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Assessment of teachers' grading practises Dauncey, William Monte 1986

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ASSESSMENT OF TEACHERS ' GRADING  PRACTISES  by WILLIAM  MONTE DAUNCEY  B.Ed., U n i v e r s i t y o f V i c t o r i a ,  1976  THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS MASTER  FOR THE DEGREE OF OF ARTS  in THE FACULTY OF GRADUATE (Department o f E d u c a t i o n a l We a c c e p t to  this  STUDIES Psychology)  t h e s i s as conforming  the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA O c t o b e r , 1986 %pj W i l l i a m Monte Dauncey, 1986  In p r e s e n t i n g  this thesis  r e q u i r e m e n t s f o r an of B r i t i s h it  understood that for  Library  s h a l l make  for reference  and  study.  I  f o r extensive copying of be  h i s or her  g r a n t e d by  s h a l l not  be  EDUCATIONAL PSYCHOLOGY  The U n i v e r s i t y o f B r i t i s h 1956 Main Mall V a n c o u v e r , Canada V6T 1Y3  D a  /an  te  OCTOBER 1 1 ,  1986  of  further this  Columbia  thesis  head o f  this  my  It is thesis  a l l o w e d w i t h o u t my  permission.  Department o f  the  representatives.  copying or p u b l i c a t i o n  f i n a n c i a l gain  University  the  f o r s c h o l a r l y p u r p o s e s may by  the  the  I agree that  agree t h a t permission department o r  f u l f i l m e n t of  advanced degree a t  Columbia,  freely available  in partial  written  Abstract  Educators  have been u s i n g t h e l e t t e r g r a d e s y s t e m o f  g r a d i n g and r e p o r t i n g s t u d e n t achievement f o r s e v e r a l decades. S i n c e i t s i n c e p t i o n , t e a c h e r s have d e r i v e d l e t t e r g r a d e s a v a r i e t y of grading techniques. to  As a r e s u l t ,  g r a d i n g has o f t e n r e c e i v e d c r i t i c i s m  question i t sr e l i a b i l i t y s t u d y was t o d e t e r m i n e reliable prior  Many a u t h o r s  and u s e f u l n e s s .  for reporting  scores  purposes.  have w r i t t e n t o a t t a c k l e t t e r g r a d e s w h i l e their  use.  Some h a v e w r i t t e n t o  a l t e r n a t i v e s t o l e t t e r grades w h i l e s t i l l  w r i t e r s have suggested  little  The p u r p o s e o f t h i s  i f l e t t e r g r a d e s c o u l d be made more  o t h e r s have w r i t t e n t o d e f e n d  techniques.  approach  f r o m t h o s e who •  by s t a t i s t i c a l l y b a l a n c i n g raw achievement  t o aggregation  suggest  this  However,  methods o f i m p r o v i n g literature  searches  r e s e a r c h h a s b e e n done t o a s s e s s  p r a c t i s e s and t h e g r a d e s t h e y award  other  grading  h a v e shown t h a t  teachers'  grading  to evaluate the  g r a d i n g methods u s e d b y 3 7 r a n d o m l y s e l e c t e d e l e m e n t a r y I n f o r m a t i o n on t h e i r  c o l l e c t e d i n t h r e e ways:  very  students.  T h i s i n v e s t i g a t i v e s t u d y was d e s i g n e d  teachers.  from  school  methods o f g r a d i n g was  ( a ) b y way o f a q u e s t i o n n a i r e , (b) b y  having the subjects weight,  t o t a l , and rank  a hypotheticals e t  of raw a c h i e v e m e n t s c o r e s , and ( c ) by h a v i n g t h e s u b j e c t s submit c l a s s r e c o r d s f o r one r e p o r t i n g p e r i o d from two s u b j e c t  iii  a r e a s , m a t h e m a t i c s and s o c i a l  studies.  each  b a l a n c e d and t h e t e a c h e r s  c l a s s were s t a t i s t i c a l l y  regraded  their  s t u d e n t s based  In o r d e r t o c o n t r o l  revised  was u s e d  aggregate  totals.  f a c t o r s , the and t h e  indicating  that  Coefficient.  t o be s i g n i f i c a n t the n u l l  e a c h o f t h e 56 c l a s s e s Analysis  s c o r e s were  from t h e b a l a n c e d aggregate  t h e Spearman Rank C o r r e l a t i o n  c o r r e l a t i o n s were f o u n d  for  and s u b j e c t i v e  f o r both the o r i g i n a l  rankings of the o r i g i n a l  compared t o t h o s e d e r i v e d  sheet,  aggregate  aggregate scores.  The  using  on t h e r e v i s e d  f o r extraneous  same g r a d i n g c r i t e r i o n  The raw s c o r e s f o r  of the class  scores  The  f o r each  record  h y p o t h e s i s s h o u l d be r e j e c t e d  studied. record  s h e e t s and q u e s t i o n n a i r e  responses a l s o r e v e a l e d : (a) t h a t received rank  46% o f t h e 1,314 s t u d e n t s i n v o l v e d  a change i n l e t t e r  correlation  students, based  coefficients.  the assignment  on f a c t o r s (b) t h a t  grade  i n spite  This  of l e t t e r  other than t o t a l  grades  o n l y 5% o f t h e r e s p o n d e n t s  assignment  (c) t h a t  was u n r e l i a b l e and  u s e d methods  that  t o t h e raw s c o r e s .  u n r e l i a b l e methods t o  scores.  none o f t h e s u b j e c t s i n t h i s  study used  methods t o compensate a s t u d e n t who has m i s s e d assignments  f o r many  score rankings.  s u g g e s t s t h a t many t e a c h e r s u s e d  weight  of the s i g n i f i c a n t  suggests that  would a p p l y t h e d e s i r e d w e i g h t i n g f a c t o r s This  i n the study  or tests.  This  suggests that  reliable  one o r more  s t u d e n t s who were  iv  a b s e n t may h a v e b e e n u n j u s t l y r e w a r d e d a g g r e g a t e s c o r e s were  o r p e n a l i z e d when  their  calculated.  (d) t h a t 76% o f t h e r e s p o n d e n t s showed a d e s i r e t o l e a r n more a b o u t  c o l l a t i n g raw s c o r e s and a s s i g n i n g  aggregate scores.  These r e s u l t s  l e t t e r grades t o , ,  s u g g e s t e d t h a t i n - s e r v i c e i n s t r u c t i o n and  p r e - s e r v i c e t r a i n i n g i n p a r t i c u l a r a s p e c t s o f g r a d i n g and r e p o r t i n g would sample.  be j u s t i f i e d  f o r many members o f t h e r e s e a r c h  A r e a s o f g r e a t e s t need a r e t h o s e c o n c e r n i n g t h e  w e i g h t i n g o f raw s c o r e s , t h e a l l o c a t i o n o f l e t t e r g r a d e s , and the c a l c u l a t i o n of compensation missed  s c o r e s f o r s t u d e n t s who h a v e  assignments.  R e s e a r c h S u p e r v i s o r : D r . H. R a t z l a f f  V  TABLE OF  CONTENTS  Abstract  i i  L i s t of Tables Acknowledgements Chapter  1 -  vi viii  Scope o f t h e Study I d e n t i f i c a t i o n of the Problem D e f i n i t i o n o f Terms Research Questions Rationale Delimitations J u s t i f i c a t i o n of the Study  1 4 12 16 17 19 20  Chapter 2 -  L i t e r a t u r e Review G r a d i n g Systems Criterion-referenced Grading Norm-referenced Grading  24 29 33 36  Chapter  Methodology Sample and P o p u l a t i o n Questionnaire Record Sheets Grading P o l i c y D a t a C o l l e c t i o n and A n a l y s i s  45 45 46 49 52 54  Chapter 4 -  Results Sample Grading Techniques Record Sheets  56 56 64 70  Chapter 5 -  C o n c l u s i o n s and F u r t h e r R e s e a r c h Summary Research Question 1 Research Question 2 Research Question 3 Research Question 4 W e a k n e s s e s To Be C o n s i d e r e d O p p o r t u n i t i e s f o r Future Research  77 77 79 86 89 91 92 94  3 -  Bibliography Appendix  A - Questionnaire  98 101  vi  L I S T OF TABLES  Table I Table I I  - F i c t i t i o u s d a t a t o be c o l l a t e d ranked - F i c t i t i o u s data a f t e r  and 50  being  s t a t i s t i c a l l y balanced  50  Table I I I  - Letter  Table IV  - D i s t r i b u t i o n by G e n d e r  57  Table V  - D i s t r i b u t i o n by Age  57  Table VI  - D i s t r i b u t i o n by u n i v e r s i t y t r a i n i n g (years) - D i s t r i b u t i o n by M e a s u r e m e n t  Table V I I  grade d i s t r i b u t i o n g u i d e l i n e s  53  57 Courses  Taken  58  Table V I I I  - D i s t r i b u t i o n by T e a c h i n g A s s i g n m e n t  58  Table IX  - D i s t r i b u t i o n by T e a c h i n g E x p e r i e n c e  58  Table X  - D i s t r i b u t i o n of Colleagues' Attitudes Toward R e p o r t C a r d M a r k s - D i s t r i b u t i o n o f A t t i t u d e Toward L e t t e r Grade E f f e c t i v e n e s s  Table XI Table X I I  Table X I I I Table XIV  T a b l e XV T a b l e XVI  60 60  - D i s t r i b u t i o n o f Agreement R e g a r d i n g P a r e n t s ' S a t i s f a c t i o n Toward L e t t e r Grade R e p o r t i n g Systems  61  - D i s t r i b u t i o n o f Agreement R e g a r d i n g S u b j e c t s ' Own G r a d i n g A b i l i t y  61  - D i s t r i b u t i o n o f Agreement R e g a r d i n g S u b j e c t s ' D e s i r e To L e a r n More A b o u t M a r k i n g and G r a d i n g  62  - D i s t r i b u t i o n o f A g r e e m e n t on Inservice Sessions .  62  Evaluation  - D i s t r i b u t i o n o f Agreement R e g a r d i n g S u b j e c t s ' O p i n i o n on P r e - s e r v i c e Training  62  vii  Table XVII  - D i s t r i b u t i o n o f Agreement R e g a r d i n g E f f e c t i v e n e s s o f t h e Report Card F o r m a t As a C o m m u n i c a t i o n Device  T a b l e X V I I I - D i s t r i b u t i o n o f G r a d i n g Methods Table XIX  - Distribution of Application  66  of Grading  Technique  66  T a b l e XX  - D i s t r i b u t i o n o f Compensation Method  Table XXI  - D i s t r i b u t i o n o f Ranks o f F i c t i t i o u s Data - Spearman Rank C o r r e l a t i o n Coefficients R e l a t i n g Raw S c o r e a n d B a l a n c e d Score T o t a l s  Table XXII  T a b l e X X I I I - D i s t r i b u t i o n o f Spearman Rank  69 72  73  T a b l e XXIV  - Distribution of Letter  T a b l e XXV  - Frequency  T a b l e XXVI  - F r e q u e n c y o f L e t t e r G r a d e Changes R e s u l t i n g From A r i t h m e t i c Errors - Frequency o f Category S h i f t R e s u l t i n g From L e t t e r G r a d e R e c a l c u l a t i o n  Table XXVII  68  Correlation  Coefficients  of Category  63  Grade Changes Shift  T a b l e X X V I I I - E f f e c t s o f r F o r Between S c o r e s on Total Score r When r ( b e t w e e n ) =+1 s T a b l e XXIX - E f f e c t on r F o r B e t w e e n S c o r e s On Total Score r When r ( b e t w l e n ) =. 65 s T a b l e XXX - Compensation F o r Missed Assignment  74 74  75 76  84  85 90  viii  Acknowledgement  I w o u l d l i k e t o e x p r e s s my supervisor, Dr. W.  D r . H. R a t z l a f f , and  B o l d t and D r . W.  I w i s h t o e x t e n d my  Szetela  g r a t i t u d e t o my  t o c o m m i t t e e members f o r t h e i r h e l p and c o u n s e l .  s i n c e r e t h a n k s and  appreciation to  w i f e , R o x a n n e , f o r h e r c o n t i n u o u s s u p p o r t and t h r o u g h o u t t h e c o u r s e o f my  Finally,  t o my  research  encouragement  studies.  c h i l d r e n , D e n i s e and D o u g l a s , a  n o t e o f g r a t i t u d e f o r t h e i r p a t i e n c e and  special  understanding.  my  1  CHAPTER 1 Scope of the Background  Study-  Information  F o r more t h a n f i f t y y e a r s , t h e  l e t t e r grade system  b e e n u s e d i n e d u c a t i o n t o r e p o r t and student achievement.  document t h e  level  However, even a f t e r decades o f  Many t e a c h e r s a c q u i r e g r a d i n g p r a c t i s e s  informally;  f r o m a c o l l e a g u e , d e p a r t m e n t h e a d , o r by  a f l e e t i n g e x p o s u r e t o an during teacher  reasonable.  Others  "acceptable" grading  have  training.  anything about g r a d i n g .  This very important  teacher's task i s often ignored i n teacher Perhaps i t i s j u s t taken t o o i n t r a c t a b l e t o be  their  may  taught  p a r t of  be a "C-"  f o r g r a n t e d , o r p e r h a p s i t seems  taught.  (Hills,  1981,  p.  316)  when i n c o n s i s t e n c i e s i n g r a d i n g p r a c t i s e s e x i s t ,  For example, a grade of o r a "C+"  i n another.  "C"  c r e d i b i l i t y w i t h the post-secondary s t u d e n t s , and  i n one  As a r e s u l t ,  g r a d i n g p r a c t i s e s become somewhat s u s p e c t  employers,  the  training.  l e v e l s of achievement are not n e c e s s a r i l y g i v e n  l e t t e r grades.  had  procedure  c a r e e r s i n the s c h o o l s w i t h o u t e v e r h a v i n g been  equal  to  using  may  I t i s s u r p r i s i n g t h a t many t e a c h e r s embark on  Consequently,  tend  school  districts.  methods t h a t seem i n t u i t i v e l y  of  use,  grading p r a c t i s e s w i t h i n the l e t t e r grade system s t i l l v a r y among t e a c h e r s , d e p a r t m e n t s , s c h o o l s , and  has  and  equal  classroom grades  and  often lose  institutions,  prospective  other i n d i v i d u a l s or agencies  that  2  depend upon r e l i a b l e academic a s s e s s m e n t s as a b a s i s f o r d e c i s i o n making.  This notion i s supported  by H i l l s  (1981) who  states, F a u l t y g r a d i n g c a n be s e r i o u s l y d e t r i m e n t a l t o s t u d e n t s . It  c a n g i v e them m i s l e a d i n g i n f o r m a t i o n a n d i n t e r f e r e  with the learning process.  I t can g i v e m i s l e a d i n g  i n f o r m a t i o n f o r o t h e r s who l e g i t i m a t e l y u s e s c h o o l as p a r t o f t h e i r p r o c e d u r e s it  i n e v a l u a t i n g people.  grades And  c a n m i s l e a d t h o s e who w o u l d s t u d y t h e i n s t r u c t i o n a l  process  t o improve i t o r t o h o l d i t a c c o u n t a b l e  society that supports  t o the  i t . ( p . 317)  However, f o r most s t u d e n t s u n r e l i a b l e c a l c u l a t i o n s o f a term's grades w i l l is  n o t c a u s e much harm.  F o r e x a m p l e , i f a "C"  a w a r d e d i n s t e a d o f a C+ o r a C- , t h e d i f f e r e n t i a l  upon t h e s t u d e n t w i l l such  as these w i l l  not vary s i g n i f i c a n t l y .  effects .  Discrepancies  s e l d o m l e a d t o i n c o r r e c t d e c i s i o n s . a s C+,  C, a n d C- a r e a l l s y m b o l s o f " s a t i s f a c t o r y " a c h i e v e m e n t .  On  t h e o t h e r h a n d , when a s t u d e n t h a s b e e n g i v e n an F when he merited a passing grade, result.  some f a r r e a c h i n g c o n s e q u e n c e s  Such an e r r o r c o u l d c o s t t h e s t u d e n t  c o u r s e , o r e v e n an e x t r a y e a r prevents  promotion.  could  credit f o r the  i n school i f a course  failure  A t t h e o t h e r end o f t h e s c a l e , a C+  i n s t e a d o f a B, o r a B i n s t e a d o f an A c o u l d r e s u l t  i n the  l o s s o f a s c h o l a r s h i p , a b u r s a r y , o r an o p p o r t u n i t y t o a t t e n d a p a r t i c u l a r l y competitive post-secondary  institution.  course, the inverse i s e q u a l l y s i g n i f i c a n t .  Of  F o r example, i f a  3  s t u d e n t i s e r r o n e o u s l y a w a r d e d a p a s s i n g g r a d e , he w i l l  be  g i v e n c r e d i t f o r a c o u r s e when i t i s n o t w a r r a n t e d a n d when he is not s u f f i c i e n t l y In  level.  e l e m e n t a r y s c h o o l s , marks and o t h e r m e a s u r e s o f  student achievement student w i l l  form t h e b a s i s f o r d e t e r m i n i n g whether  be p r o m o t e d i n t o t h e n e x t g r a d e , w h e t h e r  r e c e i v e an academic for  p r e p a r e d t o go on t o t h e n e x t  award o r whether  he w i l l  a  he w i l l  be a c a n d i d a t e  learning assistance or a special remedial class.  In  j u n i o r h i g h s c h o o l , term grades a r e used as i n t h e e l e m e n t a r y school s e t t i n g but w i t h the a d d i t i o n a l use of i d e n t i f y i n g honour r o l l  students.  S e n i o r h i g h s c h o o l s use term grades not  o n l y f o r p r o m o t i o n and r e t e n t i o n b u t a l s o t o d e t e r m i n e students w i l l will  be r e q u i r e d t o w r i t e f i n a l  be e l i g i b l e  which  exams, w h i c h s t u d e n t s  f o r s c h o l a r s h i p s and b u r s a r i e s , a n d w h i c h  s t u d e n t s s h o u l d be e n c o u r a g e d  t o attend post-secondary  institutions. A l t h o u g h t h e r e a r e t h o s e who d i s a g r e e w i t h t h e l e t t e r system o f g r a d i n g and r e p o r t i n g do a g r e e f e e l roles.  ( s e e C u r w i n , 1 9 7 8 ) , t h o s e who  i t may be one o f t h e t e a c h e r ' s most i m p o r t a n t  "One o f t h e most i m p o r t a n t p r o f e s s i o n a l  r e s p o n s i b i l i t i e s o f academic r e p o r t i n g marks performance"  staff  i s t h a t o f a l l o c a t i n g and  ( o r grades) as measures o f s t u d e n t  ( I s a a c s a n d I m r i e , 1 9 8 1 , p. 3 ) .  Curwin  suggests  t h a t t e a c h e r s s h o u l d q u e s t i o n themselves as t o t h e  reliability  of  functions.  g r a d e s i n f u l f i l l i n g t h e r e p o r t i n g and l e a r n i n g  He s t a t e s , all  "The one b a s i c r e q u i r e m e n t o f t h e r e p o r t i s t h a t  i n f o r m a t i o n r e c e i v e d must h a v e t h e same m e a n i n g t h a t was  4  s e n t by  the  grader.  G r a d e s must be  high degree of p r e d i c t a b i l i t y . ( C u r w i n , 1978 , p.  Identification  It  school  But  as  reliable  The  they don't."  reporting. large  i s a need f o r t e a c h e r s '  and  boards a l s o recognize  Handbook o f one  As  accurate  the  and  that evaluation  reliable  information  (School  schools of the  and  and  and  integral  The  Board  and  r e p o r t i n g should  be  based  District Administrative  Handbook,  reporting, consistency  community i s p r e s e r v e d ,  remains: Are  the  teachers'  r e l i a b l e and  accurate  and  educational  correctly.  current  as p o s s i b l e ?  or 1978)  among i n the  decisions  However, t h e  grading  on  relation  r e q u i r e m e n t s of a program, c o u r s e ,  accurate  not.  vital  further  classrooms i s maintained, c r e d i b i l i t y  they are  and  about p u p i l performance i n  be made more c o n f i d e n t l y and  claims  in  Administrative  that evaluation  learning.  believes  grade.  Most  district,  p a r t s of t e a c h i n g  specific  as p o s s i b l e .  s t a t e d i n the  r e p o r t i n g of p u p i l achievement are  to the  grading  need f o r r e l i a b i l i t y  Board of Trustees b e l i e v e s  With r e l i a b l e  have a  Problem  seems c l e a r t h a t t h e r e  e v a l u a t i o n and  and  60).  of the  p r a c t i s e s t o be  valid, reliable  practises  eyes can  question as  Curwin (1978), f o r  one,  5  With the i n t r o d u c t i o n of the l e t t e r grade r e p o r t cards i n B r i t i s h Columbia's elementary s c h o o l s , t h e r e i s the that teachers w i l l  have t h e b a c k g r o u n d  assumption  k n o w l e d g e and  the  resources necessary to c o l l a t e  s c o r e s , g r a d e , and  student achievement  As i n d i c a t e d p r e v i o u s l y , many  t e a c h e r s may  reliably.  n o t have t h e n e c e s s a r y u n d e r s t a n d i n g o r  to perform such t a s k s w e l l . how  training  Many t e a c h e r s s i m p l y do n o t know  t o combine s t u d e n t achievement  yield  report  s c o r e s i n s u c h a way  r e l i a b l e l e t t e r grades f o r r e p o r t i n g  as t o  purposes.  T e a c h e r s a g r e e t h a t g i v i n g and r e p o r t i n g m a r k s ( o r g r a d e s ) i s one o f t h e i r m o s t u n c o m f o r t a b l e responsibilities.  Some l a c k c o n f i d e n c e i n t h e m a r k s t h e y  a s s i g n ; o t h e r s b e l i e v e t h e i r marks a r e f a i r , them d i f f i c u l t  t o defend.  attitudes  the f a c t  lies  marks i s o f t e n u n c l e a r .  but  find  Behind these negative  t h a t the b a s i s  for•assigning  (Ahmann and G l o c k , 1981, p.  417)  As a r e s u l t , many t e a c h e r s c o m b i n e and c a l c u l a t e s c o r e s i n a manner t h a t seems i n t u i t i v e l y r e a s o n a b l e , and by v i r t u e  of  their  grades  l a c k o f knowledge,  blissfully  as b e i n g r e l i a b l e a s s e s s m e n t s  accept t h e i r  of t h e i r  letter  s t u d e n t s ' work.  Many  assume t h a t by u s i n g raw s c o r e s t h e i r t e r m a s s i g n m e n t s w i l l a p p r o p r i a t e l y w e i g h t e d when c o m b i n i n g m a r k s f o r t h e i r totals.  term  Many t e a c h e r s seem t o r e g a r d t h e mark v a l u e o f  each  a s s i g n m e n t a s b e i n g an i n d i c a t o r o f t h e w e i g h t c o n t r i b u t i n g the  t o t a l t e r m s c o r e ( i e . an a s s i g n m e n t w o r t h 100  marks  c o n t r i b u t e s t w i c e as much t o w a r d t e r m t o t a l s as d o e s an a s s i g n m e n t w o r t h 50 m a r k s ) .  I t would  seem t h a t one  be  of the  to  6  more common m e t h o d s o f c o l l a t i n g a c h i e v e m e n t r e s u l t s f o r g r a d i n g p u r p o s e s i n v o l v e s s i m p l e t o t a l l i n g o f raw averaging In  ( h i g h e s t term  total  scores  o r a v e r a g e r e c e i v e s an A  e x t r e m e c a s e s , w h e r e s t a n d a r d d e v i a t i o n s among  assignments are very d i f f e r e n t , averaging  and  aggregate  scores  u n r e l i a b l e r e p o r t i n g , as w i l l  be d e m o n s t r a t e d i n a  example.  still  A l s o , some t e a c h e r s  'rule-of-thumb' They may,  be e q u i v a l e n t t o an  'A',  percentage  s c o r e a b o v e 80 p e r c e n t  e v e n i n e x t r e m e c a s e s w h e r e an  G r a d e s o b t a i n e d f r o m t h e s e and  as b e i n g  and  parents,  r e l i a b l e by i n t e r e s t e d p a r t i e s  ( s u c h as  p r i n c i p a l s , p r o s p e c t i v e employers, i n s t i t u t i o n s ) and  and  per  credible  higher educational  a r e used as a b a s i s f o r making  important  In s h o r t , t e a c h e r s o f t e n have c o n s i d e r e d n e i t h e r  mean s c o r e s n o r t h e v a r i a b i l i t y p u p i l achievement.  As w i l l  f r o m s e v e r a l a s s i g n m e n t s may  be  o f s c o r e s when e v a l u a t i n g shown, c a l c u l a t i n g t e r m  y i e l d u n e x p e c t e d and  r e s u l t s i f t h e c l a s s a v e r a g e s and  the w e i g h t i n g  scheme o r i g i n a l l y  " I f we  in inequities"  unreliable  c h o s e n , we  hope t o  (Ahmann and  maintain  must t a k e  c o n s i d e r a t i o n the d i f f e r e n c e s i n v a r i a b i l i t y . result  totals  t h e amount o f v a r i a t i o n i n  each assignment are not c o n s i d e r e d .  426 ) .  80  to  other  s i m i l a r l y q u e s t i o n a b l e methods a r e a c c e p t e d  this will  results.  l o w e s t s c o r e o r where t h e h i g h e s t s c o r e i s l e s s  than 8 0 per cent.  decisions.  and  subsequent  i n terms of t e s t , assignment, or term  f o r e x a m p l e , c o n s i d e r any  cent i s the  a b i d e by t h e  etc.).  term  s i m p l e summations  can r e s u l t i n h i g h l y erroneous  or  into  A f a i l u r e to  Glock,  1981,  p.  do  7  Before  examining  why mean s c o r e s a n d s t a n d a r d d e v i a t i o n s  s h o u l d be e m p l o y e d , a r e v i e w o f how f i n a l typically  obtained i s i n order.  Final  o r term  course  t y p i c a l l y b a s e d on v a r i o u s t y p e s o f s t u d e n t  totals are  grades a r e  achievement,  such  as s h o r t q u i z z e s , t e r m p r o j e c t s , l a b o r a t o r y w o r k , a n d examinations.  Thus, a s s i g n i n g course  grades i n v o l v e s  these v a r i o u s measures t o o b t a i n a composite o r term  combining score i n  s u c h a way t h a t e a c h a s s i g n m e n t r e c e i v e s i t s i n t e n d e d For example, i f i t has been d e c i d e d  that the f i n a l  weight.  