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An experimental study to determine the effectiveness of two types of geometric exercises in improving… Sankey, Gerald Robert 1959

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EXPERIMENTAL STUDY TO DETERMINE THE EFFECTIVENESS OF TWO TYPES OF GEOMETRIC EXERCISES IN IMPROVING CRITICAL THINKING by G e r a l d Robert Sankey B.A., U n i v e r s i t y of B r i t i s h Columbia, 1943 B.Ed., U n i v e r s i t y of B r i t i s h Columbia, 1954 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF ARTS i n the Department of Educat ion We accept t h i s t h e s i s as conforming to the r e q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1959 i i i ABSTRACT AN EXPERIMENTAL STUDY TO DETERMINE THE EFFECTIVENESS OF TWO TYPES OF GEOMETRIC EXERCISES IN IMPROVING CRITICAL THINKING Demonstrative geometry as a s u b j e c t i n secondary schools has been j u s t i f i e d by many e d u c a t i o n a l l e a d e r s on the b a s i s that the c r i t i c a l t h i n k i n g a b i l i t y a c q u i r e d i n t h i s s u b j e c t would t r a n s f e r to s i t u a t i o n s o u t s i d e of math-ematics. However, many of the r e s e a r c h s t u d i e s i n t h i s area i n d i c a t e that very l i t t l e of t h i s c r i t i c a l t h i n k i n g a b i l i t y a c q u i r e d i n the usual course i n demonstrative geom-e t r y t r a n s f e r s to l i f e s i t u a t i o n s . The usual course i n demonstrative geometry employs a text which i n c l u d e s as a very important type of e x e r c i s e , problems i n which the p u p i l i s s u p p l i e d w i t h data e i t h e r given or assumed and t o l d p r e c i s e l y what c o n c l u s i o n s he must d e r i v e from these d a t a . That i s , the p u p i l knows the c o n c l u s i o n before he attempts to solve the problem. This p a r t i c u l a r method of p r e s e n t a t i o n i s thought by some educ-a t i o n a l l e a d e r s to d e p r i v e the student of a very important l e a r n i n g process, namely, that of d i s c o v e r y . This study i s an attempt to determine what the e f f e c t on c r i t i c a l t h i n k i n g a b i l i t y would be, i f the students i v were not t o l d p r e c i s e l y what c o n c l u s i o n they must d e r i v e , but were exposed to e x e r c i s e s i n which there were many a l -t e r n a t i v e c o n c l u s i o n s of which some may or may not be v a l i d w i t h r e s p e c t to the given or assumed d a t a . That i s , the onus f o r deter m i n i n g which a l t e r n a t i v e ( i f any) was v a l i d , was the r e s p o n s i b i l i t y of the student. Two groups c o n s i s t i n g of t h i r t y p u p i l s each at the grade ten l e v e l on the U n i v e r s i t y Entrance Program were equated on the b a s i s of the c o n t r o l v a r i a b l e s of i n t e l l -igence as determined by the " O t i s Q u i c k - S c o r i n g Mental A b i l i t y T e s t s " and c r i t i c a l t h i n k i n g as measured by the "Watson-Glaser C r i t i c a l T h i n king A p p r a i s a l " t e s t Form A. The c o n t r o l group f o l l o w e d the usual course i n geometry i n which the students were s u p p l i e d w i t h e x e r c i s e s i n which they were t o l d p r e c i s e l y what c o n c l u s i o n s they must d e r i v e . The experimental group, however, were exposed to e x e r c i s e s i n which i t was the r e s p o n s i b i l i t y of the p u p i l to d e t e r -mine which ( i f any) of the many p o s s i b l e c o n c l u s i o n s sup-p l i e d c o u l d be proven v a l i d i n terms of the data g i v e n . This experiment was conducted f o r two months, a f t e r which Form B of the "Watson-Glaser C r i t i c a l T h i n king App-r a i s a l " t e s t was g i v e n . As the groups were equated at the beginning of the study by the c o n t r o l v a r i a b l e s , d i f f e r -ences i n means between the c o n t r o l and