P. ( 1 9 7 3 ) . Computer a s s i s t e d i n s t r u c t i o n i n m a t h e m a t i c s and l a n g u a g e a r t s f o r the d e a f . F i n a l R e p o r t . 15. F l e t c h e r , J.D.( 1 973 ) . L e a r n i n g l a n g u a g e by c o m p u t e r . V o l t a R e v i e w , 7_5 , 302-11 . 16. F l e t c h e r , J . D . ( 1 9 7 4 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n f o r t h e d e a f . P a p e r p r e s e n t e d a t t h e A m e r i c a n E d u c a t i o n a l R e s e a r c h A s s o c i a t i o n a n n u a l m e e t i n g i n C h i c a g o , I l l i n o i s . 17. F o x , R. ( 1 9 7 9 a ) . Toward the f u t u r e i n e d u c a t i o n a l s y s t e m s . A m e r i c a n A n n a l s o f t h e Deaf , 124 , 521-29. 18. F o x , R. ( 1 9 7 9 b ) . M e d i a - b a s e d i n t e r a c t i v e v i s u a l i m a g e - c o n t r o l l e d ( v i s - i - c o n ) i n s t r u c t i o n d e l i v e r y s y s t e m f o r i n s t r u c t i o n of d e a f and h e a r i n g - i m p a i r e d . A m e r i c a n  A n n a l s of t h e Deaf , L24_ , 6 0 4 - 1 0 . 19. F r i l l m a n n , L. W. ( 1 9 8 2 ) . The d e v e l p m e n t of y o u r own p r o g r a m s f o r the m i c r o c o m p u t e r . A m e r i c a n A n n a l s of t h e  D e a f , 127 , 6 2 5 - 3 0 . 20. F u l t o n , R. T. ( 1 9 8 3 ) . The use of m i c r o c o m p u t e r t e c h n o l o g y i n a s s e s s i n g and t r a i n i n g c o m m u n i c a t i o n s k i l l s of young h e a r i n g i m p a i r e d c h i l d r e n . A m e r i c a n  A n n a l s of t h e Deaf , 128 , 570-76. 2 1 . G a l b r a i t h , G. ( 1 9 7 8 ) . An i n t e r a c t i v e c o mputer s y s t e m f o r t e a c h i n g l a n g u a g e s k i l l s t o d e a f c h i l d r e n . A m e r i c a n A n n a l s o f t h e Deaf , 123 , 7 0 6 - 1 1 . 22. G a l b r a i t h , G. ( 1 9 7 9 ) . I n t e r f a c i n g an i n e x p e n s i v e home c o m p u t e r t o t h e v i d e o d i s c : E d u c a t i o n a l a p p l i c a t i o n s f o r t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s o f t h e Deaf , 124 , 5 3 6 - 4 1 . 23. G a r v e y , M. ( 1 9 8 2 ) . CAI as a s u p p l e m e n t i n a m a i n s t r e a m e d h e a r i n g - i m p a i r e d p r o g r a m . A m e r i c a n A n n a l s  of t h e D e a f , 127 , 613-616. 24. G o l d b e r g , L.M. ( 1 9 8 0 ) . C r e a t i v e use of media i n s c h o o l s and p r o g r a m s f o r t h e h e a r i n g i m p a i r e d . V o l t a R e v i e w , 82 , 4 4 0-46. 150 25. Graham, R. ( 1 9 8 2 ) . The m i c r o c o m p u t e r as an administrative®educational t o o l i n e d u c a t i o n of the h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s of t h e Deaf , 12 7 , 5 9 1 - 6 0 1 . 26. G r a n t , J . and Semmes, P. ( 1 9 8 3 ) . A r a t i o n a l e f o r LOGO f o r h e a r i n g i m p a i r e d p r e s c h o o l e r s . A m e r i c a n A n n a l s o f  t h e D e a f , 128 , 564-69. 