examination  s h o u l d c o u n t t w i c e a s much a s t h e s h o r t q u i z z e s , t h e n t h e grades should r e f l e c t t h i s emphasis.  Similarly,  i f the  l a b o r a t o r y w o r k i s t o make up 25 p e r c e n t o f t h e f i n a l grade,  then  i t i s important  that extent.  t h a t i t w i l l be r e p r e s e n t e d t o  I t i s n o t uncommon f o r t e a c h e r s t o c o m m u n i c a t e  t h i s type of i n f o r m a t i o n t o t h e i r the course.  Students  students a t the beginning of  are p a r t i c u l a r l y interested  w h i c h e l e m e n t s w i l l be i n c l u d e d i n t h e f i n a l r e l a t i v e weight  how much w e i g h t  grade and t h e  s h o u l d be g i v e n t o e a c h o f  the v a r i o u s assignments i s a matter judgment i s g u i d e d instructional  i n knowing  e a c h w i l l be g i v e n .  Determining  by t h e importance  o f judgment.  This  of the various  o b j e c t i v e s , t h e t e a c h i n g emphasis g i v e n t o each  type of course The  course  a c t i v i t y , and o t h e r s i m i l a r c o n s i d e r a t i o n s .  t e a c h e r must d e c i d e o n t h e c o m p o s i t i o n  i n each course each component.  of the grades  given  a n d t h e r e l a t i v e e m p h a s i s t o be a l l o c a t e d t o Without a s s i g n i n g d e s i r e d weightings t o  a s s i g n m e n t s a n d by u s i n g o n l y t h e n a t u r a l w e i g h t i n g s ,  i t i s  8  p o s s i b l e f o r a r e l a t i v e l y minor assignment t o have a v e r y s t r o n g , i f n o t dominant, i n f l u e n c e on t h e c o u r s e g r a d e . t h e n a t u r a l w e i g h t i n g s may r e f l e c t a t o t a l l y emphasis on t h e v a r i o u s i n s t r u c t i o n a l  Also,  different  o b j e c t i v e s t h a n was  a c t u a l l y used by t h e t e a c h e r d u r i n g t h e c o u r s e . When t h e d e c i s i o n h a s b e e n made c o n c e r n i n g proportion of the f i n a l  aggregate  what  s c o r e i s t o be a l l o c a t e d t o  each measure o f s t u d e n t performance,  t h e m e a s u r e s must be  c o m b i n e d i n s u c h a way t h a t t h e d e s i r e d w e i g h t i n g i s o b t a i n e d . T h i s b r i n g s us back t o t h e i m p o r t a n c e means a n d s t a n d a r d d e v i a t i o n s .  of calculating  To i l l u s t r a t e  class  the problems o f  the v a r i o u s g r a d i n g p r a c t i s e s i n t h e w e i g h t i n g o f achievement data, which  i s t h e problem  a s i m p l e example  of i n t e r e s t i n t h i s study,  (taken from Gronlund,  consider  1974).  L e t us assume t h a t we want t o c o m b i n e s c o r e s o n a n examination  a n d s c o r e s o n a t e r m p r o j e c t , a n d t h a t we want  them t o c o n t r i b u t e e q u a l l y t o t h e f i n a l  ( o r term)  grade.  S u p p o s e t h e r a n g e o f s c o r e s o n t h e two m e a s u r e s a r e :  Range o f s c o r e s o n e x a m i n a t i o n  20 t o 120  Range o f s c o r e s o n t e r m p r o j e c t  40 t o  I f we s i m p l y a d d t o g e t h e r t h e e x a m i n a t i o n p r o j e c t score f o r each i n d i v i d u a l , determined  the f i n a l  60  s c o r e and t h e grade w i l l  l a r g e l y b y how w e l l t h e s t u d e n t s p e r f o r m e d  examination.  To d e m o n s t r a t e t h i s ,  h i g h e s t on t h e examination  be  on t h e  compare a s t u d e n t who i s  and l o w e s t on t h e term p r o j e c t  9  ( S t u d e n t A) w i t h a s t u d e n t who i s h i g h e s t on t h e t e r m and  l o w e s t on t h e e x a m i n a t i o n  project  (Student B ) .  Student A  Student B  Examination score Term p r o j e c t s c o r e  120 40  20 60  Composite  160  80  It  score  i s obvious that  s i m p l y a d d i n g t h e two s c o r e s w i l l n o t  g i v e them e q u a l r e p r e s e n t a t i o n will The  calculating examination  project In to  an a v e r a g e  Nor  score provide equal weighting. than the term  score. a situation  equate  such as t h i s ,  teachers frequently  score f o r both assignments  equivalent.  above example, t h i s w o u l d mean m u l t i p l y i n g s c o r e by two t o make t h e t o t a l  both measures o f achievement.  happens when t h i s  Examination score Term p r o j e c t s c o r e score  In  the students'  possible  The f o l l o w i n g  s c o r e 120  shows what  i s done:  Student A  Composite  attempt  t h e i n f l u e n c e o f t h e two m e a s u r e s by m a k i n g t h e  term p r o j e c t for  score.  s c o r e h a s much g r e a t e r i n f l u e n c e  maximum p o s s i b l e the  i n the composite  (x2)  Student B  120 80  20 120  200  140  10  As  the example demonstrates,  e q u a t i n g on t h e b a s i s o f  maximum p o s s i b l e s c o r e d o e s n o t p r o v i d e f o r e q u a l the composite score either..  The  examination  t h e g r e a t e r i n f l u e n c e when t h e two  emphasis i n  score s t i l l  are combined.  has  This i s  b e c a u s e t h e c o n t r i b u t i o n a g i v e n m e a s u r e makes t o a c o m p o s i t e s c o r e d e p e n d s l a r g e l y on t h e v a r i a b i l i t y ,  or spread, of  the  scores i n the s e t . To e q u a t e t h e e x a m i n a t i o n  s c o r e and  the term p r o j e c t  s c o r e , t h e v a r i a t i o n o f t h e s c o r e s i n e a c h s e t must be made equal. one set.  T h i s i s done by a d j u s t i n g t h e s t a n d a r d d e v i a t i o n o f  of the s e t s of s c o r e s so t h a t i t i s e q u a l The  method most o f t e n used i s t h e s t a n d a r d  transformation. average  to the  T-score  T h i s c h a n g e s e a c h s e t so . t h a t t h e  (mean) i s 50  class  t h e s t a n d a r d d e v i a t i o n i s 10.  and  i s n o t an e a s y t a s k w i t h o u t t h e use  knowledge.  'balanced',  weightings  However, once t h e s c o r e s c a n be  score w i t h the confidence obtained. weighted  a p p l i e d t o each  Our  some  are  transformed  t h a t the d e s i r e d weightings  I n t h i s s i m p l e e x a m p l e , t h e two equally.  This  of a computer o r a  s o p h i s t i c a t e d c a l c u l a t o r , a g r e a t d e a l o f t i m e , and statistical  other  example would then  will  assignments look l i k e  Student  A  are  this: Student  Examination T-score (weighted) Term p r o j e c t T - s c o r e (weighted)  100 80  80 100  Composite T-score  180  180  (weighted)  be  B  11  C l e a r l y , the examination equal; both  and t h e term p r o j e c t s c o r e s a r e  s t u d e n t s r e c e i v e t h e same c o m p o s i t e s c o r e .  This  i s p o s s i b l e o n l y by e q u a t i n g t h e two a s s i g n m e n t s i n terms o f means a n d s t a n d a r d d e v i a t i o n s .  In t h i s case, the standard  T - s c o r e was u s e d f o r b o t h e x e r c i s e s .  The  m a i n q u e s t i o n s t o be a d d r e s s e d  then are the  following: 1.  I s t h e r e a 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 grades  r e p o r t e d by t e a c h e r s u s i n g i n t u i t i v e methods and t h o s e r e p o r t e d when means and s t a n d a r d d e v i a t i o n s a r e u t i l i z e d a n d applied?  I n o t h e r words, i f t e a c h e r s were t o f o l l o w t h e  a d v i c e o f many a u t h o r s  and employ b a s i c s t a t i s t i c s  a g g r e g a t i n g m a r k s , w o u l d t h e r e s u l t s be d i f f e r e n t from those  when  significantly  obtained from e x i s t i n g grading p r a c t i s e s ?  2. A r e t h e r a w a c h i e v e m e n t s c o r e s c o m b i n e d a n d  weighted  reliably? 3. A r e t h e methods u s e d t o c o m p e n s a t e s t u d e n t s who h a v e missed  a s s i g n m e n t s o r t e s t s f a i r and r e l i a b l e ?  Are stuents  g i v e n g r a d e s t h a t p e n a l i z e o r r e w a r d them f o r b e i n g a b s e n t f o r a t e s t o r assignment? 4. Would a n y i m p r o v e m e n t i n r e s u l t s be o f s u c h  a  magnitude t o j u s t i f y t h e t i m e and expense r e q u i r e d t o r e t r a i n teachers? I t was t h e p u r p o s e o f t h i s s t u d y t o i n v e s t i g a t e t h e s e questions t o determine  i f teachers' aggregating  methods c o u l d be i m p r o v e d .  and g r a d i n g  12  DEFINITION OF TERMS  The  1. various  following  a r e terms  ASSIGNMENT  SCORES:  exercises,  etcetera,  that  tests,  i s the r e s u l t  completing a total  reporting largest  that  to smallest  balanced  BALANCED scores"  results  "assignment after  A t t h e end o f e a c h  on e a c h a s s i g n m e n t .  term,  For  i s then ranked  g r a d e s a r e a s s i g n e d b a s e d on  "Balanced Scores" o r  t o assignment  transformation  standard d e v i a t i o n .  An  scores.  SCORES:  undergone a l i n e a r  subject.  s t u d e n t ' s term s c o r e  and l e t t e r  refer  projects,  each s t u d e n t would r e c e i v e  the r a n k i n g s o f the t o t a l 2.  t o the  i s o b t a i n e d f o r e a c h s t u d e n t by  respective  purposes each  refer  assign h i s students during the  assignment.  o r "term s c o r e "  study:  l a b o r a t o r y work, t e r m  i n a particular  a particular  summing t h e i r  i n this  "Assignments"  a t e a c h e r might  course of i n s t r u c t i o n score"  used  When s e v e r a l  scores  to alter class  that  "statistically have  t h e mean and  a s s i g n m e n t s have b e e n  " b a l a n c e d " , t h e y have been g i v e n e q u a l means and e q u a l standard deviations. towards  Fair  contribute- e q u a l l y  t h e f i n a l , c o u r s e mark.  3. FAIR: t o mean  Balanced assignments  "just"  F o r the purpose  study, " f a i r "  i s used  o r " n o t f a v o u r i n g one more t h a n t h e ' o t h e r " .  grades are those that  individual  of t h i s  do n o t p e n a l i z e o r r e w a r d  s t u d e n t s more t h a n t h e y do o t h e r s t u d e n t s . F a i r  grades a r e a l s o  consistent.  F o r example, two s t u d e n t s h a v i n g  13  the same raw s c o r e s and s u b j e c t e d t o i d e n t i c a l  grading  c r i t e r i a would be expected t o r e c e i v e i d e n t i c a l  grades.  However, i f one o f t h e s t u d e n t s were t o r e c e i v e a h i g h e r grade than t h e o t h e r , then t h e grades would not be c o n s i s t e n t and would be c o n s i d e r e d 4.  "unfair".  LETTER GRADE:  F o r t h e purpose o f t h i s s t u d y , a  l e t t e r grade i s d e f i n e d a s : "1) a summary symbol, 2) e v a l u a t i n g a s u b s t a n t i a l segment o f achievement which i s 3) a t t a i n e d by a p u p i l i n a course and 4) a s s i g n e d by a t e a c h e r 5) f o r t h e purpose o f r e c o r d and r e p o r t " ( M i n i s t r y o f E d u c a t i o n , S c i e n c e and Technology, 1979, p. 9 ) . A l e t t e r grade s h o u l d be r e s e r v e d f o r judgements t h a t i n c l u d e e v i d e n c e a v a i l a b l e on s t u d e n t achievement i n a complete course o r a segment o f a course such as a r e p o r t i n g p e r i o d .  L e t t e r grades  are u s u a l l y d e r i v e d from t h e e v i d e n c e a v a i l a b l e i n a s e t of s c o r e s f o r each p u p i l . a s y s t e m a t i c procedure  I t i s a l s o assumed t h a t a t e a c h e r has f o r a s s i g n i n g grades.  Because a l e t t e r  grade i s "used t o r e c o r d and r e p o r t " , i t i s assumed t h a t a l e t t e r grade i s a "permanent r e c o r d u s u a l l y r e t a i n e d f o r a l o n g p e r i o d of time i n t h e s c h o o l r e c o r d system and used t o communicate w i t h i n d i v i d u a l s t u d e n t s , p a r e n t s , t e a c h e r s , and o t h e r e d u c a t i o n a l a u t h o r i t i e s and p o t e n t i a l  employers"  ( M i n i s t r y o f E d u c a t i o n , S c i e n c e and Technology, 1979, p. 10). 5. MEAN: "Mean" i s synonymous w i t h " a r i t h m e t i c mean" o r "average"  and i s a measure o f c e n t r a l tendency.  Iti s  c a l c u l a t e d by summing a s e r i e s o f numbers and d i v i d i n g t h e sum by t h e number o f numbers summed.  The v a l u e of t h e mean i s  14  a f f e c t e d by t h e i n d i v i d u a l v a l u e s o f a l l o f t h e s c o r e s i n t h e set  of data.  I n t h i s s t u d y , t h e mean i s d e n o t e d a s X  individual  and m  2  r a w s c o r e s a s X.. 1  6. R E L I A B L E :  R e l i a b l e grades are those  " d e p e n d a b l e a n d f i t t o be r e l i e d u p o n " .  that are  Grades t h a t a r e  r e l i a b l e p r o v i d e an a c c u r a t e i n d i c a t i o n o f a  student's  performance and a r e w o r t h y o f b e i n g used as a b a s i s f o r decision  making.  7. T-SCORES: standard set  scores.  "T-Scores"  are a l i n e a r transformation of  Standardized T-scores  are transformed  to a  o f d a t a h a v i n g a mean o f 50 a n d s t a n d a r d d e v i a t i o n o f 10.  C a l c u l a t i o n of T-scores score  i s achieved  ( z s c o r e ) by 10 a n d a d d i n g  by m u l t i p l y i n g a s t a n d a r d  50 t o t h e p r o d u c t .  The s h a p e  of t h e d i s t r i b u t i o n i s n o t changed w i t h t h e t r a n s f o r m e d scores. 8. STANDARD DEVIATION: " S t a n d a r d  D e v i a t i o n " i s a measure  of d i s p e r s i o n , s c a t t e r , h e t e r o g e n e i t y , o r v a r i a t i o n i n a s e t of d a t a .  A s e t of scores with great heterogeneity w i l l  some l a r g e d e v i a t i o n s c o r e s c a l c u l a t e d by f i r s t  (X.-X ).  Standard  summing t h e s q u a r e d  have  deviationi s  d e v i a t i o n s c o r e s and  t h e n d i v i d i n g t h e sum b y t h e number o f s c o r e s . root of the quotient i s the standard d e v i a t i o n .  The s q u a r e In this  s t u d y , t h e s t a n d a r d d e v i a t i o n i s d e n o t e d a s SD. 9. STANDARD SCORES:  "Standard  Scores"  c a n be u s e d t o  d e s c r i b e t h e p o s i t i o n o f a s c o r e i n a s e t o f s c o r e s by m e a s u r i n g i t s d e v i a t i o n f r o m t h e mean o f a l l s c o r e s i n standard d e v i a t i o n u n i t s .  A standard  score  (called a  z-score)  15  i s o b t a i n e d b y s u b t r a c t i n g t h e mean f r o m a n o b s e r v e d d i v i d i n g t h e d i f f e r e n c e by t h e s t a n d a r d d e v i a t i o n . and  standard d e v i a t i o n of the transformed  ( z - s c o r e s ) a r e 0 and 1 r e s p e c t i v e l y . d i f f e r e n c e between an i n d i v i d u a l  s c o r e and The mean  raw s c o r e s  I n t h i s way, t h e n , t h e  s c o r e a n d t h e mean s c o r e o f  the group, i s s c a l e d i n terms o f s t a n d a r d d e v i a t i o n u n i t s . This has t h e advantage i n t h a t a l l d e v i a t i o n scores a r e m e a s u r e d i n t h e same u n i t s . 10. courses term  TERM:  A "term"  i s an i n s t r u c t i o n a l p e r i o d where  c a n be o f f e r e d i n w h o l e o r i n p a r t .  The e n d o f e a c h  i s n o r m a l l y marked by t h e e v a l u a t i o n and r e p o r t i n g o f  student  achievement i n each o f t h e courses  period. Education  offered during that  I t i s s t i p u l a t e d by t h e B r i t i s h Columbia M i n i s t r y o f t h a t , f o r schools i n B r i t i s h Columbia, there w i l l  at least 3 reporting periods  ( o r terms) d u r i n g each  be  school  year. 11. WEIGHTING:  "Weighting"  r e f e r s t o t h e amount o f  i n f l u e n c e a p a r t i c u l a r e x e r c i s e o r assignment has i n determining  the t o t a l  score f o rthat subject.  e x e r c i s e m i g h t c o n t r i b u t e 20 p e r c e n t t o w a r d  F o r example, an the total  f o r t h e c o u r s e , m e a n i n g t h a t 20 p e r c e n t o f t h e t o t a l mark i s d e r i v e d f r o m t h a t p a r t i c u l a r a s s i g n m e n t . should normally r e f l e c t the importance on t h e o b j e c t i v e s c o v e r e d  mark course  Weighting  o r t h e emphasis p l a c e d  i n the assignment.  "NATURAL  WEIGHTING" r e f e r s t o t h e c o n t r i b u t i o n a n a s s i g n m e n t g i v e s t o t h e c o u r s e mark u s i n g o n l y r a w s c o r e d a t a .  In other  words,  for a given s e t of assignments i n a p a r t i c u l a r course,  each  16  assignment w i l l score.  c o n t r i b u t e a c e r t a i n percentage  The c o n t r i b u t i o n w i l l  of t h e raw s c o r e s . weighting".  Research  Questions  1.  by t h e v a r i a b i l i t y  T h i s raw s c o r e i n f l u e n c e i s c a l l e d  "natural  Specifically,  be d e t e r m i n e d  of the t o t a l  the questions of interest are:  I s t h e r e a 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  r a n k i n g o b t a i n e d from a teacher's course  r e c o r d and t h e  r a n k i n g o b t a i n e d from s t a t i s t i c a l l y b a l a n c i n g t h i s  same  record? 2.  Do a t e a c h e r ' s c o u r s e  assignments c o n t r i b u t e the  i n t e n d e d p o r t i o n o f marks towards t h e c o u r s e term  totals,  (Are the  from which t h e l e t t e r grades a r e d e r i v e d ,  c o l l a t e d and w e i g h t e d 3.  total?  reliably?)  Are t e a c h e r s ' grades r e l i a b l e  and f a i r  m i s s i n g one o r more a s s i g n m e n t s o r t e s t s ? compensated f a i r l y  f o r students  Are students  a n d r e l i a b l y when t h e y h a v e b e e n a b s e n t  and  h a v e n o t r e c e i v e d a s c o r e f o r one o r more a s s i g n m e n t s o r tests? 4.  Would t h e r e v i s e d r e s u l t s be o f s u c h a m a g n i t u d e t o  j u s t i f y t h e t i m e a n d e x p e n s e r e q u i r e d t o r e t r a i n t e a c h e r s and r e v i s e u n i v e r s i t y courses  and/or programs?  In t h i s study, t h e q u e s t i o n s of i n t e r e s t r e l a t e t o the  17  methods used by t e a c h e r s t o c o l l a t e a c h i e v e m e n t d a t a f o r r e p o r t i n g purposes.  The h y p o t h e s i s t o be t e s t e d i s t h a t  t e a c h e r s , f o r one r e a s o n o r a n o t h e r , do n o t c o l l a t e achievement scores r e l i a b l y .  I t i s assumed t h a t t e a c h e r s do  n o t c o n s i d e r t h e c a l c u l a t i o n o f c l a s s means o r s t a n d a r d d e v i a t i o n s when c o m b i n i n g  achievement s c o r e s .  As a r e s u l t ,  the assignment scores a r e c o n t r i b u t i n g d i s p r o p o r t i o n a t e weights  toward  the course t o t a l s .  I t i s hypothesized that the  m e t h o d m o s t commonly u s e d b y t e a c h e r s t o c o m b i n e c o u r s e  marks  i s s i m p l e summation o f t h e raw s c o r e s f o l l o w e d by r a n k i n g each student's t o t a l .  I t i s a l s o h y p o t h e s i z e d t h a t t h e summation  method o f r a n k i n g w i l l  be s i g n i f i c a n t l y d i f f e r e n t  r a n k i n g s o b t a i n e d from  s t a t i s t i c a l l y balanced  from  assignment  scores.  Rationale  P r i o r t o the i n t r o d u c t i o n o f the l e t t e r grade r e p o r t card f o r elementary  s c h o o l s i n 1979, e l e m e n t a r y  school report cards  w e r e p r i m a r i l y a n e c d o t a l , and a c h i e v e m e n t s y m b o l s  (Needs  Improvement, S a t i s f a t o r y , Good), were based l a r g e l y subjective evaluation. changed t o c o m p a r a t i v e  When t h e f o r m a t  upon  o f t h e r e p o r t was  a c h i e v e m e n t and l e t t e r grades  t o r e f l e c t t h i s a c h i e v e m e n t , t e a c h e r s were g i v e n v e r y i n - s e r v i c e t r a i n i n g on t h e new r e p o r t i n g p r o c e d u r e . British  were used little The  Columbia M i n i s t r y of Education d i d p u b l i s h b o o k l e t s  18  ( " C o n s t r u c t i o n and For Teachers" to  and  Uses o f C l a s s r o o m "Grading  T e s t s : A R e s o u r c e Book  P r a c t i c e s : I s s u e s and A l t e r n a t i v e s " )  a s s i s t teachers i n t h e i r e v a l u a t i o n of student  Although few  t h e s e b o o k l e t s w e r e made a v a i l a b l e ,  t e a c h e r s s t u d i e d them i n d e t a i l  report  i t appears t h a t  p r i o r t o using the  new  cards.  Consequently, of the importance aggregating  i t w o u l d seem t h a t few o f t h e mean and  assignment scores.  scores t o t a l  toward  absence of s t a t i s t i c a l  p a r t i a l l y due  the f i n a l  belief  t o a l a c k of time  course  a n a l y s i s and  h a v e b e e n p a r t i a l l y due  c a l c u l a t o r i s almost is still  M o s t t e a c h e r s use  o n l y the  raw  students. that  the  largest p o s s i b l e score should c o n t r i b u t e  the g r e a t e s t percentage  t h e p a s t may  aware  s t a n d a r d d e v i a t i o n when  seem t o f o l l o w t h e e r r o n e o u s  assignment w i t h the  The  teachers are  f o r determining the r a n k i n g of t h e i r  Many e d u c a t o r s  time  achievement.  and  mark.  'balancing' i n  to a lack of t r a i n i n g resources.  A  and  statistical  a n e c e s s i t y but a great deal of  teacher  r e q u i r e d t o c a l c u l a t e the s t a n d a r d i z e d  scores  t i m e t h a t some m i g h t f i n d d i f f i c u l t t o j u s t i f y  i n l i g h t of  many o t h e r p r o f e s s i o n a l c o m m i t m e n t s o f t e a c h e r s .  -  the  However,  w i t h the advent of the micro-computer, "mark-keeping" programs c a n be d e v i s e d t o t a k e t h e t i m e of the s t a t i s t i c a l  drudgery  out  b a l a n c i n g of student assignment scores.  E v e n s o , many t e a c h e r s  seem t o a b i d e by t h e i r p r e v i o u s l y  established grading practises. to  c o n s u m p t i o n and  They a r e n o t a w a r e o f t h e  need  c o n s i d e r the e f f e c t s of d i f f e r e n t v a r i a n c e s w i t h i n t h e i r  a s s i g n m e n t s c o r e s , and  t h e r e f o r e a r e o b l i v i o u s t o the need f o r  19  improved g r a d i n g p r a c t i s e s . and  states,  "The  Hills  (1981) s u p p o r t s  standard d e v i a t i o n . . .  t e a c h e r s would not t h i n k about w i t h o u t 319).  scores are c o l l a t e d ,  a l t e r n a t e and  It  notion  i s what most  some t r a i n i n g "  (p.  Perhaps i f t h e r e i s a p e r c e i v e d need f o r a change i n  t h e way  for  this  reporting  teachers w i l l  i m p r o v e d method o f c o m b i n i n g  i f a more e f f e c t i v e  s c o r e s i s n e e d e d and training  receptive to  students'  an  scores  purposes.  i s h o p e d t h a t t h e outcome o f t h i s  determine  be  study w i l l  help  method o f c o m b i n i n g  to  achievement  w h e t h e r more i n - s e r v i c e and p r e - s e r v i c e  i s r e q u i r e d t o improve the g r a d i n g p r a c t i s e s of  teachers.  Delimitations  For the purposes of t h i s at  s t u d y , t h e s a m p l e was  random f r o m t e a c h e r s o f g r a d e s f o u r t o s e v e n l e v e l  teach i n a l a r g e m e t r o p o l i t a n area of c e n t r a l Columbia. two  social  British  studies.  u s e d by t h e s a m p l e s u b j e c t s t o c o l l e c t  achievement d a t a were not e v a l u a t e d .  I t was  instruments  We  w e r e r e l i a b l e and  valid.  l e t t e r grade f o r each student or course  The student  assumed t h a t a l l  were i n t e r e s t e d  t h e c o m b i n e d t o t a l s c o r e f o r t h e t e r m and  of term  who  Examples o f t e a c h e r s ' r e c o r d s were s e l e c t e d from  s u b j e c t a r e a s : m a t h e m a t i c s and  instruments  in  selected  as d e t e r m i n e d  the  only  assigned  from the  collation  assignment scores.  