experimental groups V on t h i s . t e s t were i n v e s t i g a t e d f o r s i g n i f i c a n c e by means of " t " t e s t s . Each of the p a i r e d groups was s u b - d i v i d e d i n t o three sub-groups of ten each and c l a s s i f i e d as "super-i o r " , "average", and " i n f e r i o r " on the b a s i s of sc o r e s on the c o n t r o l v a r i a b l e s . The a n a l y s i s of the data from t h i s study i n d i c a t e s that students of " s u p e r i o r " , "average", and " i n f e r i o r " ab-i l i t y who were exposed to the experimental type of exer-c i s e d i d not show l a r g e r gains i n c r i t i c a l t h i n k i n g than those who f o l l o w e d e x e r c i s e s o u t l i n e d i n a t r a d i t i o n a l t e x t . * * # * ACKNOWLEDGMENTS i i The w r i t e r wishes to express h i s indebtedness to vario u s persons who have c o n t r i b u t e d i n important ways to the development of t h i s study. It i s d o u b t f u l that t h i s study would have proceeded beyond the p l a n n i n g stage, had i t not been f o r the a s s i s t -ance and encouragement p r o v i d e d by Dr. H.L. S t e i n and Dr. J.R. Mcintosh of the F a c u l t y of Education, The U n i v e r s i t y of B r i t i s h Columbia. A l s o v a l u a b l e suggestions and c r i t i c i s m s were made by Dr. H.P. Fawcett, C o l l e g e of Education, The Ohio State U n i v e r s i t y , Columbus, Ohio. Mr. R.B, S t i b b s , D i s t r i c t Superintendent of Schools, and Mr. C.W. McKenzie, P r i n c i p a l of Como Lake High School, School D i s t r i c t No. 43 (Coquitlam) were most h e l p f u l i n mak-ing t h i s study a d m i n i s t r a t i v e l y p o s s i b l e . F i n a l l y , the keen i n t e r e s t and a s s i s t a n c e of Dr. E.N. E l l i s , Department of Research and S p e c i a l S e r v i c e s , School D i s t r i c t No. 39 (Vancouver) was very much a p p r e c i a t e d . * * * * y i TABLE OF CONTENTS CHAPTER PAGE I. THE PROBLEM AND ITS SETTING 1 Importance of C r i t i c a l T h i n k i n g . . . . . . 1 The Unique C o n t r i b u t i o n of Mathematics to C r i t i c a l T h i n k i n g 1 C r i t i c a l T h i n k i n g as an E d u c a t i o n a l O b j e c t i v e 2 C r i t i c a l Comments on the Present Day Teaching of Geometry . . 3 Fawcett's Pr o p o s a l s . . . . . . . . . . . . 5 The B a s i s of This Study 7 The Problems of T h i s Study 8 Nature of Assumptions From Which This Study Proceeds 9 L i m i t a t i o n s of the Study . . . . . . . . . 11 D e f i n i t i o n s of Terms Used 13 Preview of Remainder of Th e s i s 15 I I . REVIEW OF RELATED RESEARCH 17 The Parker Study . . . . . 17 The Perry Study 18 The Fawcett Study 20 The Ulmer Study 23 The Gadske Study 26 v i i CHAPTER PAGE The Koppenhaver Study 28 The Lewis Study 3 0 Summary and Con c l u s i o n s 33 I I I . TEACHING PROCEDURES AND MATERIALS . . . . . . 37 P r e l i m i n a r y T r a i n i n g . . . . . . . . . . . . 37 The Teaching Procedures and M a t e r i a l s Used i n C o n t r o l Group 40 The Teaching Procedures and M a t e r i a l s Used i n Experimental Group . . 42 D e s c r i p t i o n of Log Book . . . . . . . . . . 54 F i n a l T e s t i n g 55 Summary . . . . . . 55 IV. NATURE OF CRITICAL THINKING 56 The Importance of C r i t i c a l T h i n k i n g . . . . 56 D e f i n i t i o n s of C r i t i c a l T h i n k i n g 57 E v a l u a t i o n of C r i t i c a l T h i n k i n g . . . . . . 61 R e l a t i o n s h i p Between I n t e l l i g e n c e and C r i t i c a l T h i n k i n g Tests . 67 J u s t i f i c a t i o n f o r Using Watson-Glaser Test . 70 L i m i t a t i o n s of the Watson-Glaser T e s t . . . . 72 Summary . . . . . . . . . . . . . 74 V. DESIGN AND ANALYSIS OF EXPERIMENT 75 The Subjects 75 A n a l y s i s of the P a i r e d Matching . . . . . . 79 v i i i CHAPTER PAGE Nature of C r i t e r i o n V a r i a b l e 88 A n a l y s i s of Re s u l t s . . . . . . . . . . . . 