27. Grosman, K., S i d e r s , J . and G a r r a w a y , H. ( 1 9 8 3 ) . S i g n t e a c h e r : A m i c r o c o m p u t e r a p p l i c a t i o n f o r t h e t e a c h i n g o f s i g n l a n g u a g e . A m e r i c a n A n n a l s o f t h e Deaf , 128 , 577-84. 28. H a r d i n g , R. E. and T i d b a l l , L. K. ( 1 9 8 2 ) . A n a t i o n a l m i c r o c o m p u t e r - s o f t w a r e s u r v e y of c u r r e n t m i c r o c o m p u t e r usage i n s c h o o l s f o r t h e h e a r i n g i m p a i r e d . A m e r i c a n  A n n a l s o f t h e Deaf , 127 , 6 7 3 - 8 3 . 29. H e l l e r , S. R. and M a r t i n , C. D. ( 1 9 8 2 ) . B i t s ' n b i t e s  a b o u t c o m p u t i n g : A c o m p u t e r l i t e r a c y p r i m e r . R o c k v i l l e , M.D. : Computer S c i e n c e P r e s s . 30. H i g h t , R.L. ( 1 9 8 2 ) . L i p - r e a d e r t r a i n e r : t e a c h i n g a i d f o r t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s o f t h e Deaf , 127_ , 564-68. 3 1 . I r w i n , M. G. ( 1 9 8 2 ) . CAI a t CSDF : O r g a n i z a t i o n a l s t r a t e g i e s . A m e r i c a n A n n a l s o f t h e D e a f , 12 7 , 487-494. 32. J o h n s t o n , D. K. ( 1 9 8 2 ) . D e a f s i g n : a s e r i e s of c o m p u t e r i z e d i n s t r u c t i o n a l p r o g r a m s f o r the t e a c h i n g of s i g n l a n g u a g e . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 556-58. 33. J o n e s , B. W. and G r y g a r , J . ( 1 9 8 2 ) . The t e s t of s y n t a c t i c a b i l i t i e s and m i c r o c o m p u t e r s . A m e r i c a n  A n n a l s o f t h e Deaf , 127 , 638-44. 34. K e a r s l e y , G. and o t h e r s . ( 1 9 7 7 ) . A c a i p r o g r a m to t e a c h d e a f c h i l d r e n how t o use a r u l e r : a s t u d y i n i n s t r u c t i o n a l d e s i g n . R e s e a r c h and i n f o r m a t i o n r e p o r t 77-8. 35. K e l l y , R. R. ( 1 9 8 2 ) . M i c r o c o m p u t e r s i n e d u c a t i o n : age o f romance, o r age of r e a s o n ? A m e r i c a n A n n a l s o f t h e  De a f , 127 , 6 9 3 - 9 7 . 36. L e c a v a l i e r , D. and o t h e r s . ( 1 9 8 2 ) . P u t t i n g m i c r o c o m p u t e r t e c h n o l o g y t o work f o r our h e a r i n g - i m p a i r e d s t u d e n t s . A m e r i c a n A n n a l s o f t h e Deaf , 1_2_7 , 512-21 . 151 37. M o r g a n , J . M . ( 1 9 7 5 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n f o r t h e b l i n d and d e a f . P a p e r p r e s e n t e d a t t h e a n n u a l m e e t i n g of t h e A m e r i c a n E d u c a t i o n a l R e s e a r c h A s s o c i a t i o n i n W a s h i n g t o n D. C. 38. M o t h n e r , H. Shawn, J . ( 1 9 8 2 ) . M i c r o c o m p u t e r s a r e " m a c r o c o n t r i b u t o r s " t o s p e c i a l e d u c a t i o n p r o g r a m s . A m e r i c a n A n n a l s of t h e Deaf , 12 7 , 4 4 9 - 5 1 . 39. M u r r a y , R. ( 1 9 7 9 ) . R e i n f o r c e m e n t of s p e e c h t h r o u g h t h e b a l l o o n c a p t i o n i n g of song l y r i c s . A m e r i c a n A n n a l s o f  t h e Deaf , 124 , 656-62. 