T h i s s t u d y was  not concerned  w i t h the v a l i d i t y of  the  20  educational It  should  o b j e c t i v e s f o r each o f t h e two s u b j e c t s  be r e c o g n i z e d  that within the curriculum s t i p u l a t e d  by t h e P r o v i n c i a l M i n i s t r y o f E d u c a t i o n , flexibility  i s provided  considerable  t o elementary teachers.  s e l e c t from a v a r i e t y of content, techniques,  sampled.  media,  E d u c a t o r s may  pedagogical  and w h a t e v e r e l s e i s n e c e s s a r y ,  to f u l l f i l the  demands o f t h e c u r r i c u l u m a n d t h e n e e d s o f t h e s t u d e n t s most e f f e c t i v e manner. v a r y among t e a c h e r s  Consequently, the course  o f t h e same s u b j e c t .  o b j e c t i v e s may a l s o be t a u g h t flexibility  nullifies  elementary subjects  w i t h d i f f e r e n t emphases.  any o p p o r t u n i t y  marks.  As a  emphasis, and a p p r o p r i a t e w e i g h t i n g s  w e r e assumed t o be a p p r o p r i a t e  study.  of  They  f o r t h e grade l e v e l , the  and t h e c u r r i c u l u m .  Justification  of the Study  Why i s t h i s  issue important  achievement should  a c c u r a t e l y as p o s s i b l e . detrimental t o students.  i n education?  Firstly,  be r e p o r t e d a s r e l i a b l y a n d  "Faulty grading  c a n be s e r i o u s l y  I t c a n g i v e them  misleading  i n f o r m a t i o n and i n t e r f e r e w i t h t h e l e a r n i n g p r o c e s s " 1981,  This  t o "standardize"  the o b j e c t i v e s were o u t s i d e t h e scope o f t h i s  student  may  i n terms o f u n i t s , u n i t o b j e c t i v e s ,  the v a l i d i t y ,  students,  content  U n i t s and u n i t  a s s i g n m e n t s , and a s s i g n m e n t emphasis on c o u r s e result,  i n the  p. 2 8 1 ) . S e c o n d l y , p a r e n t s ,  (Hills,  p r o s p e c t i v e e m p l o y e r s , and  21  the students themselves  view r e p o r t c a r d grades as a c c u r a t e  i n d i c a t o r s o f s t u d e n t achievement and use t h e i n f o r m a t i o n as a basis f o r decision-making  and f o r e v a l u a t i n g p e o p l e .  u n r e l i a b l e o r i n a c c u r a t e g r a d e s may l e a d t o  Thirdly,  erroneous  decisions regarding b u r s a r i e s , s c h o l a r s h i p s , diplomas, o r o t h e r such awards based on g r a d e s .  More i m p o r t a n t l y ,  improper  a s s e s s m e n t o f s t u d e n t p e r f o r m a n c e may r e s u l t i n i n c o r r e c t decisions regarding a student's course.  In addition,  success  inaccurate grading  who w o u l d s t u d y t h e i n s t r u c t i o n a l hold i t accountable p.  281). A f i f t h  education  i n a particular  process  "can m i s l e a d  t o improve i t o r t o  t o the s o c i e t y that supports  r e a s o n why t h i s  it"  (Hills,  issue, i s important t o  i s due t o t h e f a c t t h a t t h e r e a r e many  misconceptions  a n d c o n f u s i o n s among e d u c a t o r s  c o n s t i t u t e s an e f f e c t i v e g r a d i n g p r o c e d u r e . supports  those  t h i s p e r c e p t i o n and s t a t e s ,  irrational  a s t o what Hills  also  " t h e r e a r e many  i d e a s a b o u t g r a d i n g t h a t seem s o u n d u n t i l  considered i n d e t a i l .  To a v o i d some o f t h e s e  they are  irrational  n o t i o n s , a t e a c h e r must l e a r n t o r e c o g n i z e what i s w r o n g w i t h them"  (p. 280).  The  implications of this  study p e r t a i n t o teacher  p r e - s e r v i c e and i n - s e r v i c e t r a i n i n g .  I f t h e samples o f  teacher grading p r a c t i s e s are s i g n i f i c a n t l y compared t o t h e s t a t i s t i c a l l y b a l a n c e d ( T - s c o r e s ) , t h e n i t may be p r u d e n t  inferior  when  and t r a n s f o r m e d  scores  t o examine t h e p r e - s e r v i c e  t r a i n i n g teachers receive i n e v a l u a t i n g student  performance  22  and  achievement.  I s t h i s an a r e a t h a t n e e d s more a t t e n t i o n i n  the p r e - s e r v i c e t r a i n i n g of t e a c h e r s ? make c o u r s e s  t h a t g r a d i n g p r a c t i s e s can  should school d i s t r i c t s develop  t o enhance t e a c h e r g r a d i n g p r a c t i s e s ? questions i f the r e s u l t s improved.  Many a u t h o r s r e f l e c t  procedures.  Hills  Grading pitfalls;  t o improve t h e i r  important  by  be  suggesting  states, T h e r e a r e many  on t h e a s s u m p t i o n  a pupil  the  teacher  t h a t what  was  i s s a t i s f a c t o r y f o r the  i n her c a r e .  j o b t h a n was  programs  grading  p r a c t i s e s a b o u n d ; and  s a f e l y proceed  s t u d e n t s now better  t h i s importance  i s a c o m p l i c a t e d problem.  done when she was  in-service  These a r e  (1981), f o r example,  erroneous  be  show t h a t g r a d i n g p r a c t i s e s c a n  that teachers should s t r i v e  cannot  universities  i n e v a l u a t i o n mandatory f o r s t u d e n t - t e a c h e r s ?  A l s o , i f i t i s apparent improved,  Should  Good t e a c h e r s w i l l  done f o r them a s p u p i l s ,  simply c a r r y i n g forward the mistakes  t r y t o do  a  r a t h e r than  of the p a s t .  (p.  280)  On  the o t h e r hand, i f the p r e s e n t g r a d i n g p r a c t i s e s  not s i g n i f i c a n t l y  i n f e r i o r and  as t h e s t a t i s t i c a l l y b a l a n c e d  a r e i n f a c t g e n e r a l l y as grades,  that teachers, s i m i l a r to those and  t h e n we  themselves  good  conclude  i n the sample, are e v a l u a t i n g  g r a d i n g student achievement e f f e c t i v e l y .  c a s e , t h e n u n i v e r s i t i e s and  can  are  If this  s c h o o l d i s t r i c t s need not  w i t h r e v i s i n g t h e i r p r e s e n t m e a s u r e m e n t and  e v a l u a t i o n components o r programs.  The  i s the concern student  i m p l i c a t i o n would  be  2.3  t h a t t h e t r a i n i n g t e a c h e r s r e c e i v e and t h e  evaluation  t e c h n i q u e s t e a c h e r s e m p l o y a r e b o t h a d e q u a t e and  reliable.  24  CHAPTER 2 Survey of t h e L i t e r a t u r e  From t h e r e v i e w o f t h e l i t e r a t u r e ,  t h e r e a p p e a r t o be  v e r y f e w e m p i r i c a l o r i n v e s t i g a t i v e s t u d i e s done t o a s s e s s t h e grading practises of teachers. of t h e o r e t i c a l  t h e r e i s an abundance  i n f o r m a t i o n o n how t e a c h e r s s h o u l d e v a l u a t e a n d  r e p o r t the achievement o f t h e i r has  Although  s t u d e n t s , i t seems t h a t no one  a c t u a l l y t r i e d t o f i n d out i f teachers are p u t t i n g theory  into practise.  Hills  (1981) r e i n f o r c e s t h i s f a c t when he  states, There i s l i t t l e  e m p i r i c a l r e s e a r c h on g r a d i n g .  some f a c t s a r e w e l l - e s t a b l i s h e d , little  study o f such  t h e r e has been f a r t o o  an i m p o r t a n t  e v e r y o n e seems t o f e e l  entitled  topic.  Therefore,  t o an o p i n i o n , a n d no  d a t a e x i s t t o r e f u t e m o s t o f them. S e v e r a l a u t h o r s , however, have s u g g e s t e d grading f o r special  Although  ( p . 317) i n n o v a t i v e methods o f  educational situations or f o r particular  courses.  F o r e x a m p l e , D a v i d Cohen (1973) d i s c u s s e s a means o f  improving  the evaluation of the Australian science curriculum.  Gensley  ( 1 9 6 9 ) p r o v i d e s an i n s i g h t i n t o a l t e r n a t e methods o f  evaluating alternate  "gifted children".  Many o t h e r w r i t e r s  forms o f e v a l u a t i o n f o r t h e i r p a r t i c u l a r  area o r f o r t h e i r p a r t i c u l a r s p e c i a l t y s i t u a t i o n . none o f t h e a u t h o r s  advocate subject However,  o f f e r any i n s i g h t i n t o t h e adequacy o f t h e  grading p r a c t i s e s of "regular" classroom  teachers.  Other w r i t e r s e i t h e r a t t a c k o r defend  t h e use o f l e t t e r  25  g r a d e s as a symbol Stewart  of student achievement.  (1975) condemns l e t t e r  For example,  g r a d e s and p r o f e s s e s a  W.J.  new  system f o r e v a l u a t i n g the " m u l t i - f a c e t e d academic-personals o c i a l growth of elementary s c h o o l s t u d e n t s " (p. 174).  He  s t a t e s t h a t one g r a d e d o e s n o t r e p r e s e n t a d e q u a t e l y t h e c o m p l e x i t y i n a c h i l d ' s academic, growth.  social,  and e m o t i o n a l  I n s t e a d , he recommends a m u l t i - d i m e n s i o n a l  system  t h a t w o u l d accommodate ( a ) a w i d e r a n g e o f g o a l s ,  (b)  u n i q u e n e s s o f e a c h s t u d e n t ' s a b i l i t i e s and n e e d s ,  ( c ) an  a c c o u n t f o r each c h i l d ' s need t o d e v e l o p a s e l f - c o n c e p t , and  positive  (d) a n e e d t o p r o v i d e p a r e n t s w i t h more  u s e f u l and more m e a n i n g f u l i n f o r m a t i o n r e g a r d i n g a progress. would  Stewart claims that h i s e v a l u a t i o n - r e p o r t i n g  de-emphasize  skill  and s u b j e c t m a t t e r m a s t e r y b u t  s t r e s s a c h i l d ' s a b i l i t y t o use s k i l l s d e a l i n g w i t h l i f e ' s d a i l y problems. system would  of the l e t t e r  would  His multi-dimensional  f o c u s o n l y u p o n i n d i v i d u a l s and w o u l d n o t  W h i l e S t e w a r t p o i n t s o u t what may  system  and s u b j e c t m a t t e r f o r  c o m p a r i s o n s w i t h o t h e r c l a s s members as do l e t t e r  weaknesses  child's  stress  grades.  be c o n s i d e r e d by some t o be  g r a d e s y s t e m , he d o e s n o t a d d r e s s  what t e a c h e r s a r e p r e s e n t l y d o i n g t o c o p e w i t h t h e p r o b l e m s identifies. new  He c i t e s no r e s e a r c h t o j u s t i f y h i s c l a i m t h a t a  system of " e v a l u a t i o n - r e p o r t i n g " Marshall  i s required.  (1971) a l s o c r i t i c i z e s t h e l e t t e r  He c l a i m s t h a t g r a d e s  ( o r any  "Grades  grade  system.  "codes w h i c h r e f e r t o r a n k ,  g r a d e , o r p o s i t i o n on a s c a l e " ) t e n d t o be v e r y He s t a t e s ,  he  s u r v i v e p r i m a r i l y because  subjective.  they provide  26  disguise.  A l m o s t a n y t h i n g can be,  L e t t e r grades meaningless" "individual and  i s , read i n t o  . . . are general terms, (p. 350).  in  them.  themselves  M a r s h a l l i n d i c a t e s the b e n e f i t s of  d e s c r i p t i v e or nongrading"  352).  He  new  "more  interests i n teaching"  a l s o s t a t e s t h a t " t e a c h e r s are employed  t e a c h , not t o grade or psychoanalyze" "A t e a c h e r  an  system of e v a l u a t i o n  r e p o r t i n g t h a t would i n c l u d e p r o v i d i n g teachers w i t h  t i m e , g r e a t e r f r e e d o m , and (p.  and  (p. 352).  s h o u l d w a n t , be  He  to  concludes  by  stating,  a l l o w e d , and  to  s a y what he o r she means, i n w o r d s s p e c i f i c a l l y p e r t i n e n t  to  a given i n q u i r y or s i t u a t i o n "  (p. 353).  be  As w i t h  M a r s h a l l makes no m e n t i o n o f t e a c h e r s ' c u r r e n t  asked  Stewart,  grading  practises. A third  c r i t i c i s m of the  Richard Curwin  (1978).  He  l e t t e r grade system i s s t a t e d  c l a i m s t h a t "grades d o n ' t work"  because they  lack accuracy,  reliability,  and  consistency, v a l i d i t y ,  predictability.  He  (Self-Grading, Contract Grading,  offers  four  Peer Grading,  Grading) t o "reduce the dangers of the g r a d i n g (p.  61).  Although  he  by  alternatives  and  Blanket  system"  states that "research studies  clearly  i n d i c a t e t h a t t e a c h e r s g r a d e t h e same s t u d e n t s ' w o r k differently" the nature  ( p . 6 0 ) , he d o e s n o t e l a b o r a t e on t h e f i n d i n g s o r of the r e s e a r c h .  alternatives traditional  "undoubtedly  He  will  grading systems"  e n d s by be  (p.  stating that  an i m p r o v e m e n t  the  over  64).  D e f e n d e r s o f l e t t e r g r a d e s as s y m b o l s o f  student  achievement take a stance o p p o s i t e t o the authors  mentioned  27  above.  Robert  L. E b e l  (1974),  f o r example, defends  a g a i n s t the c r i t i c i s m s o f t e n aimed a t g r a d i n g . g r a d i n g c a n be  improved.  "The  He  grades claims  remedy i s n o t t o g e t r i d o f  g r a d e s b u t s i m p l y t o do a b e t t e r j o b o f g r a d i n g "  (p. 3 ) .  i n d i c a t e s t h a t a l l a l t e r n a t i v e s t o the grade are l e s s e f f i c i e n t and statistic,  Although classroom  l e s s i n f o r m a t i v e than the  the  E b e l c i t e s no  research to demonstrate  assignment scores.  shows how  equating the v a r i a t i o n of  score v a r i a b i l i t y "  f o r example, s t a t e s ,  w e i g h t i n g v a r i a b l e s t h a t a r e t o be d e v i a t i o n of t h e i r v a l u e s " u s e s e x a m p l e s t o show how is essential  stating,  t h e use "Using  "Thus  (Ebel,  a l s o support  "The  key  this  the total  1972, notion.  element i n  combined i s the  (p. 320).  standard  Like Ebel, H i l l s  also  c a l c u l a t i n g the standard d e v i a t i o n  f o r accurate grading.  d e m o n s t r a t e s how  the  component on a c o m p o s i t e d e p e n d s n o t on  Many o t h e r g r a d e d e f e n d e r s  (1981),  By u s i n g a s a m p l e o f  l e a d to improved g r a d i n g .  p o i n t s o r mean s c o r e b u t on  without  how  aggregating  student  He,  he d o e s e l a b o r a t e on  c a l c u l a t i n g t h e s t a n d a r d d e v i a t i o n s when  i n f l u e n c e o f one  Hills  how  supporters,  v a r i o u s a s s i g n m e n t s can  350).  summary  l i k e many o t h e r g r a d e  weighting  improved.  s t u d e n t m a r k s , he  p.  cost  t e a c h e r s c o l l e c t a c h i e v e m e n t i n f o r m a t i o n upon w h i c h  g r a d e s c a n be  and  "familiar  He  grade."  t o base the assignment of grades,  advocates  that  With  c o n v e r s i o n c h a r t s , he  t h e s t a n d a r d d e v i a t i o n c a n be of a hand c a l c u l a t o r . these procedures  will  c r i t i c i s m t h a t grades are meaningless"  Hills  estimated  summarizes  by  help to e x t i n g u i s h the (p.  328).  28  Gronlund classrooms.  (1981) a l s o s u p p o r t s He  states,  the use  "When l e t t e r  of l e t t e r  grades are  grades i n  supplemented  by o t h e r m e t h o d s o f r e p o r t i n g , t h e s e g r a d e s t h e m s e l v e s more m e a n i n g f u l " d e m o n s t r a t e how and  (p. 520).  He  g r a d i n g c a n be  t o o u t i l i z e s an e x a m p l e t o i m p r o v e d by m a k i n g mean s c o r e s  s t a n d a r d d e v i a t i o n s e q u a l when c o m b i n i n g  scores.  He  a l s o expresses  d i s p e r s i o n of scores.  become  the importance  and w e i g h t i n g  of c o n s i d e r i n g the  "Thus, t o p r o p e r l y w e i g h t  the  components i n a c o m p o s i t e s c o r e , t h e v a r i a b i l i t y o f the must be  taken  i n t o account"  example, Gronlund  shows how  (p. 522).  all  the v a r i a b i l i t y  (a) by u s i n g t h e r a n g e o f s c o r e s ,  s e t s o f s c o r e s t o s t a n i n e s , and  scores  However, i n h i s i n each set of  a s s i g n m e n t s c o r e s c a n be e q u a t e d u s i n g t h r e e methods:  raw  different  (b) by  converting  ( c ) , t h e most  refined  s y s t e m , by u s i n g s t a n d a r d d e v i a t i o n s . Many o t h e r a u t h o r s , Townsend & B u r k e , 1975; support  t h e use  none c i t e  Guilford  of l e t t e r  reporting student importance  ( s u c h as Ahmann & G l o c k , & F r u c h t e r , 1973)  also  g r a d e s as a method o f g r a d i n g  achievement.  But, w h i l e a l l profess  of e q u a l i z i n g the v a r i a b i l i t y any  1981;  i n a set of  r e s e a r c h t h a t would i n d i c a t e whether or  t e a c h e r s c o l l a t e and  weight  scores properly.  None  P e r h a p s by i m p r o v i n g  o f g r a d i n g as s u g g e s t e d  by t h e d e f e n d i n g  controversy surrounding  the u s e f u l n e s s of the  a symbol of s t u d e n t  authors  achievement w i l l d i m i n i s h .  the  scores, not  indicate  whether or not p r a c t i s i n g t e a c h e r s a c t u a l l y c o n s i d e r variation i n their scores.  and  the  t h e methods the  letter  grade  as  29  Grading  Systems  Over the  l a s t f i f t y years,  made t o r e p l a c e  the  s e v e r a l a t t e m p t s have been  letter-grade evaluation  marking systems or t o a b o l i s h school  system w i t h  other  marks a l t o g e t h e r .  Curwin  ( 1 9 7 8 ) has  o u t l i n e d some o f t h e  possible alternatives to  evaluation  systems i n s c h o o l s .  Although these a l t e r n a t i v e s  have not  been p a r t i c u l a r l y p o p u l a r i n the  mentioned here to r e v e a l the to i n d i c a t e the v a r i o u s evaluation The  strengths  they  are  a v a i l a b l e to teachers  and  weaknesses of  each  f i r s t a l t e r n a t i v e Curwin o f f e r s i s c a l l e d  and  t h e i r own  In t h i s system, the  the data f o r the  grades.  As  teacher  s t u d e n t s t o use  supplies in  a variant to self grading,  can  a l s o g e n e r a t e t h e i r own  the  criteria  evaluation  remain w i t h i n the  criteria,  g u i d e l i n e s of the  the  assigning the as  students long  students are  encouraged to evaluate  l e a r n a b o u t t h e m s e l v e s and question  a system. the  the  evaluation maturity  r e l i a b i l i t y of the  appropriateness,  criteria  of the  as w e l l as  on  w o r k and However,  that thereby  critics  grades r e s u l t i n g from  reliability  such  i s dependent  and  v a l i d i t y of  the  responsibility  on  the and  students.  Another option Grading".  their abilities.  I t w o u l d seem t h a t t h e  suitability,  t h e i r own  as  course.  Curwin s t a t e s t h a t the main b e n e f i t of t h i s approach i s  may  and  system.  "Self-Grading". criteria  options  past,  a v a i l a b l e to teachers  is called  Although s i m i l a r to s e l f - g r a d i n g , t h i s  "Contract  system i s  30  more s t r u c t u r e d . agreeable  I t c e n t e r s around a c o n t r a c t t h a t i s  t o b o t h s t u d e n t and  teacher.  s t i p u l a t e s t h e w o r k t o be a c c o m p l i s h e d w i t h i n which  t h e work must be  the c o n t r a c t are:  The and  completed.  (1) c r i t e r i a  contract the time  The  frame  f o u r elements  f o r successful completion  of  t h e c o n t r a c t , (2) d a t a o r r e s u l t s o f work t h a t i n d i c a t e well  the c r i t e r i a  comparison  h a v e b e e n met,  b e t w e e n t h e d a t a and  p o i n t s ) earned.  A disadvantage  (3) an a n a l y s i s o f criteria,  and  p.  Another  difficulty  or  (4) g r a d e  Students  u n r e a l i s t i c g o a l s - - t o o h i g h o r t o o low" 62).  (Curwin,  1978,  i s t h a t students i n such a  a v o i d the spontaneous e x t e n s i o n of t h e i r  the l e t t e r  to  l e a r n i n g b e y o n d what  d e s c r i b e s "Peer grade system  Grading"  as a n o t h e r  of e v a l u a t i o n .  Upon  t h e c o n t r a c t , t h e g r o u p e v a l u a t e s i t s e l f and  r e c e i v e s t h e same g r o u p g r a d e .  The  alternative  completion  e a c h member  g r o u p s c a n be  formed  t h e b a s i s o f a s u b j e c t a r e a , a homogeneous a b i l i t y around a mutual i n t e r e s t . Students generated  Curwin  on  grouping,  claims,  o f t e n a r e i n s p i r e d t o l e a r n as e n e r g y through working  to  T h i s method u t i l i z e s  c o n t r a c t f o r m u l a t e d by a g r o u p o f s t u d e n t s .  or  system  written. Curwin  of  (or  might  t e n d t o do o n l y what i s s t i p u l a t e d i n t h e c o n t r a c t and  is  how  of c o n t r a c t grading i s t h a t  " t h e c o n t r a c t s s o m e t i m e s become i n f l e x i b l e . set  of  w i t h f r i e n d s and  is  peers  on  a  common p r o j e c t , b u t a n e g a t i v e a t t i t u d e by some s t u d e n t s c a n d r a g t h e r e s t o f t h e g r o u p down. work h a r d e r  t h a n o t h e r s , t h e y may  I f some s t u d e n t s  p e r c e i v e i t as  unfair  a  3 1  to  r e c e i v e t h e same g r a d e a s t h o s e who w o r k e d l e s s  (p.  hard,  62)  A f o u r t h a l t e r n a t i v e t o g r a d i n g i s r e f e r r e d t o as "Blanket Grading".  With  r e c e i v e s t h e same g r a d e some minimum s t a n d a r d the s p e c i f i e d  this  i s met.  T h o s e s t u d e n t s who do n o t r e a c h  (p. 6 4 ) . U n l i k e Curwin's  a l t e r n a t i v e s , Blanket Grading  other  r e q u i r e s a continuous  become a n e g a t i v e f e a t u r e o f t h i s a l t e r n a t i v e  Simply any  individually  as p a r t o f t h e r e g u l a r c l a s s a c t i v i t i e s .  s y s t e m a t i c and w e l l  i n a class  ( u s u a l l y a n A o r B) p r o v i d i n g t h a t  s t a n d a r d must n e g o t i a t e a g r a d e  with the teacher"  process  system, "each s t u d e n t  evaluation  This can  since a very  o r g a n i z e d e v a l u a t i o n system i s r e q u i r e d .  d e c l a r i n g t h a t everyone w i l l  r e c e i v e an A o r B w i t h o u t  o t h e r f o r m o f e v a l u a t i o n w o u l d p r o v e t o be c o u n t e r -  p r o d u c t i v e ; s t u d e n t s w o u l d be l e s s m o t i v a t e d their potential.  Another negative aspect  t o achieve t o  of Blanket  i s t h a t a d m i n i s t r a t o r s o f t e n have a d i f f i c u l t  time  Grading  accepting  t h i s s y s t e m o f g r a d i n g , e s p e c i a l l y when a d i s p r o p o r t i o n a t e number o f A's o r B's a r e g i v e n . can  cause t h e teacher  T h i s , a c c o r d i n g t o Curwin,  " p e r s o n a l o r p r o f e s s i o n a l harm"  (p.  64).  Curwin a l s o emphasizes t h a t t h i s approach t o g r a d i n g needs t o be v e r y t h o r o u g h l y e x p l a i n e d t o t h e a d m i n i s t r a t i o n a n d t o t h e students before being In  used.  reference t o these  four a l t e r n a t e grading  Curwin s t a t e s ,  " I f you use any o f t h e a l t e r n a t i v e s  here, you w i l l  a v o i d many  schemes, presented  (although not a l l ) o f the problems  intrinsic original  t o g r a d i n g , b u t you  still  on one  (p.  64).  t h e more p o p u l a r g r a d i n g s y s t e m s , m o s t a r e of three approaches:  (a) p e r c e n t  c r i t e r i o n - r e f e r e n c e d g r a d i n g , and E a c h has  been p o p u l a r  grading,  Percent Grading,  variations  (b)  (c) norm-referenced  i n t h e p a s t a s a method o f  grades i n the e d u c a t i o n a l  converted  itself  may  setting.  which i s c u r r e n t l y the  to a percent.  With  least popular  r e p r e s e n t the grade.  t h i s method, the  A n o t h e r method o f r e p o r t i n g p e r c e n t  convert a percentage may  t o a l e t t e r grade.  r e p r e s e n t s c o r e s r a n g i n g f r o m 80% Percent Grading  has  not gained  of the o b s c u r i t y of the grades. tells  l i t t l e more t h a n  answered c o r r e c t l y . student  such  percent  averaged  percent  to  "Mathematics  grading i s to  An A,  f o r example,  100%.  popularity mainly  A s c o r e o f 80%,  because  f o r example,  of the questions  were  S u c h a g r a d e d o e s n o t r e v e a l how  much a  l e a r n e d i n r e l a t i o n t o i n t e n d e d outcomes nor does i t  r e v e a l how With  80 p e r c e n t  of  For example, mathematics  m i g h t be r e p o r t e d on a r e p o r t c a r d a s s i m p l y 73%".  grading.  