89 VI. SUMMARY AND CONCLUSIONS . . . . . . . . . . . . 95 The Importance of C r i t i c a l T h i n k i n g . . . . 95 The Purpose and Nature of This Study . . . 96 Design of Experiment . . . . . . 97 P r i n c i p a l F i n d i n g s 98 Conclusi o n s . . . . . . . . . . . . . . . . 99 Problems f o r F u r t h e r Study 101 BIBLIOGRAPHY . . . . . 102 APPENDICES 107 A. Raw score data . . . . . . . . . . . . 108 B. Sample c a l c u l a t i o n of B a r t l e t t ' s t e s t f o r homogeneity of varia n c e . . . . . 112 C. E x e r c i s e s of experimental group . . . . 115 D. E x e r c i s e s of c o n t r o l group 122 E. Sample of d a i l y l o g 126 F. S t a n d a r d i z e d t e s t s 128 * * * * i x LIST OF TABLES TABLE PAGE I. The Degree of Matching Achieved on C r i t i c a l Reasoning Scores . . . . . . . . 78 I I . The Degree of Matching Achieved on I n t e l l i g e n c e Scores . . . . . . . . . . . 84 I I I . S i g n i f i c a n c e of D i f f e r e n c e Between Means f o r C r i t i c a l T h i n k i n g 86 IV. S i g n i f i c a n c e of D i f f e r e n c e Between Means f o r I n t e l l i g e n c e . 87 V. D i f f e r e n c e i n Mean Scores on C r i t e r i o n V a r i a b l e of C r i t i c a l T h i n k i n g 90 VI. Mean Gains i n C r i t i c a l T h i n k i n g Scores . . . 93 VII . Age, Sex, I n t e l l i g e n c e Q u o t i e n t s , and C r i t i c a l T h i n k i n g Scores of the T h i r t y Matched P a i r s of P u p i l s Considered i n This Study . 109 V I I I . A Sample C a l c u l a t i o n of B a r t l e t t ' s Test f o r Homogeneity of Variance 113 * * # # X LIST OF FIGURES FIGURE PAGE 1. Q u a d r i l a t e r a l "Family" 43 2. C i r c u l a r Diagrams Aids i n D e f i n i n g Terms . . 46 * * * * CHAPTER I THE PROBLEM AND ITS SETTING IMPORTANCE OF CRITICAL THINKING ''From, the p o i n t of view of s o c i e t y the schools i n any s t a t e e x i s t to develop c i t i z e n s , or s u b j e c t s , a c c o r d i n g to the p r e v a i l i n g or dominating i d e a l s of the s t a t e or s o c i e t y . A l l s t a t e s seek to en-sure t h e i r s a f e t y , s t a b i l i t y and p e r p e t u i t y . The people of a democratic s t a t e such as Canada aim at more than t h i s . They wish to have c i t i z e n s able to p l a y t h e i r p a r t i n a democratic s t a t e , but a l s o able to make adjustments i n an e v o l v i n g and p r o g r e s s i v e s o c i a l order, so that s o c i a l s t a b i l i t y may be u n i t e d w i t h s o c i a l progress-*-". A s s u r e d l y , one of the competencies necessary f o r an e f f e c t i v e democracy i s the a b i l i t y on the p a r t of the e l e c -t o r a t e to t h i n k c r i t i c a l l y . T h i s i m p l i e s a knowledge of the methods of l o g i c a l enquiry and reasoning along w i t h some s k i l l i n a p p l y i n g these methods. II THE UNIQUE CONTRIBUTION OF MATHEMATICS TO CRITICAL THINKING Mathematics, p a r t i c u l a r l y at the secondary l e v e l i s cons i d e r e d by many a u t h o r i t i e s as a d e s i r a b l e method of developing t h i s c r i t i c a l t h i n k i n g . A c c o r d i n g to Hutchins, ^Programme of St u d i e s f o r the J u n i o r High Schools, "The Functions of the B r i t i s h Columbia System of Education, Aims and Philosophy of Education i n B r i t i s h Columbia." V i c t o r i a , B.C., Dept. of Education, King's P r i n t e r , V i c t o r i a , B.C., 1939', p. 10. 