40. N e w e l l , W. J . , S i m s , D. and M y e r s , T. ( 1 9 8 3 ) . P r i n c i p a l s and r e q u i s i t e s of c o m p u t e r a s s i s t e d i n t e r a c t i v e v i d e o i n s t r u c t i o n : A s i g n l a n g u a g e l e s s o n . A m e r i c a n A n n a l s of t h e Deaf , 12 8 , 6 6 2 - 7 2 . 41. N i c o l a y , W. L . ( 1 9 8 3 ) . Group l e a r n i n g and t h e computer : The t e a c h e r b r i n g s an a p p l e f o r t h e s t u d e n t s . A m e r i c a n A n n a l s of t h e Deaf , 128 , 5 2 1 - 2 4 i 42. N o m eland, R. ( 1 9 7 9 ) . Some c o n s i d e r a t i o n s i n s e l e c t i n g a m i c r o c o m p u t e r f o r s c h o o l . A m e r i c a n A n n a l s of t h e Deaf , 12± , 5 8 5 - 9 3 . 43. N u g e n t , G.C. S t o n e , C.G. ( 1 9 8 2 ) . The v i d e o d i s c meets t h e m i c r o c o m p u t e r . A m e r i c a n A n n a l s of t h e Deaf , 12 7 , 5 69-72. 44. O l s e n , J . B. ( 1 9 8 2 ) . Do I have t o go t o r e c e s s ? E l e c t r o n i c s u p p l e m e n t s i n l a n g u a g e i n s t r u c t i o n . A m e r i c a n A n n a l s of t h e Deaf , 12 7 , 602-608. 45. P o l l a r d G. and Shaw C. ( 1 9 8 2 ) . M i c r o c o m p u t e r r e a d i n g c o m p r e h e n s i o n i m p r o v e m e n t p r o g r a m f o r t h e d e a f . A m e r i c a n A n n a l s of t h e Deaf , 127 , 4 8 3-86. 46. R a t h e , G. H. ( 1 9 6 9 ) . C o m p u t e r - a s s i s t e d i n s t r u c t i o n : E x c i t i n g new t o o l f o r t e a c h i n g t h e d e a f . A m e r i c a n  A n n a l s o f t h e Deaf , 114 , 884-8. 47. R i c h a r d s o n , J . E. ( 1 9 8 1 ) . Computer a s s i s t e d i n s t r u c t i o n f o r t h e h e a r i n g i m p a i r e d . V o l t a R e v i e w , 8_3 , 328-35. 4 8 . R i c h a r d s o n , W. ( 1 9 7 8 ) . Computer s u p p o r t t o i n s t r u c t i o n a l m a n a g e m e n t - i n s t r u c t i o n a l s y s t e m to m a t h e m a t i c s : A m o d e l . A m e r i c a n A n n a l s of t h e Deaf , 123 , 7 12-22. 152 49. R i l e y , D. C. ( 1 9 8 3 ) . Computer a s s i s t e d e v a l u a t i o n a t t h e C a l i f o r n i a s c h o o l f o r t h e d e a f - F r e m o n t . A m e r i c a n  A n n a l s o f t h e Deaf , 128 , 585-594. 50. R o s e , S. and W a l d r o n M. ( 1 9 8 3 ) . The use of m i c r o c o m p u t e r s i n t e a c h e r t r a i n i n g p r o g r a m s . A m e r i c a n  A n n a l s o f t h e Deaf , 128 , 553-56. 5 1 . Rothman, S. and Mosmann, C. ( 1 9 7 6 ) C o m p u t e r s and  S o c i e t y . (The t e c h n o l o g y and i t s s o c i a l i m p l i c a t i o n s . ) S e c o n d E d i t i o n . C h i c a g o , P a l o A l t o , T o r o n t o , H e n e l e y - o n - T h a m e s , S y d n e y , P a r i s : S c i e n c e R e s e a r c h A s s o c i a t e s I n c . 52. R u s s e l l , J . W. ( 1 9 8 2 ) . The a p p l e m i c r o c o m p u t e r i n s c h o o l l e a r n i n g c e n t e r s . A m e r i c a n A n n a l s o f t h e Deaf , 127 , 522 - 2 8 . 