determining  the three b a s i c approaches, i n v o l v e s scores t h a t are and  the  p u r p o s e s o f g r a d e s -- e s p e c i a l l y t h e f u n c t i o n o f  supplying.information to parents"  Of  must meet some o f  he  compared t o the a c h i e v e m e n t of o t h e r  grades i t i s d i f f i c u l t  t o determine  represents e x c e p t i o n a l , average,  If  i t i s the h i g h e s t score, then  it  i s n e a r t h e mean o r m e d i a n s c o r e , t h e n  students.  i f the  80  or poor achievement.  i t i s a v e r y good s c o r e . i t i s only  If  average,  33  and  i f i t i s one o f t h e l o w e s t s c o r e s , t h e n i t r e p r e s e n t s  achievement. achievement  I t i s impossible to t e l l  poor  what l e v e l o f  80 p e r c e n t a c t u a l l y r e p r e s e n t s .  A l t h o u g h p e r c e n t g r a d i n g was o n c e a p o p u l a r method o f g r a d i n g , i t has l o s t i t s a p p e a l major systems, norm-referenced  i n f a v o r o f t h e o t h e r two  n a m e l y t h e c r i t e r i o n - r e f e r e n c e d and approaches  Criterion-referenced  to grading.  grading  Criterion-referenced grading involves expressing a student's achievement  i n r e l a t i o n t o some p r e s p e c i f i e d  standards or c r i t e r i a .  These s t a n d a r d s a r e u s u a l l y  w i t h t h e l e v e l o f mastery  concerned  t o be a c h i e v e d b y t h e s t u d e n t s a n d  a r e o f t e n s t a t e d i n t e r m s o f : ( a ) t h e s p e c i f i c t a s k s t o be performed,  and (b) t h e p e r c e n t a g e  o f c o r r e c t a n s w e r s t o be  o b t a i n e d on a t e s t t h a t measures a c l e a r l y d e f i n e d s e t o f learning objectives.  As a r e s u l t ,  these standards are  a b s o l u t e and a r e n o t r e l a t i v e t o o t h e r s t u d e n t s o r t o p r e v i o u s i n d i v i d u a l achievement. level  o r master  A l l s t u d e n t s who a c h i e v e a t t h e same  t h e same o b j e c t i v e s a c h i e v e t h e same  "No s t u d e n t i s f a i l e d  grade.  s i m p l y b e c a u s e he o r s h e a c h i e v e d  lower  than other students provided the student achieves the criterion"  ( G r a y , 1 9 8 0 , p. 4 9 0 ) . G r a d i n g i n t h e  c r i t e r i o n - r e f e r e n c e d system methods.  i s s i m p l e r t h a n many o t h e r g r a d i n g  T h o s e who r e a c h t h e s p e c i f i e d c r i t e r i o n o n e a c h  l e a r n i n g o b j e c t i v e r e c e i v e c r e d i t , a n d t h o s e who do n o t ,  fail.  34  Failure to s a t i s f y student  repeat  the  c r i t e r i o n may  the r e q u i r e d t a s k s  been a c h i e v e d .  until  the  the o b j e c t i v e s have  Consequently, nearly a l l students  c r i t e r i o n - r e f e r e n c e d system The  also necessitate that  in  the  with  the  pass.  c r i t e r i o n - r e f e r e n c e d grading  technique  m a s t e r y l e a r n i n g a p p r o a c h , makes i t r e l a t i v e l y e a s y f o r teachers  to i d e n t i f y problem areas i n t h e i r  i d e n t i f y weaknesses w i t h i n i n d i v i d u a l Criterion-referenced tests, students  had  difficulty  which o b j e c t i v e s . by  a majority  will  a l s o be  ( G r a y , p.  opportunity the  of s t u d e n t s  students  490).  and  do  not  get  f a r t h e r and  sooner than others.  level  with grasped  retaught  quickly  f a r t h e r behind "  system are p e r m i t t e d  a t t h e i r own  o f p e r f o r m a n c e on  the  l e v e l s - some w i l l  However, by  will  to  which  t o meet c r i t e r i o n )  "Thus, d e f i c i e n c i e s a r e  c o u r s e o r t e r m , most s t u d e n t s acceptable  reveal  t h e r e f o r e n e e d t o be  Students i n t h i s  to progress  criterion  f o r example, w i l l  (or f a i l e d  and  students.  Those o b j e c t i v e s t h a t were p o o r l y  revealed.  c o r r e c t e d and  curriculum  meet  t h e end  have d e m o n s t r a t e d the r e q u i r e d  of  the  an  learning  objectives. Gronlund level  (1981) s t a t e s , "To  o f a c h i e v e m e n t as a b a s i s f o r g r a d i n g  the domain of  l e a r n i n g t a s k s be  s t a n d a r d s o f p e r f o r m a n c e be and  e f f e c t i v e l y use  s p e c i f i e d and  (3) t h e m e a s u r e s o f p u p i l a c h i e v e m e n t be  referenced"  (p. 524).  easy t o s a t i s f y  requires that  clearly defined,  clearly  absolute  (2)  (1)  the  justified,  criterion  While these c o n d i t i o n s are  relatively  i n t h e m a s t e r y a p p r o a c h , t h e y become  very  difficult  t o a p p l y t o nonmastery  prompts Gronlund t o s t a t e ,  learning objectives.  "The c r i t e r i o n - r e f e r e n c e d  g r a d i n g i s much more c o m p l e x t h a n i t f i r s t Because  i n c l u d e both mastery  elementary teacher w i l l  setting the c r i t e r i a objectives. (1980)  in  a c u r r i c u l u m g u i d e , because (p. 491). Gronlund  judgments  are " l i k e l y  some unknown d e g r e e . judging achievement  Gray  t o defend such standards  t h e y a r e based p r i m a r i l y on (1981)  claims that  these  t o be c o n t a m i n a t e d by a c h i e v e m e n t s t o Thus, t h e l a c k o f r e l i a b l i l i t y i n  i n r e l a t i o n t o p o t e n t i a l , and i n j u d g i n g  improvement, would  demonstrated  with a l l  i f t h e y h a v e b e e n s e t by c u r r i c u l u m e x p e r t s  judgment"  dependability"  objectives,  are established,  "it i s difficult  p a r e n t s , even  result  i n grades o f low  (p. 524). This i s very s i g n i f i c a n t  since  improvement and l e a r n i n g p o t e n t i a l have been  w i d e l y used as a b a s i s f o r g r a d i n g t h e nonmastery  components  t h e c r i t e r i o n - r e f e r e n c e d g r a d i n g system i n elementary  schools.  I t i s a l s o i n t e r e s t i n g t o n o t e t h a t when r e p o r t i n g  student achievement  on n o n m a s t e r y  o b j e c t i v e s , rank o r d e r bas  on s c o r e s o r o n number o f o b j e c t i v e s c o m p l e t e d to  ( p . 524)  difficulty  f o r a c c e p t a b l e performance  E v e n when t h e c r i t e r i a  claims that  degree.of  and n o n m a s t e r y  have c o n s i d e r a b l e  to  of  system  most e d u c a t i o n a l programs i n t h e e l e m e n t a r y s c h o o l  setting will the  appears"  This  i s often  used  p r o v i d e some m e a s u r e o f r e l a t i v e p o s i t i o n w i t h i n t h e c l a s  Rank a n d r e l a t i v e p o s i t i o n a r e t e r m s t h a t c o n n o t e t h e norm-referenced  approach  t o grading student  achievement.  36  Norm-referenced  grading  Traditionally  norm-referenced grading  common a p p r o a c h t o g r a d i n g  i n education.  ordering  s t u d e n t s and e x p r e s s i n g  relation  t o the achievement  criterion-referenced  of h i s class-mates.  grading,  In  the r e l a t i v e  t h e extreme  s c o r e s and the  position  ranks high relative  grades.  s t u d e n t w i l l - do b e t t e r  a  class.  r e c e i v e A's  i s more c h a r a c t e r i s t i c of  several  available  receive  class  and  variations  i f a student  a high grade.  receive  the  by b o t h h i s p e r f o r m a n c e Consequently, a  and  by  particular  class  than i n a  high  t h e n o r m - r e f e r e n c e d a p p r o a c h assumes o f s t u d e n t s , most  average achievement. and a few w i l l  o f normal  fail.  A  However,  curve g r a d i n g , which  to teachers. i s the extreme  form of  will  few  of the norm-referenced technique  Normal c u r v e g r a d i n g  If his  a low g r a d e .  achievement,  i n the p o p u l a t i o n  a grade i n d i c a t i n g  students w i l l  the  i s used t o determine  i n a low a c h i e v i n g  Because  normal d i s t r i b u t i o n  receive  class.  F o r example,  i s b a s e d on r e l a t i v e  performance of the group.  achieving  that  i s low, he w i l l  s t u d e n t s ' grades are i n f l u e n c e d the  the  Assignments  i n t h e g r o u p , he w i l l  Since the grading  achieved; i t only  within  variablility  of f i n a l  achievement  not  a r e d e s i g n e d t o produce a wide range of  i t i s this  distribution  Unlike  form of norm-referenced g r a d i n g ,  tests  rank  a n o r m - r e f e r e n c e d g r a d e does  s e r v e s as t h e n o r m a t i v e g r o u p . norm-referenced  It involves  each s t u d e n t ' s achievement i n  i n d i c a t e what a s t u d e n t has a c t u a l l y describes  has been t h e most  this  i s one  37  norm-referenced grading. of  In t h i s  s t u d e n t s r e c e i v e each grade.  distribution  i n this  system, a f i x e d A commonly u s e d  percentage grade  s y s t e m a s s i g n s t h e t o p 5% a n A, t h e n e x t  24% a B, t h e m i d d l e 40% a C, t h e n e x t 24% a D, a n d t h e l o w e s t 7% a f a i l i n g  grade  ( G r a y , 1 9 8 0 , p. 4 8 8 ) . A w e a k n e s s w i t h  a p p r o a c h i s t h a t some s t u d e n t s must r e c e i v e f a i l i n g regardless of t h e i r  levels  of achievement.  this  grades  F o r example, a  s t u d e n t who a c h i e v e s a s c o r e o f 70% may r e c e i v e a  failing  g r a d e i f h i s s c o r e i s one o f t h e l o w e s t i n t h e g r o u p .  On t h e  o t h e r h a n d , i f 70% r e p r e s e n t e d a h i g h s c o r e , t h e n t h e s t u d e n t would r e c e i v e a h i g h grade.  A n o t h e r w e a k n e s s i s t h a t t h e same  g r a d e d o e s n o t n e c e s s a r i l y r e p r e s e n t t h e same l e v e l o f achievement.  I n one c l a s s ,  a B; i n a n o t h e r c l a s s ,  the  derelicts,  Many s t o r i e s  have been t o l d  n o r m a l c u r v e g r a d i n g was u s e d . fillers"  allow the rest stories  i n c o u r s e s where  g r a d e s and t h e r e b y  o f the s t u d e n t s t o pass t h e course.  grading"  t o norm-referenced grading i s  ( G r a y , 1 9 8 0 , p. 4 8 8 ) . T h i s s y s t e m h a s  o n l y two p o s s i b l e g r a d e s ; e i t h e r who a c h i e v e s a t a l e v e l  Pass o r F a i l .  Any s t u d e n t  t h a t i s a t o r a b o v e t h e minimum  acceptable s t a n d a r d , r e c e i v e s the "Pass" grade. behind t h i s  These  t h e weaknesses o f normal curve g r a d i n g .  Another v a r i a t i o n "Pass-Fail  story,  The t h e o r y was t h a t t h e s e  would absorb t h e f a i l i n g  highlight  how  a n d i n one A m e r i c a n a i r f o r c e  s t u d e n t s ' w i v e s were p e r s u a d e d t o e n r o l l  "class  yield  t h e same a c h i e v e m e n t m i g h t be  e q u i v a l e n t t o a C o r a D. non-academics,  a s t u d e n t ' s a c h i e v e m e n t may  The  rationale  type o f g r a d i n g i s t h a t such a system takes t h e  38  pressure  o f f students  might n o r m a l l y  and  a v o i d due  e n c o u r a g e s them t o t a k e to f e a r of r e c e i v i n g  However, s t u d i e s have shown t h a t s t u d e n t s motivated  t o do  approach. the  their  best  "Thus, p a s s - f a i l  grading  (Gray,  . . .  1980,  p.  In g e n e r a l  converting  standardized assigning  variation  score grading".  raw  scores  s c o r e s between 5 5 and  main a d v a n t a g e o f t h i s  important in  a way  various  can  This technique  the  be  65  (Gray,  1980,  "we  score grading  and  t h e .T s c o r e s .  different  489).  considered  of equal  weight to each of the combining  the  scores.  For  s o on.  combine  fact  degrees  that  A The  can w e i g h t  and  to  assignments  marks.  to assign a d e s i r e d  c o n t r i b u t i n g assignments However,  the  assignments  i m p o r t a n c e when c o m b i n i n g teachers  scores  of  Another advantage  i s that teachers  allows  and  T h i s i s an  can m e a n i n g f u l l y  Seldom a r e a l l t e s t s  score grading  T scores  above m i g h t r e c e i v e an  differentially. t o be  the  to  system i s t h a t a r i t h m e t i c  had p.  grading  involves  6 4 m i g h t r e c e i v e a B and  p e r f o r m e d on  contributing tests  Standard  discouraged"  or assignment  t h a t a d j u s t s a p p r o p r i a t e l y f o r the  standard  of  and  average T score value.  grading  f e a t u r e because  variability"  any  to norm-referenced  z scores, or T scores, averaging  g r a d e s b a s e d on  operations  less  fulfill  be  grade.  pass-fail  motivation,  should  from each t e s t  example, a v e r a g e T s c o r e s o f and  t o be  they  489).  A more s a t i s f a c t o r y "standard  tend  does n o t  i t s use  a lower  u s i n g the  purposes of g r a d e s — c o m m u n i c a t i o n ,  prediction.  is  i n courses  courses  before  "Good judgment has  to  enter  39  i n t o the grading process. that norm-referenced  . . . The  p o i n t t o keep i n mind i s  g r a d i n g s i m p l y rank o r d e r s the  students;  it  i n d i c a t e s n o t h i n g about a c t u a l l e v e l of achievement"  p.  490). One  of the major c r i t i c i s m s of the extreme form of  norm-referenced  grading i s the f a c t t h a t a f i x e d percentage  students r e c e i v e each grade.  As  i m p l i e s t h a t a small percentage receive f a i l i n g achievement. British  (Gray,  grades,  variation standard  of students w i l l  always  levels  of  However, t o o v e r c o m e t h e n e g a t i v e a s p e c t s , of Education  to norm-referenced  I t suggests  another of  score g r a d i n g but w i t h a grade d i s t r i b u t i o n based  on  establishing  grading.  (1979) o f f e r s  the  t h e use  student a b i l i t y  different  stated previously, this  r e g a r d l e s s of the  Columbia M i n i s t r y  of  r a t h e r t h a n on a n o r m a l c u r v e .  t h e g r a d e d i s t r i b u t i o n makes t h i s  The  methods o f  approach  from t h e o t h e r methods o f n o r m - r e f e r e n c e d  grading  already mentioned. Essentially,  an a b i l i t y - b a s e d  g r a d i n g d i s t r i b u t i o n means  t h a t the grade d i s t r i b u t i o n f o r a g i v e n c l a s s ability  l e v e l s of the students  p r o p o r t i o n of d i f f e r e n t the a b i l i t y Ministry  l e v e l s w i t h i n the group"  that, for a particular g i v e n a t one  i n that particular  grades assigned  o f E d u c a t i o n , p.  l e v e l than  26).  class, i n any  (British  Therefore, a larger other.  the  class.  i s predetermined  "The by  Columbia  i t i s possible  number o f g r a d e s may Some d i s t r i b u t i o n s  h a v e l e v e l s w h e r e no g r a d e s a r e a w a r d e d . ability-based  reflects  To c r e a t e s u c h  d i s t r i b u t i o n r e q u i r e s the e s t i m a t i o n of  the  be may  an  40  general a b i l i t y the necessary  level  of students w i t h i n the c l a s s .  i n f o r m a t i o n c a n be o b t a i n e d f r o m s t a n d a r d i z e d  achievement t e s t scores or from g e n e r a l a b i l i t y both.  I n f o r m a t i o n on  student  ability  from p a s t performance r e c o r d s , such or school records.  tests,  c a n a l s o be  obtained  f o r each c l a s s .  students  cards  grading It is  t o p o i n t out t h a t the grades or p e r c e n t i l e  assigned to i n d i v i d u a l  or  as p r e v i o u s r e p o r t  Using t h i s i n f o r m a t i o n , a  d i s t r i b u t i o n c a n be d e t e r m i n e d important  Normally,  rankings  d u r i n g the e s t i m a t i o n  process  a r e n o t t o be c o n s i d e r e d a s e x p e c t a t i o n l e v e l s f o r t h e students A's  may  so c a t e g o r i z e d .  F o r e x a m p l e , s t u d e n t s who  n o t be t h e same s t u d e n t s who  p e r c e n t i l e on t h e s t a n d a r d i z e d While standard  t h e use  receive  s c o r e d above the  96  test.  of T scores m a i n t a i n s  the advantages  s c o r e g r a d i n g , a g r a d e d i s t r i b u t i o n b a s e d on  a b i l i t y overcomes the problems of p r e d e t e r m i n e d These methods, combined w i t h t h e use the d i s t r i b u t i o n of c o l l a t e d  of  of  student  failures.  "natural breaks"  scores to determine  letter  in grade  c u t - o f f p o i n t s , " o f f e r s a very s a t i s f a c t o r y approach to  the  assignment of l e t t e r grades"  of  E d u c a t i o n , p.  27).  grading procedure involved i n this  ( B r i t i s h Columbia M i n i s t r y  T h i s v a r i a n t t o the has  b e e n a d o p t e d by t h e s c h o o l  district  study.  There are s e v e r a l reasons a p p r o a c h t o g r a d i n g has  why  the  r e m a i n e d one  methods o f e v a l u a t i n g and Firstly,  norm-referenced  norm-referenced  o f t h e most  grading student  popular  achievement.  g r a d e s b a s e d on r e l a t i v e a c h i e v e m e n t a p p e a r t o  be  41  more r e a d i l y u n d e r s t o o d  by p a r e n t s , a d m i n i s t r a t o r s ,  p r o s p e c t i v e e m p l o y e r s , a n d o t h e r s who h a v e a n i n t e r e s t i n student  achievement.  R e l a t i v e p o s i t i o n i n a group o r c l a s s ,  as i n d i c a t e d b y t h e l e t t e r g r a d e , c a n be c o m p r e h e n d e d q u i c k l y and  easily.  Very l i t t l e  i n f o r m a t i o n n e e d s t o accompany t h e  l e t t e r g r a d e t o e x p l a i n i t s m e a n i n g ; due t o i t s f r e q u e n t u s e and  familiarity  i t i s a l m o s t common k n o w l e d g e t h a t an A  r e p r e s e n t s o u t s t a n d i n g work w h i l e a D o r E i n d i c a t e s t h a t t h e student  has e x p e r i e n c e d  considerable d i f f i c u l t y .  grading  systems r e q u i r e c h e c k l i s t s o r g r a d i n g  Other  criteria to  p r o v i d e meaning t o t h e l e t t e r grades.  These l i s t s  i n t e r p r e t e d and u n d e r s t o o d  before  v a l u e c a n be d e r i v e d  from t h e a s s o c i a t e d l e t t e r  grade.  Secondly,  parents  full  g e n e r a l l y a r e i n t e r e s t e d i n k n o w i n g how  w e l l t h e i r c h i l d performed r e l a t i v e t o the others class.  n e e d t o be  The c o m p e t i t i v e n a t u r e  of people,  d r i v e s them t o "keep up w i t h t h e J o n e s " ,  i n the  t h e same s o r t t h a t e m e r g e s when  d i s c u s s i n g t h e i r c h i l d ' s academic achievement.  F o r example,  t h e y m i g h t want t o know i f t h e i r c h i l d ' s A was a h i g h A o r a low A o r how many o t h e r s  i n t h e c l a s s r e c e i v e d an A.  People  o f t e n a p p e a r t o u s e r e l a t i v e p o s i t i o n a s an i n d i c a t o r o f s u c c e s s , w h e t h e r i t be i n b u s i n e s s , education.  industry, s o c i e t y , or  The f u r t h e r up t h e r a n k i n g s c a l e a p e r s o n i s t h e  more s u c c e s s f u l he i s p e r c e i v e d t o b e . A t h i r d reason  why n o r m - r e f e r e n c e d g r a d i n g m e t h o d s h a v e  b e e n more common i s due t o t h e p r e d i c t i v e q u a l i t i e s o f t h i s grading  system.  Many o f t h e u s e s o f g r a d e s a r e p r e d i c t i v e i n  42  nature.  F o r example,  abilities  e m p l o y e r s want t o be a b l e t o p r e d i c t  and s u c c e s s o f t h e s t u d e n t s t h e y h i r e .  Colleges  u n i v e r s i t i e s use grades t o p r e d i c t the s u c c e s s of applicants.  " I f a l l students r e c e i v e d n o t h i n g but  g r a d e s , i t w o u l d be v e r y d i f f i c u l t p e r s o n n e l , f o r example, all  Because  coefficient  their pass-fail  t o s e l e c t f r o m among a p p l i c a n t s (Gray,  of scores, the  since  1980,  the norm-referenced system attemps  p r o d u c e maximum v a r i a b i l i t y  and  f o r college admissions  a p p l i c a n t s w o u l d h a v e t h e same g r a d e s "  p. 4 8 9 ) .  the  to  correlation  i s e n h a n c e d and becomes more u s e f u l  for prediction  purposes than c o e f f i c i e n t s d e r i v e d from o t h e r g r a d i n g systems. A f o u r t h r e a s o n why  n o r m - r e f e r e n c e d g r a d i n g has  m a i n t a i n e d i t s p o p u l a r i t y i s due  t o the r e l a t i v e ease  s e t t i n g s t a n d a r d s and g r a d e d i s t r i b u t i o n s . i n s t i t u t i o n s u s i n g the extreme g r a d i n g , the normal distribution.  For  of  educational  form of norm-referenced  curve i s used t o e s t a b l i s h the  I n t h i s c a s e , t h e s t a n d a r d s and  grade  grade  d i s t r i b u t i o n s between v a r i o u s c l a s s e s o r c o u r s e s remain s i m i l a r regardless of course content or student levels.  ability  Consequently, the norm-referenced g r a d i n g system i s  e a s i e r t o a d m i n i s t e r and t o a p p l y .  Once t h e f i n a l  score  r a n k i n g has b e e n a c h i e v e d , t h e number o f g r a d e s t o be a t each  level  c a n be e a s i l y d e t e r m i n e d .  Even t h e  variations  o f n o r m - r e f e r e n c e d g r a d i n g , t h o s e t h a t do n o t s t r i c t l y to the normal curve d i s t r i b u t i o n ,  allotted  adhere  a r e more e a s i l y a d m i n i s t e r e d  t h a n most o f t h e o t h e r g r a d i n g t e c h n i q u e s . disadvantages of the c r i t e r i o n - r e f e r e n c e d  One  of t h e main  systems, f o r  43  example, i s the d i f f i c u l t y  of formulating the c r i t e r i o n  standards f o r a c c e p t a b l e performance.  and  With a norm-referenced  a p p r o a c h , t h e s e t a s k s a r e much s i m p l e r ; t h e a d m i n i s t r a t i o n o f g r a d e s i s more m e c h a n i c a l and m a t h e m a t i c a l , r e q u i r i n g t i m e and  less  judgment from t h e t e a c h e r .  Another reason f o r the p o p u l a r i t y of norm-referenced approaches  i s due  to the m o t i v a t i o n a l aspects.  One  of the  main p u r p o s e s of grades i s t o m o t i v a t e s t u d e n t s t o p e r f o r m as close to their potential  as p o s s i b l e .  Norm-referenced grading  has b e e n shown t o m o t i v a t e s t u d e n t s more e f f e c t i v e l y t h a n most o t h e r m e t h o d s o f g r a d i n g .  For example,  c r i t e r i o n - r e f e r e n c e d approaches  to grading create  motivation i n students. were p a s s - f a i l , achievement)  Gray  (1980) s t a t e s ,  student motivation  (and  systems  less a l l courses  subsequent  would decrease a c r o s s the board"  Norm-referenced  "if  do  c a n c a p i t a l i z e on t h e  (p. 492). competitive  n a t u r e o f s t u d e n t s and m o t i v a t e them t o do t h e i r  best.  In B r i t i s h Columbia, the M i n i s t r y of Education s t i p u l a t e d t h a t a l l p u b l i c s c h o o l s would w i t h a seven l e v e l twelve.  report comparative  achievement  l e t t e r grade system i n grades f o u r t o  T h i s d e c i s i o n was  b a s e d on t h e r e s u l t s o f a s u r v e y  c o n d u c t e d by t h e M i n i s t r y i n t h e l a t e  1970s.  T h i s method o f  r e p o r t i n g n e c e s s i t a t e d t h e u s e o f some f o r m o f n o r m - r e f e r e n c e d g r a d i n g procedure w i t h i n the school system.  B o o k l e t s were  p u b l i s h e d by t h e M i n i s t r y t o p r o v i d e g u i d e l i n e s and t o a s s i s t teachers i n u t i l i z i n g  norm-referenced techniques i n t h e i r  classrooms.  The  r e p o r t i n g and  g r a d i n g methods used i n t h e  elementary schools of the school d i s t r i c t s t u d y f o l l o w t h e s e g u i d e l i n e s and this  study.  involved i n this  are o u t l i n e d i n chapter  3  45  CHAPTER 3 Methodology  I t was  the purpose of t h i s  m e t h o d s u s e d by  37 randomly s e l e c t e d t e a c h e r s .  