2 " c o r r e c t n e s s i n t h i n k i n g may be more d i r e c t l y , and more i m p r e s s i v e l y taught through mathematics than any other way"^. U l l s v i k suggests that the p a r t i c u l a r type of. math-ematics best s u i t e d to developing t h i s c r i t i c a l r easoning i s demonstrative geometry. "Though i t i s , of course, p o s s i b l e to l e a r n to rea-son d e d u c t i v e l y without the a i d of i n s t r u c t i o n i n demonstrative geometry, no b e t t e r example of an ab-s t r a c t l o g i c a l system w i t h i n the reach of secondary p u p i l s has y e t been d i s c o v e r e d " ^ . I l l CRITICAL THINKING AS AN EDUCATIONAL OBJECTIVE I t i s , t h e r e f o r e , not s u r p r i s i n g to f i n d Brown r e -p o r t i n g that i n a p o l l of 700 teachers of mathematics s e l -ected at random from the N a t i o n a l C o u n c i l of Teachers of Mathematics m a i l i n g l i s t n e a r l y h a l f the teachers l i s t e d as the most important o b j e c t i v e i n t e a c h i n g demonstrative geom-e t r y , the development of a " h a b i t of c l e a r t h i n k i n g and pre-c i s e e x p r e s s i o n " . They l i s t e d as second i n importance the " g i v i n g of knowledge of f a c t s and p r i n c i p l e s of geometry" 4. R.M. Hutchins, Higher Learning i n America, Yale U n i v e r s i t y Press, New Haven, Conn., 1936, p. 84. ^General Education i n a Free S o c i e t y , Harvard Press, Cambridge, Mass., 1945, p.164, c i t e d by Bjarne U l l s v i k "An Attempt to Measure C r i t i c a l Judgement", School Science and  Mathematics, V o l . 49, 1949, p.446. 4Kenneth E. Brown, "Why Teach Geometry", The. Math-ematics Teacher, March, V o l . 43, 1950, p.105. 3 I t would, appear that demonstrative geometry at the tent h grade l e v e l i s taught c h i e f l y as a course i n c l e a r l o g i c a l t h i n k i n g , r a t h e r than the a c q u i s i t i o n of f a c t s pe-c u l i a r to geometry. B e a t l y s t a t e s "... i t i s g e n e r a l l y agreed that the important f a c t s of geometry can be mastered below the tenth grade through i n d u c t i o n based on o b s e r v a t i o n , measurement ..."^. IV CRITICAL COMMENTS ON THE PRESENT DAY TEACHING OF GEOMETRY Questions may be asked now as to whether t h i s objec-t i v e of c r i t i c a l t h i n k i n g has been a c h i e v e d . Some author-i t i e s s t a t e that the usual course and the methods employed f a l l short of t h i s o b j e c t i v e . Fawcett concludes "the usual course i n demonstrative geometry does not improve the r e -f l e c t i v e t h i n k i n g of the p u p i l s " ^ . U l l s v i k b e l i e v e s that teachers accept the o b j e c t i v e of c r i t i c a l t h i n k i n g , but gi v e very l i t t l e evidence of attempting to achieve i t . ^Ralph B e a t l y , "The T h i r d Report of the Committee on Geometry", The Mathematics Teacher, Vol..28, 1935, p.334 6 H a r o l d P. Fawcett, "The Nature of Proof" T h i r t e e n -t h Yearbook, The N a t i o n a l C o u n c i l of Teachers of Mathem-a t i c s , Bureau of P u b l i c a t i o n s Teacher C o l l e g e , Columbia U n i v e r s i t y , 1938, p.119.-4 . . . f o r teachers of geometry r e a d i l y g i v e v e r b a l acceptance that l o g i c a l or c r i t i c a l t h i n k i n g i s a primary o b j e c t i v e . Yet few teachers can i l l u s t r a t e any method used d i r e c t l y to teach t h i s o b j e c t i v e . ' 7 Fawcett s t a t e s that the present method of t e a c h i n g geometry c r e a t e s a s i t u a t i o n which i s very seldom i f ever encountered i n a c t u a l l i f e . In p a r t i c u l a r the student i s , ...faced w i t h data day a f t e r day, e i t h e r g i v e n or assumed, t o l d p r e c i s e l y what c o n c l u s i o n s he must d e r i v e from these data or j u s t what i t i s he must prove. Does not such a p r a c t i c e v i o l a t e the very s p i r i t of the s c i e n t i f i c method? Where i n the world is' the p r a c t i c e found except i n demonstrative geometry class-rooms and i n c o u n t r i e s where thought c o n t r o l i s common.