53. S a r a p a t a , S. L. ( 1 9 8 3 ) . The e f f e c t i v e use of c o m p u t e r s a t T o w n s h i p h i g h s c h o o l D i s t r i c t 214. A m e r i c a n A n n a l s  of t h e Deaf , 128 , 681-84. 54. S h a n a h a n , D. ( 1 9 8 2 ) . The com p u t e r -- a t e c h n o l o g y t h a t b r e a k s t he sound b a r r i e r . A m e r i c a n A n n a l s o f t h e Deaf , 127 , 4 7 6 - 8 2 . 55. S i m s , D. and o t h e r s . ( 1 9 7 9 ) . A p i l o t e x p e r i m e n t i n c o m p u t e r a s s i s t e d s p e e c h r e a d i n g i n s t r u c t i o n u t i l i z i n g t h e d a t a a n a l y s i s v i d e o i n t e r a c t i v e d e v i c e ( D A V I D ) . A m e r i c a n A n n a l s o f t h e Deaf , 124 , 6 1 8 - 2 3 . 56. S l o v i c k , L. ( 1 9 8 2 ) . CAI a t CSDF : M i c r o c o m p u t e r - b a s e d a u t h o r i n g s y s t e m s . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 536 - 4 5 . 57. S m a l d i n o , S. E., S c h l o s s , P. J . and G o l d s m i t h , L. ( 1 9 8 3 ) . A n a l y s i s of the r e l a t i v e i n s t r u c t i o n a l e f f i c i e n c y o f m i c o c o m p u t e r b a s e d i n s t r u c t i o n and t e a c h e r d i r e c t e d i n s t r u c t i o n f o r h e a r i n g i m p a i r e d and n o r m a l h e a r i n g y o u t h . A m e r i c a n A n n a l s o f t h e D e a f , 128 , 642-47. 58. S q u i r e , E. ( 1 9 7 7 ) The c o m p u t e r an e v e r y d a y m a c h i n e . S e c o n d E d i t i o n . Don M i l l s , O n t a r i o : A d d i s o n - W e s l e y ( C a n a d a ) L i m i t e d . 59. S t a c y , E.M. ( 1 9 8 2 ) . S t u d e n t s : h a n d l e w i t h C.A.R.E. ( c o m p u t e r a s s i s t e d r e m e d i a t i o n and e n r i c h m e n t ) . A m e r i c a n A n n a l s o f t h e Deaf , 127 , 617-24. 60. S t o k e r , R. G. ( 1 9 8 3 ) . A c o m p u t e r a s s i s t e d d i a g n o s t i c and p r e s c r i p t i v e t o o l f o r t e a c h i n g s p e e c h t o the d e a f . A m e r i c a n A n n a l s o f t h e Deaf , 128 , 62 5 - 3 0 . 153 61. S t o k e r , R. G . ( 1 9 8 3 b ) . On c o m p u t e r s and t h e h e a r i n g i m p a i r e d . V o l t a R e v i e w , 8_5_ , 3 64-65. 62. S t o r m , R. D. ( 1 9 8 3 ) . A m o d el f o r t h e i m p l e m e n t a t i o n of m i c r o c o m p u t e r use i n t o a p r o g r a m f o r t h e h e a r i n g i m p a i r e d . A m e r i c a n A n n a l s of t h e Deaf , 128 , 5 3 5-52. 63. S t u c k l e s s , E. R. ( 1 9 8 3 ) . The m i c r o c o m p u t e r i n t h e i n s t r u c t i o n of h e a r i n g i m p a i r e d s t u d e n t s : T o o l or d i s t r a c t i o n . A m e r i c a n A n n a l s of t h e Deaf , 128 , 5 1 5-20. 64. S u p p e s , P. ( 1 9 7 3 a ) . E v a l u a t i o n of c o m p u t e r - a s s i s t e d i n s t r u c t i o n i n e l e m e n t a r y m a t h e m a t i c s f o r h e a r i n g - i m p a i r e d s t u d e n t s . P s y c h o l o g y and E d u c a t i o n s e r i e s . 65. S u p p e s , P. ( 1 9 7 3 b ) . Computer a s s i s t e d i n s t r u c t i o n f o r d e a f s t u d e n t s . A m e r i c a n A n n a l s o f t h e Deaf , 116 , 500-8. 