t h e i r methods o f g r a d i n g was way  collected  o f a q u e s t i o n n a i r e , (b) by h a v i n g  total, and  study t o e v a l u a t e the  and  rank  social  The female  the s u b j e c t s  scores, and  reporting period.  s a m p l e was  s e l e c t e d a t random f r o m a l i s t  of male  s e l e c t e d c o n s i s t e d o f t e a c h e r s who schools.  t e a c h at the  At t h i s  level,  in  Columbia.  a c c e s s i b l e p o p u l a t i o n from w h i c h the sample  i n elementary  and  t e a c h a t the grades f o u r t o seven l e v e l  a l a r g e m e t r o p o l i t a n area of c e n t r a l B r i t i s h  level  by  weight,  achievement  f o r one  on  Population  t e a c h e r s who  The  (a)  the s u b j e c t s submit t h e i r mathematics  s t u d i e s c l a s s record sheets  Sample and  Information  i n t h r e e ways:  a h y p o t h e t i c a l s e t o f raw  ( c ) by h a v i n g  grading  was  intermediate  teachers  c u s t o m a r i l y teach a l l of the M i n i s t r y p r e s c r i b e d s u b j e c t s t o one  class.  The  s i z e s o f most e l e m e n t a r y  n o r m a l l y range from twenty f i v e t o t h i r t y  school classes students.  Teachers  are r e s p o n s i b l e f o r a d m i n i s t e r i n g the p r e s c r i b e d c u r r i c u l a , and  f o r m e a s u r i n g , e v a l u a t i n g , g r a d i n g , and  achievement. instruments assignments.  In the elementary  r e p o r t i n g student  school s e t t i n g ,  measurement  c o n s i s t p r i m a r i l y o f t e a c h e r made t e s t s  and  46  Questionnaire A q u e s t i o n n a i r e was g i v e n t o e a c h member o f t h e s a m p l e o f teachers  i n order  t o g a i n some i n s i g h t i n t o t h e i r  experience,  t h e i r knowledge  for grading  p u r p o s e s , and t h e i r k n o w l e d g e  (particularly  standard  of c o l l a t i n g  achievement of basic  scores  statistics  d e v i a t i o n ) . A L i k e r t - t y p e s c a l e was  u s e d f o r some q u e s t i o n n a i r e  items  and t h e c l o s e d f o r m f o r m a t  was u s e d t o o b t a i n t h e d e m o g r a p h i c information  teaching  (Appendix A ) .  and g r a d i n g  Such q u e s t i o n s  procedure  as t h e f o l l o w i n g  were a s k e d : 1. My c o l l e a g u e s  a t t h i s school  t a k e r e p o r t c a r d marks  seriously. 2. L e t t e r g r a d e s a r e an e f f e c t i v e m e t h o d o f i n f o r m i n g parents  of t h e i r c h i l d ' s progress  and a c h i e v e m e n t .  3. To t h e b e s t o f my k n o w l e d g e ,  parents  are generally  s a t i s f i e d w i t h t h e l e t t e r grade system of r e p o r t i n g . 4. I f e e l v e r y award  comfortable  w i t h the l e t t e r grades I  students. 5. I am c o n f i d e n t t h a t t h e l e t t e r g r a d e s I a s s i g n a r e  accurate  and r e l i a b l e .  6. I w o u l d assigning  l i k e t o l e a r n more a b o u t c o l l a t i n g a n d  l e t t e r g r a d e s t o raw s c o r e s .  7. More i n - s e r v i c e s e s s i o n s on g r a d i n g should  and r e p o r t i n g  be o f f e r e d . 8. U n i v e r s i t i e s s h o u l d  instruction  o f f e r more p r e - s e r v i c e  i n e f f e c t i v e grading  and r e p o r t i n g .  9. The r e p o r t c a r d f o r m a t a l l o w s  sufficient  information  t o be c o m m u n i c a t e d t o p a r e n t s , s t u d e n t s , e t c . 10. I n . t h e s p a c e p r o v i d e d , b r i e f l y d e s c r i b e how  you  c o m b i n e a s s i g n m e n t and t e s t s c o r e s t o d e t e r m i n e l e t t e r 11. I n r e f e r e n c e t o t h e method d e s c r i b e d i n #10, o t h e r s u b j e c t s a r e a l s o g r a d e d t h i s way? ( a l l mathematics,  lanauaae a r t s ,  P.E.,  French)  music,  science, social  studies, a r t ,  t e r m s c o r e f o r a s t u d e n t who  f o r one o r more t e s t s o r a s s i g n m e n t s .  you  has been a b s e n t  In o t h e r words,  you c o m p e n s a t e f o r a l e g i t i m a t e l y m i s s e d  how  do  assignment?  The q u e s t i o n n a i r e a l s o c o l l e c t e d d a t a u s i n g completion format.  which  subjects,  12. I n t h e s p a c e p r o v i d e d , b r i e f l y d e s c r i b e how arrive at a f i n a l  grades.  the  S u c h q u e s t i o n s as t h e f o l l o w i n g  were  asked: 1. W h i c h i s y o u r age c a t e g o r y ? ( <25,25-30 , 31-40 ,41-50 , 51-60 ,>60)  2. How  many y e a r s t e a c h i n g e x p e r i e n c e do y o u  ( c o m b i n e b o t h p u b l i c and (  (years)  have?  private)  0-2,3-5,6-10,11-15,16-20,>20)  3. How  many c o u r s e s i n s t a t i s t i c s  e v a l u a t i o n do y o u h a v e ?  o r m e a s u r e m e n t and  (disregard unit value)  4. What i s y o u r t e a c h i n g a s s i g n m e n t ? part  time)  (full  (0,1,2,3,>3)  time,  48  5.  I f y o u r a n s w e r t o #4 was  teaching assignment  (percentage  " p a r t time", e x p l a i n your  of time, s u b j e c t s , etc.)  I n c l u d e d w i t h t h e q u e s t i o n n a i r e was  a sample of  fictitious  achievement scores f o r f i v e f i c t i t i o u s  the weight  t h a t each assignment c o n t r i b u t e d t o the  course  score.  The  respondents  were asked  t h e s c o r e s u s i n g t h e method most f a m i l i a r s e r v e d as a g r a p h i c d e m o n s t r a t i o n commonly u s e d by  Fictitious The raw  final  t o c o l l a t e and t o them.  rank  This  Data  h y p o t h e t i c a l d a t a c o n s i s t e d o f s t u d e n t names,  The  and  teachers.  e a c h a s s i g n m e n t was  score.  students  of t h e c o l l a t i n g methods  s c o r e s on e a c h o f t h e f i c t i t i o u s  weight  five  assignments,  and  their the  t o c o n t r i b u t e t o the t o t a l  t e a c h e r s were asked  to weight,  term  c o l l a t e , and  rank  the assignment s c o r e s u s i n g t h e i r accustomed methods. Subsequently,  t h e s e r a n k i n g s w e r e a n a l y z e d and  r a n k i n g s o f t h e same d a t a a f t e r been s t a t i s t i c a l l y  balanced  purposes,  assignments  prior  t h e raw  were t r a n s f o r m e d  to being weighted  r e v i s e d t o t a l was r a n k i n g o f t h e raw  assignment scores  the had  balanced.  For comparison fictitious  t h e raw  compared t o  then ranked score data.  and  and  s c o r e s on e a c h o f t o T-scores  collated.  Each  compared t o the  the  and student's  teachers'  By a n a l y z i n g t h e r e s u l t s  of  49  t h e f i c t i t i o u s d a t a , i t was p o s s i b l e t o d e t e r m i n e  the  potential  teachers  f o r e r r o r and l a c k o f r e l i a b i l i t y when  c o l l a t e student  achievement scores.  h y p o t h e t i c a l data Table  I.  An e x a m p l e o f t h e  supplied to the subjects i s l i s t e d i n  The b r a c k e t t e d i n f o r m a t i o n ( w e i g h t e d  was n o t s u p p l i e d t o t h e r e s p o n d e n t s  total  and i s l i s t e d  i n d i c a t e t h e d i s t r i b u t i o n o f t h e raw s c o r e s .  score)  here only t o  Table I I  d i s p l a y s t h e same d a t a a f t e r i t h a s b e e n b a l a n c e d  so t h a t each  a s s i g n m e n t now h a s a mean o f 50 and a s t a n d a r d d e v i a t i o n o f 10.  Statistical  b a l a n c i n g was a p p l i e d b e f o r e t h e a s s i g n m e n t  s c o r e s were w e i g h t e d  and c o l l a t e d .  In this  study, the ranking  o f t h e " W e i g h t e d T o t a l S c o r e s " . was -the m a i n p o i n t o f i n t e r e s t . Of p a r t i c u l a r i n t e r e s t i n t h i s e x a m p l e i s how t h e s t u d e n t rankings i n Table  II differ  from those  d e m o n s t r a t e s how, e v e n w i t h o n l y f i v e  i n Table  I.  students,  statistical  b a l a n c i n g c a n h a v e a n o t i c e a b l e e f f e c t on s t u d e n t With  This  rankings.  a l a r g e r number o f s t u d e n t s , t h e e f f e c t may be e v e n more  pronounced. grades,  S i n c e t h e r a n k i n g s a r e used t o determine  letter  i t i s i m p e r a t i v e t h a t t h e c o l l a t e d s c o r e s be a s  r e l i a b l e as p o s s i b l e .  Record  Sheets  E x a m p l e s o f t e a c h e r s ' r e c o r d s w e r e s e l e c t e d f r o m two s u b j e c t a r e a s : mathematics and s o c i a l two  record sheets  studies.  o b t a i n e d from the respondents  s t u d e n t s ' names, t h e r a w s c o r e s f o r t h e v a r i o u s and  tests, the students' collated  Each o f t h e revealed the assignments  s c o r e s and l e t t e r g r a d e s ,  as  50  ASSIGNMENTS raw s c o r e s  WEIGHTED TOTAL RANK SCORE RANK  5  TOTAL SCORE  57  95  [64.4]  [3]  [72.7]  [1]  58  80  83  [70.0]  [1]  [71.7]  [2]  72  52  71  75  [63.0]  [4.5]  [66.4]  [3]  75  95  45  83  25  [64.6]  [2]  [53.8]  [4]  73  83  60  63  36  [63.0]  [4.5]  [45.8]  [5]  WEIGHTS ( %) 10  20  20  10  40  NAME  1  2  1 . Student A  50  55  65  2. S t u d e n t B  69  60  3. S t u d e n t C  45  4. S t u d e n t D 5. Student E  3  4  [X ]  [62][73][56][71][63]  [SD]  [14][16][ 8][11][31]  m  Table I - F i c t i t i o u s  d a t a t o be c o l l a t e d  ASSIGNMENTS T-scores NAME  TOTAL SCORE  and ranked  WEIGHTED TOTAL RANK SCORE RANK  1  2  1 . Student A  41  39  61  37  60  47.6  4  51. 8  2  2. Student B  55  42  53  58  56  52.8  1  52.7  1  3. S t u d e n t C  38  49  45  50  54  47.2  5  49 . 2  3  4. Student D  59  64  36  61  38  51.6  2  47.2  5  5. Student E  58  56  55  43  41  50.6  3  48.7  4  WEIGHTS (%) 10  20  20  10  40  50  50  50  50  50  10  10  10  10  10  m SD X  Table I I - F i c t i t i o u s  3  4  5  data a f t e r being s t a t i s t i c a l l y  balanced  51  w e l l a s t h e w e i g h t i n g t h a t e a c h a s s i g n m e n t was t o c o n t r i b u t e to  the collated  scores.  A t t h e end o f a t e r m  (just p r i o r t o the d i s t r i b u t i o n of  report c a r d s ) , copies of the record sheets f o r both a r e a s were c o l l e c t e d from  the respondents.  Each c l a s s  s h e e t was s u b j e c t e d t o t h e f o l l o w i n g p r o c e d u r e . of  a computer, t h e a s s i g n m e n t raw s c o r e s were  balanced  and c o n v e r t e d t o T - s c o r e s .  c o l l a t e d and ranked  utilizing  subject  With  record the a i d  statistically  They w e r e t h e n  t h e same a s s i g n m e n t  weighted,  weightings  as u s e d b y t h e t e a c h e r .  The r e v i s e d t o t a l s and r a n k i n g s w e r e  returned t o the o r i g i n a l  respondent  hoped t h a t , by h a v i n g t h e r e s p o n d e n t  t o be r e g r a d e d . regrade  I t was  the balanced  r e s u l t s , a l l p r o c e d u r a l and s u b j e c t i v e f a c t o r s a f f e c t i n g t h e s t u d e n t s ' grades  w o u l d be h e l d c o n s t a n t f o r b o t h t h e o r i g i n a l  and  sets of data.  the balanced  The d i f f e r e n c e s i n t h e r a n k i n g s o f t h e raw s c o r e a n d t h e transformed  s c o r e s w e r e a n a l y z e d i n two ways.  r a n k i n g s were compared t o d e t e r m i n e statistically  i f t h e r e were  s i g n i f i c a n t differences i n the c o r r e l a t i o n  b e t w e e n t h e two r a n k i n g s .  Secondly,  l e t t e r grades  f r o m b o t h t h e raw s c o r e and t h e T - s c o r e to  determine  grade.  resulting  r a n k i n g s were compared  how many s t u d e n t s r e c e i v e d a c h a n g e i n l e t t e r  The r e s u l t s f r o m t h e s e a n a l y s e s w e r e c o m p i l e d and  tabulated. found  F i r s t l y , the  A complete  documentation  o f t h e r e s u l t s c a n be  i n c h a p t e r s f o u r and f i v e o f t h i s  study.  52  Grading  Policy  In order  t o promote c o n s i s t e n c y i n the a l l o c a t i o n  l e t t e r grades i n the elementary  school  d i s t r i c t used i n t h i s  in effect a policy  how  the  study  has  l e t t e r grade frequency  determined f o r each c l a s s . t h a t the ability  distribution  school outlining  should  be  s h o u l d be b a s e d  states on.student  d e r i v e d from the n a t i o n a l p e r c e n t i l e s of  s t a n d a r d i z e d achievement t e s t r e s u l t s . a d m i n i s t e r i n g the  the  E s s e n t i a l l y , the p o l i c y  l e t t e r grade d i s t r i b u t i o n estimates  setting,  This i s achieved  s t a n d a r d i z e d Canadian Achievement Test  t o the i n t e r m e d i a t e g r a d e s once each s c h o o l y e a r .  a s s i s t i n the establishment  o f an a p p r o x i m a t e  for that class.  Table  i n order  them i n r e l a t i n g n a t i o n a l p e r c e n t i l e s t o l e t t e r distributions..  100  on t h e CAT  b e t w e e n 7 6 and  95,  4 b e t w e e n 61 and  b e t w e e n 2 6 and  40,  3 b e t w e e n 6 and  5, t h e n  approximately  approximately  7 s h o u l d r e c e i v e a B,  grade students  25,  9 b e t w e e n 41 and and  should and  r e c e i v e an  so on.  The  are urged to c o n s i d e r a l s o the standards  A,  of  allocating  l e t t e r grades. f o l l o w e d , then  and  as  a c h i e v e m e n t f o r t h e i r p a r t i c u l a r g r a d e when  strictly  4  district  acceptable  be  7 60,  none b e t w e e n 0  g u i d e l i n e s s u g g e s t o n l y an a p p r o x i m a t e d i s t r i b u t i o n teachers  assist  national percentile, 75,  three students  to  the  to  I f , f o r example, i n a g i v e n c l a s s 3  s c o r e d b e t w e e n 96 and  (CAT)  grade  III illustrates  g u i d e l i n e s t h a t are s u p p l i e d to teachers  by  The  r e s u l t i n g n a t i o n a l p e r c e n t i l e s f o r each c l a s s are used  distribution  of  However, i f t h e g u i d e l i n e s w e r e t o the three students  w i t h the  highest  NATIONAL PERCENTILE  LETTER GRADE  96 - 100  A  76 -  95  B  61 -  75  C+  41 -  60  C  26 -  40  C-  6 -  25  D  0 -  5  E  Table I I I - L e t t e r grade d i s t r i b u t i o n  guidelines  c u m u l a t i v e s c o r e s from the v a r i o u s term assignments  would  r e c e i v e the A's, w h i l e the next seven h i g h e s t would  receive  the B's, e t c e t e r a . the a b i l i t y class"  This procedure "takes i n t o  consideration  l e v e l s of the p u p i l s i n a p a r t i c u l a r grade o r  ( B r i t i s h C o l u m b i a M i n i s t r y o f E d u c a t i o n , 1979, p. 26)  However, t h e s c h o o l d i s t r i c t p o l i c y a l s o s t a t e s , " I n c o n s i d e r i n g t h e c u m u l a t i v e marks f o r each s u b j e c t , b r e a k s " were used f u r t h e r t o e s t a b l i s h distributions"  (School D i s t r i c t  letter  "natural  grade  P o l i c i e s and R e g u l a t i o n s ) .  T h i s a p p r o a c h i s a l s o a d v o c a t e d by t h e B r i t i s h  Columbia  M i n i s t r y o f E d u c a t i o n i n t h e i r b o o k l e t on g r a d i n g  practises.  " N a t u r a l b r e a k s " r e f e r t o t h e gaps t h a t appear i n t h e r a n k e d d i s t r i b u t i o n of students' cumulative scores.  The g a p s c a n b  u s e d a s g r a d e c u t - o f f p o i n t s t o s e p a r a t e one g r a d e c a t e g o r y  54  from another.  C o m b i n i n g t h e n a t u r a l b r e a k s and t h e g r o u p  a b i l i t y methods t o d e t e r m i n e t h e l e t t e r g r a d e allows  "teachers  distribution  t o make j u d i c i o u s d e c i s i o n s a s t o what  c o n s t i t u t e s h i g h and l o w a c h i e v e m e n t "  (British  M i n i s t r y of Education,  Using  1979, p. 2 6 ) .  Columbia  these  procedures  to e s t a b l i s h the l e t t e r grade d i s t r i b u t i o n f o r each c l a s s h i g h l i g h t s the importance of combining assignment  scores  reliably.  D a t a C o l l e c t i o n and A n a l y s i s The t e a c h e r s w e r e g i v e n r e c o r d s h e e t s  a t the beginning  t h e r e p o r t i n g p e r i o d on w h i c h t o r e c o r d t h e a c h i e v e m e n t for both sheets  academic s u b j e c t s .  Information  f r o m t h e q u e s t i o n n a i r e s was c o l l a t e d  tabulated.  The a c h i e v e m e n t s c o r e s  analyzed. and  f o r e a c h o f t h e two  s u b j e c t s were s t a t i s t i c a l l y b a l a n c e d  "balanced"  scores  A t t h e end o f t h e t e r m t h e r e c o r d  and t h e q u e s t i o n n a i r e s w e r e c o l l e c t e d and  s t u d e n t s were ranked  of  and a g g r e g a t e d ,  and t h e  b a s e d on t h e a g g r e g a t e d s c o r e .  This  r a n k i n g was c o r r e l a t e d w i t h t h e t e a c h e r s '  u s i n g t h e Spearman Rank C o r r e l a t i o n C o e f f i c i e n t r  ranking , .  ranKs  A d d i t i o n a l l y , the r e s u l t s from the r e g r a d i n g of the balanced  d a t a were compared t o t h e g r a d e s a s s i g n e d  teachers' o r i g i n a l  data.  The number o f s t u d e n t s  a c h a n g e i n l e t t e r g r a d e was r e c o r d e d  using the  who  and d o c u m e n t e d .  received The  d i r e c t i o n and m a g n i t u d e o f t h e c h a n g e was a l s o t a b u l a t e d . From t h e t a b u l a t e d r e s u l t s ,  i t was p o s s i b l e t o  55  generalize  as t o whether t e a c h e r s ,  sample, c o u l d on the  benefit  revised grading  f r o m i n - s e r v i c e and p r e - s e r v i c e  techniques.  reliable.  training  I t a l s o became a p p a r e n t ,  r e s u l t s , whether o r not grading  s h o u l d be made more  s i m i l a r t o those i n the  p r a c t i s e s c a n be a n d  from  56  CHAPTER 4 Results  The  data  categories:  collected  i n t h e s t u d y were d i v i d e d  (a) d e m o g r a p h i c  (b) d a t a c o n c e r n i n g t h e toward  g r a d i n g and  grading record  four  i n f o r m a t i o n concerning the  subjects' attitudes  reporting,  t e c h n i q u e s , and  into  (c) a n a l y s i s  and  perceptions  of the  (d) a n a l y s i s o f t h e  sample,  sample's  s u b j e c t s ' course  sheets.  Sample A sample o f 37 r e s p o n d e d  37  t o the  s u b j e c t s was first  sheets),  3 4 responded  regraded  record sheets).  withhold  their  completed both the  regraded 31  m a t h e m a t i c s and s c o r e s and from  56  classes.  distributions through  studies.  The  f o r 1,314  Tables  IV t h r o u g h  of the  s u b j e c t s ' responses  and 31  (survey  submitted  frequency  data  t o g r a d i n g and  school  IX p r o v i d e t h e  distributions  reporting.  the  Of  f o r both  sample p r o v i d e d  and  to  submitted  questionnaires.  elementary  t o the a t t i t u d e  and  only  of  raw students  frequency  sample's demographic v a r i a b l e s . the  record  subjects elected  subjects  completed  grades  XVII d i s p l a y  pertaining  and  of  34  25 p r o v i d e d r e g r a d e d  social  letter  of the  A total  While a l l  (copies of t h e i r  set of data  record sheets  record sheets  respondents,  second  Three  questionnaire.  i n the study.  data request  to the  regraded  used  Tables X the  perception questions  57  Demographic  Variables  a) G e n d e r Male  24  Feraale  8  Total  34  T a b l e I V - D i s t r i b u t i o n by  b) Age  Gender  (years) L e s s t h a n 25  0  25-30  0  31-40  25  41-50  8  51-60  1  G r e a t e r t h a n 60  ... 0  Total  34  T a b l e V - D i s t r i b u t i o n by Age c) Y e a r s o f  (years)  university two  0  three  1  four  10  B.Ed  15  MA o r MEd  7  other  ( i e diploma). 1  Total  34  T a b l e V I - D i s t r i b u t i o n by U n i v e r s i t y  Training  (years)  58  d) Number o f measurement a n d / o r  evaluation  none  11  one  21  two  1  three  1  More t h a n t h r e e . . .  0  Total  by Measurement C o u r s e s  part  time  3  full  time  31 34  Table VIII - D i s t r i b u t i o n  Experience  by T e a c h i n g  Assignment  (years) 0-5  0  6-10  7  11-15  15  16-20  9  Greater than Total Table  Taken  assignment  Total  f) Teaching  taken  . 34  Table VII - D i s t r i b u t i o n  e) T e a c h i n g  courses  IX - D i s t r i b u t i o n  20  ... 3 34  by T e a c h i n g E x p e r i e n c e  (years)  59  Of  t h e 34 s u b j e c t s c o m p l e t i n g t h e s e c o n d  set of  data,  most ( 7 4 % ) w e r e m a l e t e a c h e r s and m o s t ( 7 4 % ) w e r e i n t h e 31 40 y e a r age  category.  Twenty f o u r p e r c e n t o f t h e  w e r e i n t h e 41 t o 50 y e a r age completed 2 9 % had  a B a c h e l o r ' s d e g r e e made up  degree.  t i m e t e a c h e r s and  completed  w h i l e 3 2 % had In old  had  2 1 % had  completed  ( 9 1 % ) were  b e t w e e n 11 and  15  years  Twenty s i x p e r c e n t o f t h e t e a c h e r s  one  had  Many o f t h e s u b j e c t s  measurement and/or e v a l u a t i o n c o u r s e  n o t t a k e n any measurement o r e v a l u a t i o n c o u r s e s .  g e n e r a l , the t y p i c a l  m a l e t e a c h e r who  b e t w e e n 11 and  who  44% of the sample w h i l e  4 4 p e r c e n t had  16 .to 20 y e a r s t e a c h i n g e x p e r i e n c e . had  respondents  N e a r l y a l l of the respondents  teaching experience.  (62%)  Teachers  f o u r y e a r s u n i v e r s i t y e x p e r i e n c e and  a Master's full  category.  to  was  respondent  employed f u l l  was  a 31 t o 40  t i m e and who  15 y e a r s o f t e a c h i n g e x p e r i e n c e .  h e l d a B a c h e l o r ' s d e g r e e and  had  completed  one  He  year  had typically  measurement  and/or e v a l u a t i o n course.  A t t i t u d e s and Tables  P e r c e p t i o n s Toward G r a d i n g  X through  of and  s u b j e c t s were t o respond  and  (SD), D i s a g r e e  S t r o n g l y Agree  (SA).  The  and  achievement.  on a f i v e - p o i n t s c a l e t h e  personal feeling.  Strongly Disagree (A),  r e p o r t i n g student  agreement between the f e e l i n g e x p r e s s e d t h e i r own  Reporting  XVII r e f l e c t the sample's a t t i t u d e  p e r c e p t i o n t o w a r d s g r a d i n g and The  and  i n each  extent  statement  f i v e o p t i o n s were:  (D), Undecided  (U), Agree  60  ) My c o l l e a g u e s seriously.  at t h i s school  t a k e r e p o r t c a r d marks  SD  0  D  0  U  1  A  15  SA  18  Total  34  Table X - D i s t r i b u t i o n of colleagues' a t t i t u d e s r e p o r t c a r d marks  toward  h) L e t t e r g r a d e s a r e an e f f e c t i v e method o f i n f o r m i n g o f t h e i r c h i l d ' s p r o g r e s s and a c h i e v e m e n t . SD  1  D  5  U  2  A  22  SA Total Table XI - D i s t r i b u t i o n of a t t i t u d e effectiveness  very  parents  4 34 toward l e t t e r  grade  To t h e b e s t o f my k n o w l e d g e , p a r e n t s a r e g e n e r a l l y s a t i s f i e d w i t h the l e t t e r grade system of r e p o r t i n g . SD  0  D  2  U  1  A  28  SA Total  3 34  T a b l e X I I - D i s t r i b u t i o n o f agreement r e g a r d i n g p a r e n t s s a t i s f a c t i o n toward l e t t e r grade r e p o r t i n g systems.  I am v e r y c o n f i d e n t t h a t t h e l e t t e r g r a d e s I a s s i g n a r e a c c u r a t e and r e l i a b l e . SD  0  D  0  U  4  A  23  SA. .  7  Total  34  T a b l e X I I I - D i s t r i b u t i o n o f agreement r e g a r d i n g own g r a d i n g a b i l i t y  subjec  62  (k)  I w o u l d l i k e t o l e a r n more a b o u t c o l l a t i n g a n d a s s i g n i n g l e t t e r g r a d e s t o raw s c o r e s . SD  0  D  5  U  3  A  16  SA  10  Total  3~4  T a b l e XIV - D i s t r i b u t i o n o f agreement r e g a r d i n g s u b j e c t s ' d e s i r e t o l e a r n more a b o u t m a r k i n g a n d g r a d i n g (1) M o r e i n - s e r i v c e be o f f e r e d .  