^ Fawcett a l s o notes that t h i s method of p r e s e n t a t i o n d e p r i v e s a student of a very important method of l e a r n i n g , namely; that of d i s c o v e r y . In a d d i t i o n he has no exper-ience i n checking the v a l i d i t y of statements that are not true . At no time does the student have experience i n checking the v a l i d i t y of a statement that i s not c o n s i s t e n t w i t h given data...Is i t not j u s t as im-por t a n t to know how to d i s p r o v e a hypothesis as i t i s to prove one.9 ^Bjarne U l l s v i k , "An Attempt to Measure C r i t i c a l Judgement", School Science and Mathematics, V o l . 4 9, 1949, p.446. 8 H a r o l d P. Fawcett, "Quod erat Demonstrandum", The  Mathematics Teacher, V o l . 49.. Jan., 1956, p.5 9 I b i d . , p.4. V FAWCETT'S PROPOSAL 5 With t h i s i n mind Fawcett suggests a new approach to geometry theorems and e x e r c i s e s . The method proposed suggests that the aim or the statement to be proved be omit-ted and that i t be l e f t up to the student to suggest v a r i o u s r e l a t i o n s h i p s t hat may seem p o s s i b l e to prove. That i s , the onus f o r determining what i s to be proved l i e s w i t h the s tudent. A comparison of the present procedure and Fawcett's proposed procedures i s as f o l l o w s : Present P r o c e d u r e ^ 1. A statement of the g e n e r a l p r o p o s i t i o n ( i n case of theorems). 2. A statement of the " g i v e n " or " h y p o t h e s i s " . 3. A statement of what i s to be proved or the c o n c l u s i o n . 4. The a c t u a l proof of the a l r e a d y accepted con-c l u s i o n . Proposed Procedure 1. A statement of the " g i v e n " or the "assumed data " . 2. A statement of the hypothesis or hypotheses suggested by the data. up e x e r c i s e s and current demonstrative This procedure f o r s e t t i n g theorems i s employed by most of the geometry t e x t s . 3. The t e s t i n g of each hypothesis l e a d i n g to proof or d i s p r o o f . 4. A statement of the general p r o p o s i t i o n ( i n the case of theorems). The major d i f f e r e n c e s between the present procedure and Fawcett's p r o p o s a l are as f o l l o w s : 1. The term " h y p o t h e s i s " i s used i n the sense of a p r o p o s i t i o n to be t e s t e d r a t h e r than as the "g i v e n " or "assumed d a t a " . 2. The statement of the gen e r a l p r o p o s i t i o n ( i n the case of theorems only) i s d e f e r r e d u n t i l the ten-t a t i v e h y p o t h e s i s has been t e s t e d f o r proof or d i sproof. Fawcett c l a i m s : The process of f o r m u l a t i n g hypotheses i n the study of any problem and of checking the v a l i d i t y of these hypotheses as a b a s i s f o r s t i l l f u r t h e r study i s a process of l a r g e importance i n the search f o r tru t h . . . a n d i t i s a process to which the t e a c h i n g of geometry can make a s i g n i f i c a n t c o n t r i b u t i o n . 1 2 Dewey s t r e s s e s the importance of hypothesis formul-a t i o n i n h i s f i v e steps f o r r e f l e c t i v e t h i n k i n g : 1. Some i n h i b i t i o n of d i r e c t a c t i o n r e s u l t i n g i n conscious awareness of a "f o r k e d - r o a d s i t u a t i o n " . 2. An i n t e l l e c t u a l i z a t i o n of the f e l t d i f f i c u l t y lead-ing to a d e f i n i t i o n of the problem. 3. The i d e n t i f i c a t i o n of v a r i o u s hypotheses...to i n i t i a t e and guide o b s e r v a t i o n and other oper-a t i o n s i n the c o l l e c t i o n of f a c t u a l m a t e r i a l . 11 Fawcett, op. c i t . , p. 5. -^Fawcett, "Quod er a t Demonstrandum", p. 4 7 4. E l a b o r a t i o n of each hypothesis by reasoning and the t e s t i n g of the hypotheses. 5. A c t i n g on the b a s i s of the p a r t i c u l a r h y p o t h e s i s s e l e c t e d i n step f o u r , thereby p r o v i d i n g the u l t i m a t e test-*-^. VI THE BASIS OF THIS STUDY This study proceeds on the b a s i s of a c c e p t i n g Faw-c e t t ' s procedure f o r s e t t i n g up of the geometric theorems and e x e r c i s e s but w i t h a v a r i a t i o n of h i s second s t e p . 