66. V o n f e l d t , J.R. S u b t e i n y , J . ( 1 9 7 5 ) . D e s c r i p t i o n and e v a l u a t i o n of t h e W e b s t e r ' s D i a c r i t i c a l m a r k i n g s . Computer a s s i s t e d i n s t r u c t i o n a l p r o g r a m . Summary r e p o r t . 67. V o n f e l d t , J.R. ( 1 9 7 8 ) . A n a t i o n a l s u r v e y of the use of c o m p u t e r a s s i s t e d i n s t r u c t i o n i n s c h o o l s f o r t h e d e a f . J o u r n a l o f E d u c a t i o n a l T e c h n o l o g y S y s t e m s , 1_ , 29-38 . 68. W a l k e r , R . J . ( 1 9 8 0 ) . An u p d a t e on c o m p u t e r s i n the c l a s s r o o m . 69. W a t s o n , P. ( 1 9 7 9 ) . The u t i l i z a t i o n of t h e c o m p u t e r w i t h t h e h e a r i n g i m p a i r e d and t h e h a n d i c a p p e d . A m e r i c a n  A n n a l s of t h e D e a f , 124 , 6 70-80. 70. Ward, R. D. and R o s t r o n , A. B. ( 1 9 8 3 ) . C o m p u t e r - a s s i s t e d l e a r n i n g f o r t h e h e a r i n g i m p a i r e d : An i n t e r a c t i v e w r i t t e n l a n g u a g e e n v i r o n m e n t . V o l t a R e v i e w , 85_ , 3 4 6-52. 71. W e s s e l , M. R. ( 1 9 7 4 ) Freedom's edge : The c o m p u t e r  t h r e a t t o s o c i e t y . Don M i l l s , O n t a r i o . : A d d i s o n - W e s l e y P u b l i s h i n g Company. 72. Weyer, S.A. ( 1 9 7 3 ) . F i n g e r s p e l l i n g by c o m p u t e r . P s y c h o l o g y and e d u c a t i o n s e r i e s . 73. W i e c k , C. ( 1 9 8 0 ) . Computer r e s o u r c e s : w i l l e d u c a t o r s a c c e p t , r e j e c t , or n e g l e c t i n t h e f u t u r e ? E d u c a t i o n  U n l i m i t e d , 2 , 2 4 - 2 7. 154 74. W i l s o n , F. L. ( 1 9 8 2 ) . E n e r g y and t h e e n v i r o n m e n t : an a p p r o a c h t o t e a c h i n g m o d e l i n g t h a t b r e a k s t h e h e a r i n g - i m p a i r e d s t u d e n t ' s " l i m i t s to g r o w t h " . A m e r i c a n A n n a l s o f t h e Deaf , 12 7 , 6 4 5 - 5 1 . 75. W i t h r o w , M. ( 1 9 7 8 a ) . Computer a n i m a t i o n and l a n g u a g e i n s t r u c t i o n . A m e r i c a n A n n a l s of t h e Deaf , 1 2 3 , 723-25. 76. W i t h r o w , M. ( 1 9 7 8 b ) . Computer g r a p h i c s and l a n g u a g e i n s t r u c t i o n f o r t h e d e a f . J o u r n a l o f E d u c a t i o n a l  T e c h n o l o g y S y s t e m s , 7_ , 3 9 - 4 3 . 77. W i t h r o w , M. ( 1 9 7 9 ) . I l l u s t r a t i n g l a n g u a g e t h r o u g h c o m p u t e r g e n e r a t e d a n i m a t i o n . A m e r i c a n A n n a l s of t h e  Deaf , 1_24 , 5 4 9 - 5 2 . 78. W r i g h t , A. ( 1 9 8 1 ) I n s t r u c t i o n a l t e c h n o l o g y f o r s p e c i a l n e e d s . D i s c u s s i o n p a p e r . B. C. D e p a r t m e n t of E d u c a t i o n , V i c t o r i a , C a n ada. 79. Wyman, R. ( 1 9 7 9 ) . A u d i o v i s u a l t e c h n o l o g y f o r the 8 0 ' s . A m e r i c a n A n n a l s of t h e Deaf , 124 , 5 9 8 - 6 0 3 . 

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