s e s s i o n s on g r a d i n g and r e p o r t i n g SD  0  D  5  U  4  A  11  SA  14  Total  34  T a b l e XV - D i s t r i b u t i o n o f a g r e e m e n t in-service sessions  should  on e v a l u a t i o n o f  (m) U n i v e r s i t i e s s h o u l d o f f e r more p r e - s e r v i c e i n s t r u c t i o n i n e f f e c t i v e g r a d i n g and r e p o r t i n g . SD  0  D  3  U  4  A .  14  SA  13  Total  34"  T a b l e XVI - D i s t r i b u t i o n o f agreement r e g a r d i n g s u b j e c t s ' o p i n i o n on p r e - s e r v i c e t r a i n i n g  (n) The r e p o r t c a r d f o r m a t a l l o w s s u f f i c i e n t i n f o r m a t i o n communicated t o p a r e n t s , s t u d e n t s , e t c . SD  0  D  8  U  6  A  16  SA  to  4  Total  34  T a b l e X V I I - D i s t r i b u t i o n of agreement r e g a r d i n g e f f e c t i v e n e s s of the r e p o r t c a r d format communication device  Nearly  a l l (97%)  their colleagues  of the teachers  t r e a t m a r k i n g and  Agree;53% S t r o n g l y Agree). (71%)  grading  F i f t y nine per  A m a j o r i t y of the  of t h e i r c h i l d ' s progress  cent  of the  (44%  respondents  communicated t o p a r e n t s ,  groups.  However, 18%  statement.  parent parents  and  sufficient  students,  and  w e r e u n d e c i d e d and  In response t o the  were s a t i s f i e d w i t h the  (91%)  to  interested  disagreed  statement  s a t i s f a c t i o n , most r e s p o n d e n t s  feeli  information  other 24%  of  achievement.  sample a l s o agreed w i t h the  t h a t the r e p o r t card format allows  this  seriously  that  a g r e e d t h a t l e t t e r g r a d e s a r e an e f f e c t i v e method  informing parents  be  surveyed agreed  as  with  concerning  agreed  l e t t e r grade system  that of  reporting. In response t o the q u e s t i o n s grading  and  reporting techniques,  p e r t a i n i n g to  teachers'  a m a j o r i t y of the  subjects  64  (88%)  agreed  (68% A g r e e ;  20% S t r o n g l y A g r e e ) t h a t t h e l e t t e r  grades they  assign are r e l i a b l e  respondents  indicated  and  raw a c h i e v e m e n t  grading  Agree;  9% U n d e c i d e d ;  pre-service  instruction  pre-service  who  thought  letter  parents  of t h e i r  were s a t i s f i e d  allows  students  with  offered  one who  (c) thought  (a)  an i n t e r e s t  Grading  Techniques  that  (b)  parents  grade system o f marking,  (d)  report  card  i n f o r m a t i o n t o be communicated t o  (e) t h o u g h t  t h a t more  i n - s e r v i c e and  s e s s i o n s on e v a l u a t i o n and g r a d i n g  raw  reporting  was  Columbia M i n i s t r y of Education  sufficient  grading  The  and  respectively.  r e p o r t c a r d marks s e r i o u s l y ,  progress,  by s c h o o l d i s t r i c t s  displayed  percentages  t h e need f o r i n - s e r v i c e  respondent  the l e t t e r  and s t u d e n t s ,  pre-service  the  g r a d e s a r e an e f f e c t i v e method o f i n f o r m i n g  the B r i t i s h  parents  12% were u n d e c i d e d f o r  i n s t r u c t i o n were 15% and 9%  h i s c o l l e a g u e s took  format  a r e a were 74% and 79%  disagreed with  thought  of  i n - s e r v i c e and  and p r e - s e r v i c e s e s s i o n s w h i l e  In g e n e r a l , t h e t y p i c a l  thought  The p e r c e n t a g e s  t o t h e need f o r more i n this  collating  (76% A g r e e o r S t r o n g l y  On t h e same q u e s t i o n s ,  in-service  of respondents  scores  15% D i s a g r e e ) .  agreeing  both  However, most  a d e s i r e t o l e a r n more a b o u t  respondents  respectively.  and a c c u r a t e .  and u n i v e r s i t i e s ,  should  be  and ( f )  i n l e a r n i n g more a b o u t a g g r e g a t i n g  and  scores.  record sheets  and t h e r e s p o n s e s  s e c t i o n of the survey  t o t h e g r a d i n g and  were a n a l y z e d  t o determine the  65  grading procedures respondents approach  Although  employed a v a r i a t i o n of the  a l l of  were  f u r t h e r a c c o r d i n g t o the f o l l o w i n g g r a d i n g methods:  1. M e t h o d One student's t o t a l  - Summing raw  t o a percentage  s c o r e s and  c o n v e r t i n g each  p r i o r t o g r a d i n g by n a t u r a l  ( s e e page 5 3 ) .  2. M e t h o d Two  - Summing e a c h s t u d e n t ' s raw  c o n v e r t i n g the t o t a l  to a percentage.  scores  L e t t e r grades  and  are  a s s i g n e d b a s e d on t h e n u m e r i c a l v a l u e o f t h e p e r c e n t a g e w e l l as a s u b j e c t i v e f a c t o r . were:  the  norm-referenced  t o g r a d i n g , the sample's g r a d i n g t e c h n i q u e s  classified  breaks  u s e d by t h e s u b j e c t s .  Examples of s u b j e c t i v e f a c t o r s  (a) a d j u s t i n g l e t t e r g r a d e s  effort;  to r e f l e c t  (b) a d j u s t i n g l e t t e r g r a d e s  s t u d e n t ' s p e r f o r m a n c e f r o m one adjusting  l e t t e r grades  term  individual  t o r e f l e c t a change i n a to another;  or  t o compensate f o r missed  3. M e t h o d T h r e e - Summing w e i g h t e d s t u d e n t and  c o n v e r t i n g t h e sum  as  raw  (c)  assignments.  s c o r e s f o r each  to a percentage  prior  to  grading according to n a t u r a l breaks. 4. M e t h o d F o u r c o n v e r t i n g the t o t a l  - Summing e a c h s t u d e n t ' s raw to a percentage.  scores  L e t t e r grades  and  are  a s s i g n e d b a s e d on t h e n u m e r i c a l v a l u e o f t h e p e r c e n t a g e . method i s commonly c a l l e d  "percent grading"  5. M e t h o d F i v e - Term a s s i g n m e n t s , given l e t t e r grades student's f i n a l  p r o j e c t s and  r a t h e r than numerical  scores.  32). tests  For  averaging  e a c h l e t t e r g r a d e i s g i v e n an o r d i n a l  are  Each  grade i s the average of a l l the l e t t e r  awarded t h a t s t u d e n t d u r i n g t h e c o u r s e . purposes,  ( s e e page  This  value.  grades  66  6. M e t h o d S i x - Raw means and e q u a l collated.  scores are balanced  t o have  equal  standard d e v i a t i o n s before being weighted  The c o l l a t e d  scores are ranked  and g r a d e d  and  according  to n a t u r a l breaks.  T a b l e X V I I I g i v e s t h e f r e q u e n c y breakdown o f each g r a d i n g method.  T a b l e X I X d i s p l a y s how  applied t h e i r grading  e x t e n s i v e l y each  respondent  technique.  M e t h o d One  24  M e t h o d Two  5  Method Three  2  Method Four  2  Method F i v e  2  Method S i x  2  Total  37  T a b l e X V I I I - D i s t r i b u t i o n o f g r a d i n g method  Every  school subject  9  Core s u b j e c t s (Math, S c i e n c e S o c i a l S t u d i e s , E n g l i s h ) . . . 24 I n d i s c r i m i n a t e use Total  1 34  T a b l e XIX - D i s t r i b u t i o n o f a p p l i c a t i o n o f g r a d i n g technique  67  The r e s p o n d e n t s were a l s o a s k e d t o d e s c r i b e how determined a f i n a l  s c o r e f o r t h o s e s t u d e n t s who  one o r more t e s t s o r a s s i g n m e n t s . classified  under the f o l l o w i n g  they  have m i s s e d  T h e i r r e s p o n s e s were  methods:  1. M e t h o d One - C a l c u l a t e t h e a v e r a g e p e r c e n t a g e on o n l y the  a s s i g n m e n t s c o m p l e t e d and i g n o r e t h e m i s s e d 2.  M e t h o d Two  assignments.  - Estimate a score f o r the missed  a s s i g n m e n t by l o o k i n g a t : (a) t h e a b s e n t s t u d e n t ' s p r e v i o u s work,  (b) t h e m a r k s o t h e r s t u d e n t s o f s i m i l a r a b i l i t y o b t a i n e d  on t h e m i s s e d  assignment.  3. M e t h o d T h r e e - A s s i g n a mark o f z e r o f o r t h e m i s s e d assignment. 4. M e t h o d F o u r - C a l c u l a t e a l e t t e r p r e v i o u s w o r k and r e d u c e by one l e t t e r  grade based  on  grade f o r missed  assignment(s). 5. M e t h o d F i v e - C a l c u l a t e an a v e r a g e T s c o r e b a s e d all  on  c o m p l e t e d w o r k and a s s i g n t h a t v a l u e t o t h e m i s s e d  assignment(s). statistically  When a l l a s s i g n m e n t  s c o r e s have been  b a l a n c e d t h i s method e s s e n t i a l l y m a i n t a i n s r a n k  p o s i t i o n and d o e s n o t p e n a l i z e n o r r e w a r d t h e s t u d e n t f o r being  absent.  T a b l e XX shows t h e f r e q u e n c y o f t h e methods u s e d by t h e s a m p l e t o a r r i v e a t a mark f o r a n a b s e n t s t u d e n t .  68  T a b l e XX  The for  M e t h o d One  25  M e t h o d Two  5  Method Three  2  Method Four  1  Method F i v e  0  Other  1  Total  34  - D i s t r i b u t i o n o f c o m p e n s a t i o n method u s e d  r e s u l t s of the procedures  missed  respondents  assignments (74%)  ( T a b l e XX)  used t o compensate i n d i c a t e d t h a t most  c a l c u l a t e d an a v e r a g e s c o r e b a s e d s o l e l y  t h e work t h e a b s e n t  s t u d e n t had  completed.  r e v e a l s t h a t 15% o f t h e r e s p o n d e n t s estimate a score f o r a missed  The  use  The  data a l s o  assignment.  t o a s e t of f i c t i t i o u s  and  s t u d e n t s from h i g h e s t t o l o w e s t .  grading In  o f t h e r a n k s as d e t e r m i n e d  their  ( s e e page  48)  Table  XXI  by t h e v a r i o u s  techniques. response  t o the second  regarding the r e l i a b i l i t y  r e s e a r c h q u e s t i o n (page  scores f o r grading purposes,  and  the q u e s t i o n n a i r e responses  t e c h n i q u e s were a n a l y z e d .  16)  o f t h e a g g r e g a t i o n and w e i g h t i n g  raw  of  data  to apply  grading technique  shows t h e f r e q u e n c y  on  s u b j e c t i v e means t o  p a r t i c i p a n t s i n t h e s t u d y were asked  rank the f i v e  students  The  the sample's r e c o r d  of  sheets  pertaining to grading a n a l y s i s r e v e a l e d a h i g h degree  s i m i l a r i t y b e t w e e n t h e a g g r e g a t i o n methods e v i d e n t on  the  69  Student A B C D E 1,2,3,5,4  16  3,1,4.5,2,4.5  6  2,1,3,5,4  3  1.2.4.5.3  2  4.5,1,3,2,4.5  1  2.1.5.3.4  1  2,3,5,1,4  1  1.2.5.2.5.5.4  1  2.1.4.5.3.4.5  1  Incomplete  2 34  Total T a b l e XXI - D i s t r i b u t i o n  record  o f ranks  of f i c t i t i o u s  data  s h e e t s and t h e a g g r e g a t i o n t e c h n i q u e s d e s c r i b e d by t h e  respondents methods u s e d  on t h e q u e s t i o n n a i r e . i n response  s u r v e y were l e s s  However, t h e g r a d i n g  to the f i c t i t i o u s  data  frequent d i s c r e p a n c y concerned t o the f i c t i t i o u s  the weighting  data.  Although  The most factors  t o the f i c t i t i o u s  data.  t o be  most r e s p o n d e n t s d i d  n o t n o r m a l l y w e i g h t raw s c o r e s , many a t t e m p t e d weights  of the  c o n s i s t e n t w i t h t h e methods e v i d e n t on t h e  grade s h e e t s and i n t h e w r i t t e n d e s c r i p t i o n s .  applied  section  t o apply  x  As shown i n t a b l e X X I , 18% o f t h e sample o b t a i n e d a r a n k order  f o r the f i c t i t i o u s  t h e most common  total  s c o r e s t h a t was c o n s i s t e n t  g r a d i n g method i d e n t i f i e d  i n this  with  study (see  70  Table  XVIII).  aggregation  Nine per cent of the respondents  and w e i g h t i n g t e c h n i q u e s  many e x p e r t s  ( s e e page 2 8 ) .  t h a t are advocated  The s u g g e s t e d  t a b u l a t e d as Method 6 i n T a b l e X V I I I . used a g g r e g a t i o n  applied by  methods a r e  Many s u b j e c t s ( 4 7 % )  and w e i g h t i n g t e c h n i q u e s  t h a t were  i n c o n s i s t e n t w i t h any o f t h e o t h e r g r a d i n g m e t h o d s p r e v i o u s l y identified combining  i n t h i s study. weighted  T h e i r methods e s s e n t i a l l y i n v o l v e d  raw s c o r e s .  However, t h e y o b t a i n e d  t h a t were v e r y s i m i l a r t o b o t h t h e r a n k s weighted  raw s c o r e s  aggregated  weighted  of the  ( T a b l e I ) and t o t h e r a n k s balanced  scores  results  aggregated  of the  (Table I I ) .  The r e s u l t s o f t h e c l a s s i f i c a t i o n and t a b u l a t i o n o f t h e v a r i o u s g r a d i n g methods u s e d b y t h e r e s p o n d e n t s , Table  as t a b l e d i n  X V I I I , r e v e a l e d t h a t a 6 5 % o f t h e s a m p l e e m p l o y e d an  aggregation  technique  t h a t i n v o l v e d summing t h e raw s c o r e s a n d  converting the c o l l a t e d  scores t o a percentage  g r a d i n g by n a t u r a l b r e a k s .  prior to  The r e s u l t s a l s o showed t h a t 14%  of t h e sample used an a g g r e g a t i o n  technique  that involved  summing t h e raw s c o r e s , c o n v e r t i n g t h e c o m b i n e d s c o r e s t o a percentage,  and u s i n g t h e n u m e r i c a l  value of the percentage  w e l l as s u b j e c t i v e f a c t o r s t o determine O n l y two o f t h e 37 r e s p o n d e n t s apply the desired weighting  Record  the l e t t e r  as  grade.  (5%) used " r e l i a b l e " methods t o  f a c t o r s t o t h e raw s c o r e s .  Sheets. The r a n k i n g s o f t h e s t a t i s t i c a l l y b a l a n c e d  c o m p a r e d t o t h e r a n k i n g s o f t h e raw s c o r e t o t a l s  totals using  were  71  Spearman's R a n k - C o r r e l a t i o n C o e f f i c i e n t .  Table XXII  s u b j e c t number, t h e number o f s t u d e n t s i n e a c h o f s u b j e c t ' s two (r ) g  , and  Coefficient  c l a s s e s ( n ) , the rank  the c r i t i c a l  correlation  coefficient  S t a n l e y , J . , 1970,  Correlation  h y p o t h e s i s o f no  w i t h a t w o - t a i l e d t e s t a t the alpha=.01 l e v e l of ( G l a s s , G.,  p.  539).  t h e d i s t r i b u t i o n o f t h e Spearman Rank  the  the  v a l u e s o f Spearman's r a n k  f o r t e s t i n g the n u l l  lists  correlation significance  Table XXIII d i s p l a y s  Correlation  Coefficients. Of t h e 56 c o r r e l a t i o n s c o m p u t e d , a l l had  r  values  that  s were g r e a t e r t h a n t h e c o r r e s p o n d i n g c r i t i c a l  value.  These  r e s u l t s i n d i c a t e t h a t the c o r r e l a t i o n s between the r a n k i n g s t h e raw  s c o r e t o t a l s and  t o t a l s w e r e p o s i t i v e and hypothesis  the r a n k i n g s of the balanced  score  significant.  null  Therefore, the  ( H : r h o = 0 ) s h o u l d be r e j e c t e d a t t h e Q  .01  level  of  of  s i g n i f i c a n c e i n favour of the a l t e r n a t e h y p o t h e s i s f o r each of t h e 56 r e c o r d s h e e t s In regrade  the second their  analyzed.  s e t o f d a t a , t h e s u b j e c t s were asked  s t u d e n t s b a s e d on t h e s t a t i s t i c a l l y  totals provided.  The  l e t t e r grades  were compared t o t h e l e t t e r grades respondent. classified  The  to  balanced  b a s e d on b a l a n c e d  scores  a s s i g n e d i n i t i a l l y by  d i f f e r e n c e s b e t w e e n t h e two  a c c o r d i n g t o m a g n i t u d e and  l e t t e r grades  d i r e c t i o n of  the were  "change".  F o r e x a m p l e , a c h a n g e f r o m an i n i t i a l l e t t e r g r a d e o f B t o a balanced  s c o r e l e t t e r g r a d e o f C+  grade decrease. of  A was  was  A c h a n g e f r o m a C+  r e c o r d e d as a o n e - l e t t e r  to a balanced  r e c o r d e d as a t w o - l e t t e r grade i n c r e a s e .  letter Table  grade XXIV  72 MATHEMATICS SUBJECT #  s  n  SOCIAL  CRITICAL VALUE  R  Q  STUDIES  s  n  CRITICAL VALUE . 537  001  .941  24  .537  . 976  24  002  .873  34  <. 478  . 957  34  003  . 955  18  . 625  . 985  18  . 625  004  .983  24  .537  N/A  N/A  N/A  005  .919  33  < . 478  . 984  33  006  .954  14  .716  N/A  N/A  N/A  007  .953  27  . 505  .975  27  . 505  008  .975  14  .716  .970  14  . 716  009  N/A  N/A  N/A  . 968  21  . 576  010  . 785  25  . 526  . 903  25  . 526  Oil  .992  24  .537  . 943  33  <. 478  012  .746  20  .591  . 857  20  . 591  013  .987  16  . 6 66  . 981  36  014  N/A  N/A  N/A  . 980  24  . 537  015  .984  17  .645  .939  17  . 654  016  N/A  N/A  N/A  . 949  18  . 625  017  .937  16  . 666  . 797  16  . 666  018  .992  28  . 496  . 962  28  . 496  019  .956  13  . 745  .995  13  . 745  020  . 955  30  .478  . 960  32  <. 478  021  .977  24  . 537  N/A  N/A  022  .979  33  < . 478  . 876  32  <. 478  023  . 988  32  < . 478  . 957  31  <. 478  024  .821  16  .666  . 900  16  . 666  025  .931  23  . 549  . 947  23  . 549  026  .984  29  . 487  .976  27  . 505  027  .929  16  .666  . 918  16  . 666  028  . 986  24  .537  . 902  24  . 537  029  .986  28  . 496  . 869  28  . 496  030  .972  25  . 526  . 960  25  . 526  031  .999  16  . 666  . 875  16  . 666  Total  643  <. 478  <. 478  <. 478  N/A  671  T a b l e X X I I - Spearman Rank C o r r e l a t i o n C o e f f i c i e n t s ( R ) R e l a t i n g Raw S c o r e a n d B a l a n c e d S c o r e T o t a l s F o r (a) M a t h e m a t i c s a n d ( b ) S o c i a l S t u d i e s Q  73  Frequency Score I n t e r v a l 0.970  Math  S.S.  -  1.000  14  9  0. 940 -  0.969  6  9  0.910  -  0.939  4  2  0.880 -  0.909  0  3  0.850  -  0.879  1  4  0. 820 -  0.849  1  0  0. 790 -  0.819  0  1  0. 760 -  0.789  1  0  0.730  -  0.759  1  0  0 . 700 -  0.729  0  0  28  28  Total  T a b l e X X I I I - D i s t r i b u t i o n o f Spearman Rank Coefficients shows t h e f r e q u e n c y , letter  grade  Ministry  and t h e d i r e c t i o n o f t h e  changes.  For a n a l y s i s was d i v i d e d  the magnitude,  purposes the range of l e t t e r  of Education  letter  grade i n t e r p r e t a t i o n s :  w e r e g r o u p e d i n t o t h e Above A v e r a g e C+, C, a n d C- w e r e g r o u p e d  Letter  (A t o E )  Above  g r a d e s A and B  category;  letter  grades  i n t o the Average c a t e g o r y ; and  g r a d e s o f D and E w e r e g r o u p e d  category.  grades  i n t o three c a t e g o r i e s i n accordance with the  A v e r a g e , A v e r a g e , and B e l o w A v e r a g e .  letter  Correlation  i n t o the  Below  Average  74  One l e t t e r  grade i n c r e a s e  238 (18. 1%)  One l e t t e r  grade decrease  313 (23.8%)  Two l e t t e r  grade i n c r e a s e  28 (2.1%)  Two l e t t e r  grade decrease  23 (1.8%)  Three  letter  grade i n c r e a s e . . . .  4 (0.3%)  Three  letter  grade decrease....  1 (0.1%)  No c h a n g e i n l e t t e r  1314 (100 . 0% )  Total T a b l e XXIV  707 ( 5 3 . 8%)  grade  - Distribution of letter  The d i f f e r e n c e s i n l e t t e r  category s h i f t s  changes  grade were a l s o a n a l y z e d t o  d e t e r m i n e how many " c h a n g e s " w o u l d r e s u l t category t o another.  grade  i n a shift  f r o m one  T a b l e XXV shows t h e f r e q u e n c y o f  t h a t r e s u l t e d when t h e o r i g i n a l  were r e p l a c e d by l e t t e r  letter  grades based on s t a t i s t i c a l l y b a l a n c e d  scores.  Above A v e r a g e t o A v e r a g e  112  (8.5%)  A v e r a g e t o Above A v e r a g e  5 4 (4.1%)  Below Average  t o Average  4 4 (3.3%)  t o Below Average  29 (2.2%)  Average  L e t t e r grade change b u t no c h a n g e i n c a t e g o r y No l e t t e r  grades  368 (28 . 1%)  g r a d e / c a t e g o r y change ..707  (53.8%)  Total 1314 (100. 0% ) T a b l e XXV - F r e q u e n c y o f c a t e g o r y s h i f t  75  The r e s u l t s o f t h e l e t t e r Tables XXIII,  grade comparison, l i s t e d i n  X X I V , a n d XXV, i n d i c a t e d t h a t  grades i n i t i a l l y  awarded  t o s t u d e n t s w e r e c h a n g e d when t h e  s t u d e n t s were r e g r a d e d on t h e b a s i s totals. all  46% o f t h e 1,314  of the balanced score  T h i r t y nine per cent of the r e v i s e d grades  grades) a l s o involved Finally,  c a t e g o r y changes.  t h e sample's r e c o r d  d e t e r m i n e how many l e t t e r raw s c o r e t o t a l s .  ( o r 18% o f  s h e e t s were a n a l y z e d t o  g r a d e s w e r e b a s e d on  miscalculated  T a b l e XXVI d i s p l a y s t h e f r e q u e n c y o f  e r r o r s , as w e l l as t h e d i r e c t i o n and magnitude o f t h e l e t t e r grade c o r r e c t i o n . changes  T a b l e X X V I I shows t h e f r e q u e n c y o f c a t e g o r y  t h a t r e s u l t e d when i n c o r r e c t raw s c o r e t o t a l s  r e c a l c u l a t e d and t h e c o r r e s p o n d i n g l e t t e r  grades  revised.  One l e t t e r  grade i n c r e a s e  2 (0.2%)  One l e t t e r  grade decrease  6 (0.4%)  Two l e t t e r  grade increase  0 (0.0%)  Two l e t t e r  grade decrease  2 (0.2%)  Corrections  were  that d i d not  affect letter  grade  No e r r o r s Total T a b l e XXVI - F r e q u e n c y o f l e t t e r arithmetic errors  53 ( 4 . 0 % ) 1251 ( 95. 2%)  1314 (100 . 0% ) grade changes r e s u l t i n g from  76  Above A v e r a g e Average Below  t o Average  4  (0.3%)  t o Above A v e r a g e  1  (0.1%)  t o Average  0  (0.0%)  t o Below A v e r a g e  2  (0.2%)  3  (0.2%)  Average  Average Letter  g r a d e change  no change No  letter  but  i n category  g r a d e change  1304  (99 . 2%)  Total 1314 (100.0% ) T a b l e XXVII - F r e q u e n c y o f c a t e g o r y s h i f t r e s u l t i n g f r o m l e t t e r grade r e c a l c u l a t i o n  The  a n a l y s i s of the r e c o r d  o f t h e 1,314  computed  raw  1% o f t h e s t u d e n t s r e c e i v e d of the c a l c u l a t i o n  assigned  This  the  incorrect  errors.  However, o n l y  letter  5%  about  g r a d e s as a  Of t h e t e n  improperly  i n an i n c o r r e c t  concludes the r e s u l t s  section  contain a short  of  category  t h i s study.  summary, an a n a l y s i s  i n response t o the q u e s t i o n s of i n t e r e s t , limitations,  research.  about  well.  Chapter f i v e w i l l data  score, t o t a l s .  grades, seven r e s u l t e d  p l a c e m e n t as  that  s t u d e n t g r a d e s a s s i g n e d by t h e sample were b a s e d  on i n c o r r e c t l y  result  sheets revealed  and  finally,  the p o s s i b i l i t i e s  of the  an o u t l i n e  of  for further  77  CHAPTER 5 C o n c l u s i o n s and Recommendations F o r F u r t h e r  Study  Summary The  general problem t h a t t h i s  c o n s i d e r e d was t o d e t e r m i n e be r e v i s e d the  investigative  i f t e a c h e r s ' g r a d i n g methods c o u l d  so as t o i n c r e a s e t h e r e l i a b i l i t y  l e t t e r grades t h e y award t o s t u d e n t s .  adequately almost  study  and f a i r n e s s o f  I t was d i f f i c u l t t o  d e a l w i t h t h i s p r o b l e m i n one s t u d y .  I t w o u l d be  i m p o s s i b l e t o a n a l y z e e a c h o f t h e many c o m p o n e n t s  comprised  i n t h e m a r k i n g and g r a d i n g p r o c e s s e s .  the scope o f t h i s  Consequently,  s t u d y was r e s t r i c t e d t o f o c u s o n l y o n t h e  e f f e c t s of applying s t a t i s t i c a l  b a l a n c i n g t o raw a c h i e v e m e n t  scores p r i o r t o t h e c a l c u l a t i o n of student term  totals.  t h i s perspective, the following questions of interest  1.  From  evolved:  I s t h e r e a 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 r a n k i n g s  of t h e aggregated  s c o r e s c a l c u l a t e d by t e a c h e r s  i n t u i t i v e methods and t h e r a n k i n g s o f a g g r e g a t e d  using balanced  scores?  2. A r e t h e t e r m d e r i v e d , aggregated  totals,  from which t h e l e t t e r grades a r e  and w e i g h t e d  reliably?  3. A r e t e a c h e r s ' g r a d e s r e l i a b l e and f a i r ?  4. Would t h e r e v i s e d r e s u l t s be o f s u c h  a magnitude as t o  78  justify  t h e t i m e and expense r e q u i r e d t o r e - e d u c a t e  teachers?  The raw s c o r e s s u p p l i e d b y t h e s a m p l e i n t h e f i r s t d a t a were c o n v e r t e d t o T - s c o r e s , w e i g h t e d , obtain a " s t a t i s t i c a l l y balanced" listed  on t h e r e c o r d s h e e t s .  d a t a w e r e made i d e n t i c a l respondents. asked and  and c o l l a t e d t o  score f o r each  The w e i g h t i n g s  student  f o r the balanced  t o t h o s e used i n i t i a l l y by t h e  I n t h e second  t o use t h e b a l a n c e d  a l s o t o complete  total  set of  s e t o f d a t a , t h e s u b j e c t s were  scores t o regrade  their  the questionnaire l i s t e d  students,  i n A p p e n d i x A.  Spearman Rank C o r r e l a t i o n C o e f f i c i e n t s w e r e c a l c u l a t e d t o compare t h e r a n k i n g s o f t h e raw s c o r e t o t a l s w i t h t h e r a n k i n g s of  the s t a t i s t i c a l l y balanced  totals.  The c r i t i c a l  Spearman's Rank C o r r e l a t i o n C o e f f i c i e n t  values of  f o r t e s t i n g the n u l l  h y p o t h e s i s o f no c o r r e l a t i o n w i t h a t w o - t a i l e d t e s t .01) w e r e o b t a i n e d f r o m G l a s s a n d S t a n l e y ( 1 9 7 0 ,  (alpha =  p. 539) w i t h  the a p p r o p r i a t e n values corresponding t o the c l a s s  sizes.  The l e t t e r g r a d e s  b a s e d on raw s c o r e s w e r e c o m p a r e d t o t h o s e  based on b a l a n c e d  scores t o determine  different  l e t t e r grades  s t a t i s t i c a l l y balanced purposes.  i f significantly  w o u l d r e s u l t when raw s c o r e s w e r e p r i o r t o being aggregated  The r e s u l t s o f t h e c o m p a r i s o n  f o r grading  were r e c o r d e d i n  t e r m s o f t h e c h a n g e i n l e t t e r g r a d e t h a t o c c u r r e d when t h e balanced  s c o r e t o t a l s r e p l a c e d raw s c o r e t o t a l s .  changes were a n a l y z e d t o d e t e r m i n e  The g r a d e  how many s t u d e n t s  would  h a v e r e c e i v e d a c a t e g o r y c h a n g e ( s e e page 73) i f t h e i r original  grades  were r e p l a c e d w i t h b a l a n c e d  score  grades.  79  Tables and  X X I V a n d XXV d i s p l a y t h e r e s u l t s o f t h e s e  analyses.  determine  comparisons  The raw s c o r e g r a d e s w e r e a l s o a n a l y z e d t o  how many s t u d e n t s  m i s c a l c u l a t e d term t o t a l s . that resulted  r e c e i v e d raw s c o r e g r a d e s b a s e d o n The numbers o f c a t e g o r y  from m i s c a l c u l a t e d g r a d e s were a l s o  The r e s u l t s o f t h e s e a n a l y s e s  shifts  recorded.  are tabulated i n Tables  XXVI a n d  XXVII. The q u e s t i o n n a i r e was u s e d t o c o l l e c t d a t a p e r t a i n i n g t o the sample's demographic v a r i a b l e s ,  t h e sample's a t t i t u d e and  p e r c e p t i o n o f g r a d i n g and r e p o r t i n g , and t h e sample's techniques. XXI  The r e s u l t s a r e t a b u l a t e d i n T a b l e s  i n chapter  Research  grading  IV through  four.  Question  In response  1  t o the f i r s t  research question regarding the  d i f f e r e n c e between t h e r a n k i n g s o f t h e raw s c o r e t o t a l s and the rankings o f balanced  score t o t a l s ,  Spearman  C o r r e l a t i o n C o e f f i c i e n t s were c a l c u l a t e d s u b j e c t ' s two r e c o r d s h e e t s .  Rank  f o r each o f t h e  The r e s u l t s i n d i c a t e d t h a t t h e  r a n k i n g s o f t h e raw s c o r e t o t a l s w e r e s i g n i f i c a n t l y a n d p o s i t i v e l y c o r r e l a t e d with the rankings of the balanced totals  ( s e e page 7 1 ) . The v a l u e s o f t h e Spearman  score  Rank  C o r r e l a t i o n C o e f f i c i e n t s r a n g e d f r o m +.746 t o +.999 ( s e e T a b l e XXIII).  From t h e s e r e s u l t s i t c a n be c o n c l u d e d  that there i s  a s i g n i f i c a n t r e l a t i o n s h i p between t h e r a n k i n g s o f t h e raw s c o r e t o t a l s c a l c u l a t e d by t h e s u b j e c t s and t h e r a n k i n g s o f  80  the  balanced  score t o t a l s .  I t c a n a l s o be c o n c l u d e d  methods u s e d by t h e s u b j e c t s t o a g g r e g a t e reporting the  purposes are reasonably  statistical  British order  Columbia  totals  scores  totals,  there w i l l  letter  authors.  positive and t h e b a l a n c e d  be a s i g n i f i c a n t  scores.  by many  with  g r a d e s on t h e r a n k  significant  between t h e l e t t e r  method o f c o m b i n i n g a student  when compared  t h e method u s e d i n  between t h e raw s c o r e t o t a l s  suggest  correlation  reliable  grading,  s c h o o l s , bases  of the aggregate  correlations  raw s c o r e s f o r  b a l a n c i n g methods a d v o c a t e d  Since norm-referenced  that the  and p o s i t i v e  grades r e s u l t i n g  from  each  I n o t h e r words, t h e l e t t e r  grade  r e c e i v e s u n d e r t h e raw s c o r e method o f c o m b i n i n g  should,  i n most c a s e s ,  be s i m i l a r  he w o u l d r e c e i v e when t h e b a l a n c e d  score technique  B o t h methods s h o u l d  yield  for  I t c a n be c o n c l u d e d ,  a given  class.  whole, t h e s t u d e n t s  should  to the l e t t e r  similarly  distributed then,  receive reasonably  grade  i s applied.  letter  grades  t h a t on t h e reliable  grades  ( s e e page 2 ) . However, o f t h e 1,314 s t u d e n t s 46%  r e c e i v e d a change i n l e t t e r  b a s e d on b a l a n c e d (Table XXIV).  score  totals  g r a d e when t h e i r r a t h e r than  T h i s would s u g g e s t  Since  by, f a c t o r s  other  s e v e r a l respondents  than  g r a d e s were  raw s c o r e  totals  t h a t , f o r many s t u d e n t s , t h e  a s s i g n m e n t o f g r a d e s was u n r e l i a b l e influenced  i n v o l v e d i n this, study,  and was b a s e d on, o r  the t o t a l  score  rankings.  i n q u i r e d about c o n v e r t i n g the  T-scores  on t h e r e c o r d s h e e t s  t o per cent  possible  that the values of the converted  scores, i t i s per cent  scores  were  81  i n f l u e n c i n g f a c t o r s f o r some s u b j e c t s d u r i n g t h e  regrading  process.  arbitrary  The  lower  per  cent  scores  (based  on an  maximum o f 275)  resulting  why  grades decreased than increased  more l e t t e r  from the T-scores would a l s o e x p l a i n (see  Table  XXIV). In reference practises 46%  ( s e e page 2 ) , t h e  of the  students  misleading formulate 18%  l e t t e r grade changes suggest  in this  study  e r r o n e o u s d e c i s i o n s and 1,314  students  i n category  most l i k e l y  conclusions.  ( T a b l e XXV).  In a d d i t i o n , that  These s t u d e n t s  g e n e r a l l y t o c a t e r t o the  a v e r a g e , a v e r a g e , and  above a v e r a g e a b i l i t y  example, students  have a v e r a g e a b i l i t y  who  placed  are  c o u l d be  program f o r students  e i t h e r case,  could  erroneously  For  be for  "below  enrolled in  w i t h above average a b i l i t y .  the average student's  satisfactorily  below  groups.  i n a s p e c i a l program designed  average a c h i e v e r s " or they enriched  to  t o s u f f e r the consequences of erroneous d e c i s i o n s  as a c a d e m i c p r o g r a m s t e n d  erroneously  lead others  r e c e i v e d l e t t e r grade changes  shifts  that  r e c e i v e d i n c o n s i s t e n t and  information that could p o t e n t i a l l y  of the  resulted  t o the consequences of u n r e l i a b l e g r a d i n g  a c a d e m i c n e e d s may  not  an In  be  met.  In l i g h t of the c u r r e n t  literature,  the r e s u l t s  of  Spearman Rank C o r r e l a t i o n C o e f f i c i e n t s w e r e somewhat surprising. c a l c u l a t e d by  Why the  are the rankings subjects)  o f t h e raw  score  so s t r o n g l y s i g n i f i c a n t  p o s i t i v e l y c o r r e l a t e d w i t h the rankings  totals  (as  and  of the balanced  score  82  totals i n this  study?  Many a u t h o r s  have s u p p o r t e d  the notion  t h a t r a w s c o r e s c a n o n l y be c o l l a t e d a n d w e i g h t e d when t h e y h a v e b e e n b a l a n c e d  t o h a v e e q u a l means a n d e q u a l  s t a n d a r d d e v i a t i o n s ( s e e page 2 7 ) . Glock  (1981) s t a t e ,  scheme o r i g i n a l l y  inequities"  have f a i l e d for  F o r e x a m p l e , Ahmann a n d  " I f we hope t o m a i n t a i n t h e w e i g h t i n g  c h o s e n , we must t a k e i n t o c o n s i d e r a t i o n t h e  differences i n variability. in  A f a i l u r e t o do t h i s w i l l  (p. 426). But these  and many o t h e r  t o mention the importance  "between" s c o r e s .  appears t h a t t h e rank  o f t h e rank  From t h e r e s u l t s o f t h i s correlation coefficient  scores can i n f l u e n c e t h e rank Indeed, the " i n e q u i t i e s "  for  f o r between  However, t h e s e  case w i t h t h e example t a k e n study.  Gronlund  other authors)  d e v i a t i o n s c a n be  e f f e c t s of combining deviations. the f i r s t B scores is  Such i s t h e  (1974) on page 8 o f  has used t h e extreme s i t u a t i o n  correlation  and a v e r y  ( a s have  large negative  (r = -1) t o e m p h a s i z e t h e -  scores with d i f f e r e n t  standard  I n t h e i r e x a m p l e s , s t u d e n t A s c o r e s v e r y h i g h on  a s s i g n m e n t and v e r y l o w on t h e f i r s t  l o w on t h e s e c o n d w h i l e  and h i g h on t h e s e c o n d .  seldom t h e case w i t h s c o r e s taken  sheets.  correlation  i n e q u i t i e s c a n a l s o be  from Gronlund  of large v a r i a b i l i t y  between s c o r e s rank  scores.  t h a t r e s u l t when a g g r e g a t i n g raw  a m p l i f i e d by a l a r g e n e g a t i v e rank c o r r e l a t i o n .  this  correlation  study, i t  o r e l i m i n a t e d w i t h a l a r g e p o s i t i v e rank  between s c o r e s .  result  authors  order of the aggregated  scores with large d i f f e r e n c e s i n standard reduced  reliably  student  But, t h i s  from t e a c h e r s ' r e c o r d  More commonly, s t u d e n t s t e n d t o m a i n t a i n a r e l a t i v e l y  83  s t a b l e rank p o s i t i o n w i t h i n the c l a s s .  Above a v e r a g e  t e n d t o o b t a i n t h e a b o v e a v e r a g e s c o r e s o n most  students  assignments  w h i l e t h e below average s t u d e n t s tend t o achieve t h e lower scores.  T h e r e f o r e , t h e r a n k i n g s f o r between raw s c o r e s would  more l i k e l y elementary "unusual"  be p o s i t i v e .  teachers q u e s t i o n assignments class rankings.  questioned the v a l i d i t y fictitious  I t i s i n t e r e s t i n g t o note  data  that result i n  F o r e x a m p l e , some s u b j e c t s  of the f i f t h  assignment i nt h e  ( s e e A p p e n d i x A) b e c a u s e t h e r a n k i n g s o n t h a t  assignment f a i l e d  t o f i t t h e r a n k i n g p a t t e r n e s t a b l i s h e d by  the other f o u r assignments. r a n k i n g on t h e f i r s t  Students  four assignments  high i n the ranking of the f i f t h rank  that  who p l a c e d h i g h i n t h e should place  assignment a l s o .  relatively Although  a  c o r r e l a t i o n o f r =+1 w o u l d be e x t r e m e l y d i f f i c u l t t o s 1  o b t a i n i n a c l a s s o f twenty of  rank p o s i t i o n suggests  p o s i t i v e rank  likely  t h e r e m i g h t be a r e a s o n a b l y  Considering the results of t h i s  o f p o s i t i v e rank c o r r e l a t i o n s  s c o r e s may h a v e r e d u c e d  f o r between  t h e e f f e c t o f v a r i a n c e on t h e sample's  scores.  c o r r e l a t i o n h a s on a g g r e g a t e  equally.  class  s t u d y and t h e  To d e m o n s t r a t e t h e e f f e c t t h a t t h e b e t w e e n s c o r e  examples.  strong  s t a n d a r d d e v i a t i o n v a l u e s i n t h e raw s c o r e d a t a , t h e  presence  aggregate  students, the s t a b i l i t y  c o r r e l a t i o n f o r b e t w e e n s c o r e s i n many  record sheets. different  or t h i r t y  totals,  rank  consider the following  I n each case, t h e assignments  a r e t o be  The raw s c o r e t o t a l s a n d t h e b a l a n c e d  weighted  score  a r e c a l c u l a t e d b y summing t h e a p p r o p r i a t e s c o r e s .  totals  F o r each  84  example, t h e c r i t i c a l correlation  value  coefficient  (alpha=.10;  n=6) o f t h e r a n k e d  f o r raw s c o r e t o t a l s w i t h  balanced  score t o t a l s balanced  i s r = .829. The b r a c k e t t e d d a t a a r e t h e s scores.  Student  1  Assignment  2  Total  A  100  [ 6 4 . 3]  40 [64 .8]  140  B  83  [ 5 9 . 1]  31  [57 .3]  114 [ 1 1 6 . 4 ]  C  58 [ 5 1 . 5]  26  [53 .1]  84 [ 1 0 4 . 6 ]  D  31  [ 4 3 . 3]  15  [43 .9]  46  E  25  [ 4 1 . 5]  12 [41 .4]  37 [ 8 2 . 9 ]  F  21  [ 4 0 . 3]  10 [39 .7]  31  X  53  [129 .1]  [ 87.2]  [ 80.0]  22. 3  m  . 32.9 11. 9 S.D r ( b e t w e e n ) = +1 r (total) s s T a b l e X X V I I I - E f f e c t o f r f o r b e t w e e n s c o r e s on t o t a l r when r f b e t w e e n ) =+1  Table XXVIII d i s p l a y s t h e r e s u l t i n g coefficient  ( r =+1).  are rearranged Table XXIX),  correlation  + . 942 .  score  coefficient i s  When t h e s c o r e s o f t h e s e c o n d  assignment  t o become r a n k o r d e r e d a s 2,3,1,5,6,4 ( a s i n  t h e between s c o r e rank  correlation  becomes +.657 w h i l e t h e r a n k c o r r e l a t i o n aggregate  correlation  ( r =+1) f o r r a w s c o r e t o t a l s w i t h b a l a n c e d s  t o t a l s when t h e b e t w e e n s c o r e s r a n k very large  rank  score  raw s c o r e s w i t h a g g r e g a t e  coefficient  coefficient for  balanced  s c o r e s becomes  85  ;udent  1  2  Total  A  100  [ 6 4 . 3]  31  [ 5 7 . 3]  131  [121.6]  B  83  [59. 1]  26  [ 5 3 . 1]  109  [112.2]  C  58 [ 5 1 . 5]  40 [64. 8]  98 [ 1 1 6 . 3 ]  D  31  [ 4 3 . 3]  12 [ 4 1 . 4]  43  [ 84.7]  E  25  [ 4 1 . 5]  10 [ 3 9 . 7]  35  [ 81.2]  F  21  [40. 3]  15  36  [ 84.2]  [ 4 3 . 9]  X •m  53  22 .3  S.D.  32. 9  11. 9  r  . 657  s Table  Assignment  r  s  = . 942  X X I X - E f f e c t o f r f o r b e t w e e n s c o r e s on t o t a l s c o r e r when r ( b e t w e e n ) =.657  I f t h e o r d e r o f the second assignment i s a l t e r e d  to  3,1,5,6,4,2 t h e r  f o r between s c o r e s and t h e r f o r t o t a l s s s c o r e s become +.14 a n d +.83 r e p e c t i v e l y . F i n a l l y , i f the ranks  a r e c h a n g e d t o 6,5,4,3,2,1 t h e n t h e r  s c o r e s and r  s  f o r between  f o r t o t a l s c o r e s become -1 a n d +.31.  It i s interesting o n l y t h e l a s t has a rank t o t a l s and b a l a n c e d (ie.  g  t o note  that,  correlation  score t o t a l s  with these  examples,  coefficient  f o r raw s c o r e  that i s not s i g n i f i c a n t  < .829) a t t h e a l p h a = . 1 0 l e v e l o f s i g n i f i c a n c e  T h e s e e x a m p l e s show how c h a n g e s i n t h e r a n k coefficient  f o r between s c o r e s a f f e c t  coefficient  f o r raw s c o r e t o t a l s a n d b a l a n c e d  (n=6).  correlation  the rank  correlation score  C o n s i d e r i n g a h i g h m a j o r i t y o f t h e sample i n t h i s  totals.  study  86  compute t o t a l s b y summing raw s c o r e s and  (see Table  c o n s i d e r i n g c l a s s assignments are expected  X V I I I page to correlate  p o s i t i v e l y w i t h e a c h o t h e r , i t becomes more a p p a r e n t r a n k i n g o f t h e raw s c o r e t o t a l s ranking of the balanced  In  Question  response  reliability  score t o t a l s i n t h i s  i n spite  variability.  t o t h e second r e s e a r c h q u e s t i o n r e g a r d i n g t h e a n d w e i g h t i n g o f raw s c o r e s f o r  t h e sample's r e c o r d s h e e t s and t h e  q u e s t i o n n a i r e responses analyzed.  study,  2  of the aggregation  grading purposes,  why t h e  correlated highly with the  o f t h e many l a r g e d i f f e r e n c e s i n r a w s c o r e  Research  p e r t a i n i n g t o grading techniques  the aggregation  techniques  Based on t h e s e c o e f f i c i e n t s obtained it  were  The a n a l y s i s r e v e a l e d a h i g h d e g r e e o f s i m i l a r i t y  between t h e a g g r e g a t i o n methods e v i d e n t on t h e r e c o r d and  66)  c a n be c o n c l u d e d  d e s c r i b e d on t h e q u e s t i o n n a i r e .  r e s u l t s and on t h e rank  correlation  (as d i s c u s s e d i n Research  that this  scores i n a reasonably  sheets  Question 1 ) ,  s a m p l e o f s u b j e c t s c o l l a t e d raw  reliable  manner.  The a n a l y s i s o f t h e d a t a a l s o i n d i c a t e d t h a t m o s t respondents scores.  d i d not attempt  t o apply weighting  As i n d i c a t e d p r e v i o u s l y i n t h i s s t u d y  w e i g h t i n g raw s c o r e s a n d how much t o w e i g h t professional  judgement.  f a c t o r s t o raw (page 7 ) ,  i s a matter f o r  However, many s u b j e c t s  seemed  o b l i v i o u s t o t h e f a c t t h a t by n o t w e i g h t i n g , s m a l l and relatively  i n s i g n i f i c a n t a s s i g n m e n t s may e a s i l y c o n t r i b u t e a s  87  much o r more t o an a g g r e g a t e d project. weights  s c o r e as does a major t e s t o r  Most o f t h e respondents and t h e r e b y  "natural weight" who d i d a t t e m p t  study d i d not apply  allowed each assignment t o c o n t r i b u t e i t s  toward  the aggregated  t o weight  assignment's t o t a l  i n this  score.  t h e raw s c o r e s c o n s i d e r e d an  p o s s i b l e mark t o be t h e w e i g h t i n g  For example, an assignment t h a t has a t o t a l 100  was t h o u g h t  aggregate  Many o f t h o s e  factor.  p o s s i b l e score of  b y many t o c o n t r i b u t e t w i c e a s much t o an  s c o r e as would an a s s i g n m e n t t h a t has a t o t a l  p o s s i b l e s c o r e o f 50.  The e x a m p l e o n page 9 o f t h i s  study  d e m o n s t r a t e s t h e i n a p p r o p r i a t e n e s s o f t h i s method a s a means to weight  raw s c o r e s .  Assignments w i t h a l a r g e r  total  p o s s i b l e v a l u e may p o s s i b l y c o n t r i b u t e l e s s t o w a r d aggregate  an  s c o r e t h a n does an assignment w i t h a s m a l l e r  possible value.  The k e y f a c t o r s i n r e l i a b l e  total  weighting are the  standard d e v i a t i o n values r a t h e r than the t o t a l p o s s i b l e scores authors and  ( s e e page 1 0 ) .  T h i s n o t i o n was s u p p o r t e d  a s Ahmann a n d G l o c k  Gronlund  ( s e e page 6 ) , E b e l  ( s e e page 2 8 ) .  results of this  In l i g h t of these  study would suggest  weighting techniques  a r e l e s s than  facts, the  that the subjects' reliable.  e f f e c t on t h e l e t t e r g r a d e s r e p o r t e d i n t h i s  profound  study.  on n a t u r a l w e i g h t i n g s  u n r e l i a b l e w e i g h t i n g methods ( s e e T a b l e have r e c e i v e d an a g g r e g a t e  such  ( s e e page 2 7 ) ,  U n r e l i a b l e w e i g h t i n g m e t h o d s may h a v e h a d a  of t h e s u b j e c t s e i t h e r r e l i e d  by  Since  95%  or applied  X V ) , many s t u d e n t s  s c o r e t h a t was n o t i n d i c a t i v e  may  of  t h e emphasis p l a c e d on t h e a s s i g n m e n t s and c o u r s e o b j e c t i v e s .  88  For example, a minor  assignment  d e a l i n g w i t h o n l y a few c o u r s e  c o n c e p t s c o u l d h a v e h a d more i n f l u e n c e o n t h e a g g r e g a t e  score  than d i d a comprehensive  course  objectives.  p r o j e c t that addressed  However, i f t h e r a w s c o r e s h a d b e e n p r o p e r l y  b a l a n c e d and weighted  t o r e f l e c t t h e emphasis o f t h e c o u r s e ,  t h e n many s t u d e n t s i n t h i s s t u d y w o u l d  have l i k e l y  d i f f e r e n t a n d more r e p r e s e n t a t i v e a g g r e g a t e Furthermore,  based  score.  o n t h e r a n k i n g o f t h e new  Consequently,  a p p r o p r i a t e l y weighted reliability  received a  some s t u d e n t s may h a v e a l s o r e c e i v e d d i f f e r e n t  l e t t e r grades scores.  several  l e t t e r grades based  aggregate  on b a l a n c e d and  r a w s c o r e s h a v e g r e a t e r v a l i d i t y and  as i n d i c a t o r s of t h e s t u d e n t s ' r e l a t i v e  achievement. C o n s i d e r i n g t h e p o s s i b l e consequences o f u n r e l i a b l e grading practises  ( s e e page 2 ) , t h e r e s u l t s o f t h i s  study  s u g g e s t t h a t many s t u d e n t s may h a v e r e c e i v e d m i s l e a d i n g and i n c o n s i s t e n t i n f o r m a t i o n i n the form o f u n r e l i a b l e grades.  D e c i s i o n makers, u s i n g these grades  i n f o r m a t i o n , c o u l d be p r o n e For example, t h e l e t t e r  when i n f a c t ,  decisions.  a w a r d e d some s t u d e n t s may  i n d i c a t e t h a t t h e c o u r s e o b j e c t i v e s have been completed  as a source o f  t o making erroneous  grades  letter  successfully  t h e g o a l s h a v e n o t b e e n met.  I n such  i n s t a n c e s , s t u d e n t s c o u l d be p r o m o t e d t o t h e n e x t c o u r s e o r l e v e l when s u c h a p r o m o t i o n could also occur.  i s not j u s t i f i e d .  The o p p o s i t e  S t u d e n t s may be r e t a i n e d t o r e p e a t o r  r e v i e w t h e c o u r s e o b j e c t i v e s when i n f a c t t h e m a t e r i a l h a s been w e l l m a s t e r e d  and such a r e t e n t i o n i s n o t w a r r a n t e d .  89  Others  may  a l s o be m i s g u i d e d  e x a m p l e , t h o s e who  by u n r e l i a b l e g r a d e s .  n o r m a l l y use  student grades  e v a l u a t i n g c o u r s e s , programs, or p e d a g o g i c a l implement unnecessary  c o n c l u s i o n s and weighted  techniques,  In s h o r t , l e t t e r grades  u n r e l i a b l e w e i g h t i n g p r a c t i s e s may and may  as a means o f  be  derived  mislead others to formulate  decisions.  Raw  s c o r e s s h o u l d be b a l a n c e d  Research  In  few  Question  response  the r e l i a b i l i t y respondents' compared.  The  teachers weight  t o the t h i r d  score  one  s t u d y , i t c a n be raw  scores  concluded  reliably.  f a i r n e s s of the sample's grades,  score grades  and  balanced  r e s u l t s w e r e r e c o r d e d and  grades  r e p l a c e d raw  f a i r n e s s of the grades, aggregate  content  research question pertaining  the change t h a t o c c u r r e d t o b o t h when b a l a n c e d  and  3  and  raw  and  objectives.  B a s e d on t h e r e s u l t s o f t h i s that r e l a t i v e l y  from  incorrect  i n s u c h a manner a s t o make t h e a g g r e g a t e  the v a r i o u s course  the  lacking i n validity  r e p r e s e n t a t i v e o f t h e e m p h a s i s p l a c e d on t h e c o u r s e and  may  o r i n c o r r e c t m o d i f i c a t i o n s b a s e d on  unreliable information.  reliability  For  o r more a s s i g n m e n t s  score grades  l e t t e r g r a d e and score grades.  missed  the were  t a b u l a t e d i n terms of  t h e methods used t o  s c o r e s f o r s t u d e n t s who  to  category To  assess  calculate  r e c e i v i n g a score  were a n a l y z e d .  T h e s e r e s u l t s w o u l d i n d i c a t e t h a t , i n some  on  90  circumstances,  students  c o u l d be u n f a i r l y p e n a l i z e d o r  rewarded f o r m i s s i n g an a s s i g n m e n t .  The f o l l o w i n g e x a m p l e  d e m o n s t r a t e s how a s t u d e n t m i g h t be p e n a l i z e d b y m i s s i n g an a s s i g n m e n t when means and s t a n d a r d  deviations are not  considered.  Student  ASSIGNMENT SCORES (%) 1 2 3  A  50  30  100  60  B  40  28  ab  34  C  30  26  74  43  D  10  20  60  30  Mean  33  26  78  S.D.  17  4  20  Table  XXX - C o m p e n s a t i o n f o r m i s s e d  Table  XXX shows how s t u d e n t  assignment  B has dropped t o t h e t h i r d  r a n k p o s i t i o n on t h e b a s i s o f t h e f i r s t e v e n t h o u g h he h a s c o n s i s t e n t l y r a n k e d third  Total  two a s s i g n m e n t second.  (ie. T-scores), preserved.  balanced  scores  t h e n h i s s e c o n d p l a c e r a n k i n g w o u l d be  The b a l a n c e d  s c o r e a v e r a g e s f o r s t u d e n t s A, B, C,  D w o u l d be 6 0 , 5 5 , 4 9 , a n d 37 r e s p e c t i v e l y .  student  B has  On t h e o t h e r h a n d , i f t h e  m i s s e d a s s i g n m e n t were c a l c u l a t e d by a v e r a g i n g  and  By m i s s i n g t h e  a s s i g n m e n t w i t h i t s h i g h e r mean s c o r e , s t u d e n t  b e e n p e n a l i z e d one r a n k p o s i t i o n .  scores,  Clearly,  B has n o t been p e n a l i z e d n o r rewarded under t h e  91  balanced  s c o r e method o f  compensation.  The r e s u l t s o f t h i s s t u d y w o u l d s u g g e s t grades  may l a c k r e l i a b i l i t y  assignments,  the technique  that teachers"  a n d , when s t u d e n t s h a v e  missed  f o r c o m p e n s a t i o n may n o t a l w a y s  be  fair.  Research  Question  4  In c o n s i d e r i n g t h e f o u r t h r e s e a r c h q u e s t i o n r e g a r d i n g t h e j u s t i f i c a t i o n o f t h e t i m e and expense r e q u i r e d t o r e t r a i n teachers, the responses  t o the a t t i t u d i n a l  section of the  q u e s t i o n n a i r e were a n a l y z e d and t h e r e s u l t s t a b u l a t e d i n Tables X I I I through  XVII.  These r e s u l t s ,  i n conjunction with  the p r e v i o u s l y d i s c u s s e d r e s u l t s , would i n d i c a t e i n - s e r v i c e i n s t r u c t i o n and p r e - s e r v i c e t r a i n i n g  that i n particular  a s p e c t s o f g r a d i n g a n d r e p o r t i n g w o u l d be j u s t i f i e d members o f t h e r e s e a r c h s a m p l e .  Areas  f o r many  o f g r e a t e s t need appear  t o be t h o s e c o n c e r n i n g t h e r e l i a b l e w e i g h t i n g o f r a w s c o r e s , the r e l i a b l e a l l o c a t i o n o f l e t t e r grades,  and t h e r e l i a b l e  c a l c u l a t i o n o f c o m p e n s a t i o n s c o r e s f o r s t u d e n t s who h a v e missed  assignments.  Current  literature  i n d i c a t e s t h a t many t e a c h e r s a r e  uneasy o r d e f e n s i v e c o n c e r n i n g t h e i r grades procedures  and g r a d i n g  ( s e e page 5 ) . D u r i n g t h e c o u r s e o f t h i s  t h i s n o t i o n was v e r i f i e d  study,  i n f o r m a l l y on s e v e r a l o c c a s i o n s .  Comments, s u c h a s " . . . s u r e hope t h e s e m a r k s a r e a l r i g h t " , o r  92  "I've  n e v e r been t r a i n e d i n t h i s a r e a " ,  r e m a r k s w e r e f r e q u e n t l y made by comments and  the  and  other  similar  respondents.  These  t h e u n c e r t a i n t y a c c o m p a n y i n g them w o u l d  t h a t t i m e d e v o t e d t o p r e - s e r v i c e and  suggest  i n - s e r v i c e w o u l d be  well  spent.  W e a k n e s s e s To  The sound.  Be  Considered  framework of the proposed study Many o f t h e  randomization  A l t h o u g h t h i s p r o j e c t e n c o u n t e r e d few e x i s t were c o n s i d e r e d  to adversely One  was  a f f e c t the  i n t o the  study.  being  p a r t i c i p a t e may  T h o s e who  concerned the  For  As  enough  The  the  sample  study  declined  of data are  not  h a n d , p e r h a p s o n l y t h o s e who  may  would the  have  unique  to to  particularly  procedures or about  o f t h e i r g r a d e s may  the  possible bias  t h o s e who  e x a m p l e , t h o s e who  about t h e i r grading  sample.  a result, a bias  p a r t i c i p a t e d may  have d e p r i v e d  non-participants.  other  serious  t o t a l l y r e p r e s e n t a t i v e of  contributed a particular bias while  reliability  not  that  results.  sample not  target population.  defensive  wherever p o s s i b l e .  t o be m i n o r and  comprised e n t i r e l y of v o l u n t e e r s .  r e s u l t from the  be  a f f e c t the  s u f f i c i e n t s i z e f o r an a d e q u a t e s t u d y ,  have been i n t r o d u c e d  to  shortcomings, those  of the most s e r i o u s o b s t a c l e s  A l t h o u g h of  considered  extraneous f a c t o r s that could  r e s u l t s w e r e c o n t r o l l e d by  did  was  the  have v o l u n t e e r e d . are confident  their  On  the  grading  93  techniques  a r e d e f e n s i b l e o r t h o s e who t a k e a p a r t i c u l a r  i n t e r e s t i n m a r k i n g and g r a d i n g v o l u n t e e r e d t o become members of t h e sample.  Teachers belonging  t o t h e s e and o t h e r  such  g r o u p s s h o u l d be i n c l u d e d i n t h e s a m p l e s i n c e g e n e r a l i z a t i o n s will  be made a b o u t t h e p o p u l a t i o n t o w h i c h t h e y  belong.  However, w i t h v o l u n t e e r s a m p l e s , t h e s e v a r i a b l e s a r e d i f f i c u l t to  control. Other weaknesses i n t h i s  study concerned  the  q u e s t i o n n a i r e t h a t was u s e d t o c o l l e c t d a t a on g r a d i n g techniques.  The q u e s t i o n o f f e r i n g  c o l l a t e d and ranked respondents.  fictitious  d a t a t o be  p o s e d p a r t i c u l a r p r o b l e m s f o r many o f t h e  Most r e c o g n i z e d , from t h e i n f o r m a t i o n g i v e n i n  the d i r e c t i o n s ,  t h a t some s o r t o f w e i g h t i n g was r e q u i r e d , e v e n  when t h e y d i d n o t c u s t o m a r i l y w e i g h t  raw s c o r e s .  Some i g n o r e d  t h e d i r e c t i o n s on w e i g h t i n g and a p p l i e d t h e i r r e g u l a r g r a d i n g methods.  Others  attempted  t o accommodate t h e d i r e c t i o n s b y  d e v e l o p i n g new a n d u n f a m i l i a r s t r a t e g i e s t o w e i g h t  t h e raw  scores i n the question. The  fictitious  although  data s e c t i o n posed another  l e s s s e r i o u s and u n r e l a t e d t o t h e one p r e v i o u s l y  discussed. aggregate  An o p p o r t u n i t y f o r t h e r e s p o n d e n t s  t o c a l c u l a t e an  s c o r e f o r a s t u d e n t who h a d b e e n a b s e n t  been i n c l u d e d i n t h e f i c t i t i o u s provided a t h i r d  source  aspect of grading.  data.  should  This would  of information f o r that  Although  the w r i t t e n responses topic.  weakness,  have  have  particular  a d e q u a t e , t h e r e c o r d s h e e t s and  were t h e o n l y s o u r c e s  of data f o r t h i s  As a r e s u l t o f t h e s e w e a k n e s s e s , t h e f i c t i t i o u s  data  94  section i n this  study  s h o u l d be r e v i e w e d  and r e v i s e d b e f o r e  b e i n g used on o t h e r s i m i l a r r e s e a r c h p r o j e c t s . A n o t h e r minor weakness concerned  the balanced  t o t a l s t h a t were g i v e n t o t h e r e s p o n d e n t s raw s c o r e s , T - s c o r e s  t o regrade.  Unlike  do n o t h a v e a maximum p o s s i b l e s c o r e ;  r a t h e r , they a r e continuous. s u p p l i e d t o the respondents  When t h e b a l a n c e d t o be r e g r a d e d ,  For those  respondents  T-scores  a maximum  s h o u l d h a v e b e e n i n c l u d e d f o r t h o s e who u t i l i z e grading techniques.  raw s c o r e  were  score  per cent  who i n q u i r e d , a  s c o r e o f 275 was p r o v i d e d a s t h i s w o u l d e x c e e d a l l b a l a n c e d s c o r e t o t a l s and t h e r e f o r e would y i e l d p e r c e n t a g e s 100 p e r c e n t .  Although  among t h e r e s p o n d e n t s , flaw the r e s u l t s .  than  t h i s w e a k n e s s c a u s e d some c o n f u s i o n i t was n o t c o n s i d e r e d s e r i o u s enough t o  Rather,  better understanding  less  i t may h a v e c o n t r i b u t e d t o w a r d  of the d i f f i c u l t y  teachers  when t h e y a s s i g n l e t t e r g r a d e s t o a g g r e g a t e d  a  experience  scores  ( s e e page  79) .  Future  Research  With  t h e i n t r o d u c t i o n o f c o m p u t e r s i n t o most s c h o o l s , t h e  o p p o r t u n i t i e s f o r improvement i n t h e measurement, e v a l u a t i o n , g r a d i n g , and r e p o r t i n g o f s t u d e n t  achievement have expanded  d r a m a t i c a l l y a n d o f f e r many new a r e a s These a r e a s  f o r future research.  h a v e b e e n d i v i d e d i n t o two m a i n s e c t i o n s t o  facilitate discussion.  The f i r s t  area of research  p o s s i b i l i t i e s deals s p e c i f i c a l l y with those  topics related to  95  teachers' grading practises.  The s e c o n d a r e a d e a l s  measurement a n d e v a l u a t i o n o f s t u d e n t global  with  a c h i e v e m e n t o n a more  scale.  While  this  study touched  o n l y a few a s p e c t s o f t e a c h e r  g r a d i n g p r a c t i s e s , i t l e f t many q u e s t i o n s u n a n s w e r e d . same t i m e , i t r a i s e d more q u e s t i o n s questions  that s t i l l  n e e d t o be a d d r e s s e d  regarding the appropriateness classroom  situation.  to T-scores z scores. if  first  study.  i s the concern  of u s i n g T-scores  i n the  r e q u i r e s t h a t t h e r a w s c o r e s be c o n v e r t e d t o  F u r t h e r s t u d i e s s h o u l d be c a r r i e d o u t t o  determine  i s a p p r o p r i a t e f o r w e i g h t i n g and  raw a c h i e v e m e n t  Research  Among t h e  The l i n e a r t r a n s f o r m a t i o n o f r a w s c o r e s  t h e use o f T-scores  combining  t o be r e s o l v e d .  At the  scores.  opportunities exist  i n the r e p l i c a t i o n of t h i s  One p o s s i b i l i t y w o u l d be t o d e t e r m i n e  an e f f e c t o n t e a c h e r s ' g r a d i n g p r a c t i s e s .  i f l o c a t i o n has  F o r example, a  study could i n v o l v e sampling  teachers  from d i f f e r e n t  of t h e p r o v i n c e t o determine  i fdifferences i n grading  p r a c t i s e s c a n be a t t r i b u t e d t o g e o g r a p h i c  location.  regions  I t might  be a r g u e d t h a t t e a c h e r s w i t h s u p e r i o r g r a d i n g p r a c t i s e s a r e t h o s e who l i v e  i n close proximity to universities.  Computerized record keeping another  a r e a t h a t s h o u l d a l s o be s t u d i e d .  g i v e n computer programs t h a t w i l l and  a n d mark management i s  weight  r e l i a b l y balance,  aggregate,  r a w a c h i e v e m e n t s c o r e s , w o u l d t h e y be w i l l i n g t o  a l t e r t h e i r present approach?  I f teachers are  g r a d i n g p r a c t i s e s f o r t h e newer c o m p u t e r  I f i t c a n b e shown t h a t t e a c h e r s w o u l d  readily  96  accept  t h e new  computer g r a d i n g method, t h e n s t u d i e s would  a l s o h a v e t o be done t o a s c e r t a i n t h e m o s t e f f e c t i v e u s e f u l computer program c u r r e n t l y T h i s s t u d y has  and  available.  possibly identified a relationship  (a) t h e e f f e c t s d i f f e r e n t s t a n d a r d d e v i a t i o n s h a v e on s c o r e t o t a l s and  b)  the rank  between s c o r e s .  The  between s c o r e s .  correlation coefficients  l a r g e p o s i t i v e rank  correlations  t h e r e l a t i o n s h i p c o u l d b e s t be a p p l i e d t o  grading  practises.  Another f u t u r e research p o s s i b i l i t y  how  well  scores a c t u a l l y c o r r e l a t e .  As  t h a t t h e more c a p a b l e  a t t a i n t h e h i g h e r marks w h i l e t h e the  lower  scores.  The  w o u l d t h e r e f o r e be r e l a t i v e l y conducted  to determine  i f this  Studies  sets of classroom indicated  classroom  r e l a t e s t o the  c o r r e l a t i o n c o e f f i c i e n t s f o r between s c o r e s . be done t o d e t e r m i n e  should  i n t h i s study, i t student would  p o s i t i o n of each  stable.  rank  achievement  less able student  rank  i f  s c o r e s and, i f  s o , how  achieve  for  S t u d i e s s h o u l d be done t o d e t e r m i n e  t h i s r e l a t i o n s h i p a p p l i e s t o a l l s e t s o f raw  w o u l d be e x p e c t e d  raw  e f f e c t s of l a r g e d i f f e r e n c e s i n v a r i a n c e  a p p e a r t o be d i m i n i s h e d by for  between  Research  normally  would student  should  be  i s a c t u a l l y t r u e f o r most  classes. The  second area f o r f u t u r e r e s e a r c h , the g e n e r a l t o p i c  measurement and to  e v a l u a t i o n of student  be a d d r e s s e d .  reliability Grading  a c h i e v e m e n t , a l s o needs  More s t u d i e s n e e d t o be done t o e x p l o r e  the  of teacher c o n s t r u c t e d e v a l u a t i o n i n s t r u m e n t s .  procedures  c a n be  of  " s t a t e of the a r t " , but u n l e s s  the  97  i n s t r u m e n t s used t o measure s t u d e n t a c h i e v e m e n t a r e and  valid,  student grades  v a l i d i t y and  fairness.  will  lack  reliability,  S t u d i e s n e e d t o be u n d e r t a k e n  a n s w e r s u c h q u e s t i o n s as t h e 1. A r e  still  to  following:  teacher constructed tests r e l i a b l e  2. A r e t h e r e ways t o i m p r o v e t h e s e 3. A r e  reliable  and  valid?  instruments?  t h e r e b e t t e r ways f o r t e a c h e r s t o c o n s t r u c t  measurement  instruments?  T h e s e a r e q u e s t i o n s t h a t s h o u l d be  Another  possibility  investigated.  f o r f u t u r e r e s e a r c h i n v o l v e s the  medium u s e d t o a c q u i r e m e a s u r e m e n t d a t a on achievement.  student  W i t h c o m p u t e r s b e c o m i n g more p o p u l a r i n s c h o o l s ,  s t u d i e s s h o u l d be p e r f o r m e d c l a s s r o o m t e s t s c a n be  to determine  improved  through  i f the r e l i a b i l i t y t h e use  of  of  the  computer.  With  the a v a i l a b i l i t y of computers t o a s s i s t t e a c h e r s i n  e v a l u a t i n g s t u d e n t a c h i e v e m e n t , i t i s hoped t h a t f u t u r e research w i l l measuring,  o f f e r new  and more r e l i a b l e  e v a l u a t i n g , g r a d i n g , and  achievement.  methods of  r e p o r t i n g student  98  Bibliography  Ahmann, J . S., & G l o c k , M. D. ( 1 9 8 1 ) . 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M e a s u r e m e n t a n d e v a l u a t i o n i n t e a c h i n g ( 4 t h e d . ) . New Y o r k : M a c M i l l a n . G u i l f o r d , J . P., & F r u c h t e r , B. ( 1 9 7 3 ) . F u n d a m e n t a l s t a t i s t i c s i n p s y c h o l o g y a n d e d u c a t i o n ( 5 t h e d . ) . New Y o r k : McGraw-Hill. Hills,  J . R. ( 1 9 8 1 ) . M e a s u r e m e n t a n d e v a l u a t i o n i n t h e c l a s s r o o m . Columbus: M e r r i l l .  H o p k i n s , K. D., & S t a n l e y , J . C. ( 1 9 8 1 ) . E d u c a t i o n a l a n d p s y c h o l o g i c a l measurement and e v a l u a t i o n ( 6 t h e d . ) . E n g l e w o o d C l i f f s , New J e r s e y : P r e n t i c e - H a l l . H o p k i n s , C. D., & A n t e s , R. L. ( 1 9 7 9 ) . C l a s s r o o m Atasca, I l l i n o i s : Peacock.  testing,  H o r r o c k s , J . E., & S c h o o n o v e r , T. I . ( 1 9 6 8 ) . M e a s u r e m e n t f o r teachers. Columbus:Merril1. I s a a c s , G. , & I m r i e , B. ( 1 9 8 1 ) . A c a s e f o r p r o f e s s i o n a l j u d g m e n t when c o m b i n i n g m a r k s . A s s e s s m e n t and E v a l u a t i o n i n H i g h e r E d u c a t i o n , j5, 3-25. J o h n s o n , D. M., & V a n O s d o l , B. M. ( 1 9 7 4 ) . A c o m p u t e r p r o g r a m for r e l i a b l e grade assignment. J o u r n a l of E d u c a t i o n a l D a t a P r o c e s s i n g , 1~L(2) , 11-19. L i e n , A. J . ( 1 9 7 6 ) . M e a s u r e m e n t a n d e v a l u a t i o n o f l e a r n i n g . Dubuque, I o w a : Brown. L i n d v a l l , C. M. ( 1 9 6 7 ) . M e a s u r i n g p u p i l a c h i e v e m e n t a n d a p t i t u d e . San F r a n c i s c o : H a r c o u r t , B r a c e & W o r l d Lyman, H. B. ( 1 9 7 8 ) . T e s t s c o r e s and what t h e y mean. E n g l e w o o d C l i f f s , New J e r s e y : P r e n t i c e - H a l l . M a r s h a l l , M. S. ( 1 9 7 1 ) . Why g r a d e s S o c i e t y , 9 9 , 350-353.  a r e argued.  S c h o o l and  1  M e h r e n s , W. A., & Lehmann, I . J . ( 1 9 8 4 ) . M e a s u r e m e n t and e v a l u a t i o n i n e d u c a t i o n and p s y c h o l o g y ( 3 r d e d . ) . New Y o r k : CBS C o l l e g e . M i n i s t r y of E d u c a t i o n , P r o v i n c e of B r i t i s h Columbia. (1979). C o n s t r u c t i o n and u s e o f c l a s s r o o m t e s t s . V i c t o r i a , BC: Author. M i n i s t r y of E d u c a t i o n , P r o v i n c e of B r i t i s h Columbia. (1979). G r a d i n g p r a c t i s e s : I s s u e s and a l t e r n a t i v e s . V i c t o r i a , BC: A u t h o r . N e l s o n , C. H. ( 1 9 7 0 ) . M e a s u r e m e n t and e v a l u a t i o n i n t h e c l a s s r o o m . New Y o r k : M a c M i l l a n . R a t z l a f f , H. C. ( 1 9 7 9 ) . A t o E a p p r o a c h e s t o g r a d i n g achievement. V e c t o r , 2 1 ( 1 ) , 22-28. S t e w a r t , W. J . ( 1 9 7 5 ) . A m u l t i - d i m e n s i o n a l e v a l u a t i n g - r e p o r t i n g system i n t h e elementary R e a d i n g I m p r o v e m e n t , 12, 1 7 4 - 7 6 . T e n b r i n k , T. D. ( 1 9 7 4 ) . E v a l u a t i o n - A p r a c t i c a l t e a c h e r s . New Y o r k : M c G r a w - H i l l .  student  school.  guide f o r  Townsend, E. A., & B u r k e , P. J . ( 1 9 7 5 ) . U s i n g s t a t i s t i c s i n c l a s s r o o m i n s t r u c t i o n . New Y o r k : M a c M i l l a n . W i c k , J . W. ( 1 9 7 3 ) . E d u c a t i o n a l m e a s u r e m e n t - Where a r e we g o i n g and how w i l l we know when we g e t t h e r e . Columbus Merri11.  101  Appendix  The  A  f o l l o w i n g q u e s t i o n n a i r e was  used t o  i n f o r m a t i o n on t h e s u b j e c t s ' d e m o g r a p h i c  v a r i a b l e s , on  a t t i t u d e s and p e r s p e c t i v e s t o w a r d g r a d i n g , grading  p r a c t i s e s and t e c h n i q u e s .  I t was  s u b j e c t a t t h e end o f t h e d a t a c o l l e c t i o n  collect  and on  their  distributed period.  their  t o each  102 Respondent # GRADING TECHNIQUES SURVEY S e c t i o n I - Demographic I n f o r m a t i o n DIRECTIONS:  C i r c l e the l e t t e r t h a t corresponds o r most a p p r o p r i a t e r e s p o n s e .  t o the correct  1. How many y e a r s t e a c h i n g e x p e r i e n c e do y o u h a v e ? both p u b l i c and p r i v a t e s c h o o l e x p e r i e n c e ) a. 0-5 b. 6-10 c. 11-15 d. 16-20 e. more t h a n 2 0 2. What i s y o u r t e a c h i n g a. f u l l t i m e b. p a r t t i m e  (combine  assignment?  I f " p a r t time", d e s c r i b e your t e a c h i n g (percentage, subjects taught, e t c . )  assignment  3. How many S t a t i s t i c s c o u r s e s o r M e a s u r e m e n t and E v a l u a t i o n c o u r s e s have you completed? ( d i s r e g a r d u n i t v a l u e ) a. none b. one c. t w o d. t h r e e e. more t h a n t h r e e 4. How many y e a r s o f u n i v e r s i t y h a v e y o u c o m p l e t e d ? a. two b. t h r e e c. f o u r d. c o m p l e t e d B a c h e l o r o f E d u c a t i o n d e g r e e e. c o m p l e t e d MA o r MEd d e g r e e f. other (explain: 5. W h i c h i a. b. c. d. e. f.  )  s y o u r age c a t e g o r y ? l e s s t h a n 25 y e a r s 25-30 y e a r s 31-40 y e a r s 41-50 y e a r s 51-60 y e a r s g r e a t e r t h a n 60 y e a r s  S e c t i o n I I - G r a d i n g and R e p o r t i n g DIRECTIONS: Y o u a r e t o e x p r e s s , on a f i v e - p o i n t s c a l e , t h e e x t e n t o f agreement between t h e f e e l i n g e x p r e s s e d i n e a c h s t a t e m e n t a n d y o u r own p e r s o n a l f e e l i n g . The f i v e p o i n t s a r e : S t r o n g l y D i s a g r e e ( S D ) , D i s a g r e e ( D ) , Undecided ( U ) , Agree ( A ) , S t r o n g l y Agree ( S A ) . You a r e t o e n c i r c l e t h e l e t t e r ( s ) w h i c h b e s t i n d i c a t e s how c l o s e l y y o u agree o r d i s a g r e e w i t h t h e f e e l i n g e x p r e s s e d i n each statement. 1. My c o l l e a g u e s a t t h i s s c h o o l t a k e r e p o r t c a r d m a r k s v e r y seriously. SD  D  U  A  SA  103 2. L e t t e r g r a d e s a r e an e f f e c t i v e m e t h o d o f i n f o r m i n g p a r e n t s o f t h e i r c h i l d ' s p r o g r e s s and a c h i e v e m e n t . SD  D  U  A  SA  3. To t h e b e s t o f my k n o w l e d g e , p a r e n t s a r e g e n e r a l l y s a t i s f i e d w i t h the l e t t e r grade system of r e p o r t i n g . SD  D  U  A  SA  4. I am v e r y c o n f i d e n t t h a t t h e l e t t e r g r a d e s I a s s i g n a r e a c c u r a t e and r e l i a b l e . SD  D  U  A  SA  5. I w o u l d l i k e t o l e a r n more a b o u t c o l l a t i n g and l e t t e r g r a d e s t o raw s c o r e s . SD  D  U  A  SA  6. More i n - s e r v i c e s e s s i o n s on g r a d i n g be o f f e r e d . SD  D  U  A  assigning  and r e p o r t i n g  should  SA  7. U n i v e r s i t i e s s h o u l d o f f e r more p r e - s e r v i c e i n s t r u c t i o n i n e f f e c t i v e g r a d i n g and r e p o r t i n g . SD  D  U  A  SA  8. The r e p o r t c a r d f o r m a t a l l o w s s u f f i c i e n t i n f o r m a t i o n t o be c o m m u n i c a t e d t o p a r e n t s , s t u d e n t s , e t c . SD DIRECTIONS:  D  U  A  SA  Answer t h e f o l l o w i n g i n the space  provided.  10. B r i e f l y d e s c r i b e how y o u c o m b i n e a s s i g n m e n t and t e s t scores to determine l e t t e r grades. (Use b a c k o f page i f necessary)  I n r e f e r e n c e t o t h e m e t h o d d e s c r i b e d i n #10, w h i c h s u b j e c t s a r e ' g r a d e d t h i s way? ( a l l s u b j e c t s , m a t h e m a t i c s , l a n g u a g e a r t s , s c i e n c e , s o c i a l s t u d i e s , a r t , P.E., m u s i c , F r e n c h ) B r i e f l y d e s c r i b e how y o u a r r i v e a t a f i n a l t e r m s c o r e f o r a s t u d e n t who h a s b e e n a b s e n t f o r one o r more t e s t s o r assignments. I n o t h e r w o r d s , how do y o u c o m p e n s a t e f o r a l e g i t i m a t e l y m i s s e d a s s i g n m e n t ? (Use b a c k o f page i f necessary)  104 DIRECTIONS: The f o l l o w i n g r e c o r d s h e e t r e p r e s e n t s t h e r a w s c o r e s ( p e r ce n t ) t h a t f i v e s t u d e n t s o b t a i n e d on f i v e assignments. Each a s s i g n m en t had a t o t a l p o s s i b l e s c o r e o f 100. The f ris t a s s i g n m e n t r e p r e s e n t e d a b o u t 10% o f t h e c o u r s e ; t h e s e c o n d a n d t h i r d a b o u t 20% e a c h : t h e f o u r t h a b o u t 10%; a n d t h e f i f t h , t h e f i anl t e s t , a b o u t 4 0 % . Use t h e m e t h o d s y o u n o r m a l l y u s e ( a s i n d i c a t e d i n PART I I #10 a b o v e ) t o c a l c u l a t e and r e c o r d t h e T o t a l S c o r e f o r e a c h s t u d e n t , I n d i c a t e t h e r a n k o f e a c h s t u d e n t (1 = h i g h e s t ; 2 = n e x t h i g h e s t ; e t c ) i n t h e space p r o v i d e d . ASSIGNMENTS  raw s c o r e s  NAME 1. 2. 3. 4. 5.  Student Student Student Student Student  A B C D E  D  1  2  3  4  5  50 69 45 75 73  55 60 72 95 83  65 58 52 45 60  57 80 71 83 63  95 83 75 25 36  Thank y o u f o r t a k i n g t h e t i m e t o c o m p l e t e  SCORE  this  survey.  RANK  

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