1 4 The w r i t e r i s proposing to modify Fawcett's second step by supplying the student w i t h m u l t i p l e hypotheses that might be suggested by the d a t a ^ . Whereas, Fawcett would have the student propose h i s own hypotheses, the w r i t e r suggests that the students be s u p p l i e d w i t h s e v e r a l of these to be t e s t e d . In other words, the onus f o r s u p p l y i n g hypotheses i s taken away from the. student. The primary reason f o r adopting t h i s v a r i a t i o n has been that the w r i t e r has found that having students supply t h e i r own hypotheses i s very time consuming. A l s o , there has been a tendency on the 1 3 J o h n Dewey, How We Think, D.C. Heath & Co., Boston, 1933, p.107. ^ F a w c e t t ' s second step i s a statement of the hypoth-e s i s or hypotheses suggested by these d a t a . That i s , Faw-c e t t would have the students supply t h e i r own hypotheses. l^See appendix page 118 f o r sample e x e r c i s e s . 8 p a r t of many students to s e l e c t t r i v i a l hypotheses and to miss the important i d e a s . VII THE PROBLEMS OF THIS STUDY The c h i e f problems of t h i s study a r e : 1. To develop and to present s u i t a b l e geometric theor-ems and e x e r c i s e s of the " m u l t i p l e choice hypotheses' type which may be e f f e c t i v e l y used i n the t e a c h i n g of grade ten students i n order to s t i m u l a t e c r i t -i c a l t h i n k i n g . 2. To develop s u i t a b l e t e a c h i n g techniques f o r pr e s e n t -ing e x e r c i s e s and theorems of the " m u l t i p l e choice hypotheses" type. 3. To evaluate the e f f e c t i v e n e s s of these e x e r c i s e s and teaching procedures i n connection w i t h c r i t i c a l t h i n k i n g which i n c l u d e s the f o l l o w i n g : (a) To a s c e r t a i n whether the students i n an exper-imental group who have had e x e r c i s e s of the " m u l t i p l e c h o ice hypotheses" type give evidence (as determined by comparison of f i n a l t e s t scores) of g r e a t e r growth i n a b i l i t y to t h i n k c r i t i c a l l y than those i n a c o n t r o l group who are equated on the b a s i s of age, i n t e l l i g e n c e , 9 c r i t i c a l t h i n k i n g a b i l i t y and were exposed to the " t r a d i t i o n a l " 1 6 type of geometric e x e r c i se s and theorems. (b) To a s c e r t a i n the r e l a t i v e e f f e c t i v e n e s s of the experimental and c o n t r o l methods at the v a r i o u s l e v e l s of a b i l i t y . V I II NATURE OF ASSUMPTIONS FROM WHICH THIS STUDY PROCEEDS The major assumptions of t h i s study are based upon experimental evidence r e p o r t e d i n the l i t e r a t u r e and the opi n i o n s of those whom the w r i t e r c o n s i d e r s competent i n such m a t t e r s . The reader i s r e f e r r e d to Chapters II and IV f o r an account of the suppo r t i n g evidence from which the f o l l o w i n g assumptions are j u s t i f i e d . 1 . In a democracy, i t i s of v i t a l importance to educ-ate c i t i z e n s to t h i n k c r i t i c a l l y . The f i r s t p a r t of t h i s chapter i s devoted to the support and j u s t -i f i c a t i o n of t h i s assumption. - L b " T r a d i t i o n a l " geometric e x e r c i s e s r e f e r s to those assi g n e d to the c o n t r o l groups where the "aim" (which i s the c o n c l u s i o n ) i s p r e c i s e l y s t a t e d and i s c h a r a c t e r i s t i c of most of the demonstrative geometry t e x t s i n c u r r e n t use i n high s c h o o l s . 10 2. A b i l i t y to t h i n k c r i t i c a l l y or c e r t a i n aspects of that a b i l i t y can be improved, by c e r t a i n e d u c a t i o n a l experiences among which demonstrative geometry may be i n c l u d e d . 3. A b i l i t y to t h i n k c r i t i c a l l y may be measured by paper and p e n c i l t e s t s such as the "Watson-Glaser • C r i t i c a l T h i nking A p p r a i s a l T e s t " 1 7 . 4. C r i t i c a l t h i n k i n g as measured by the "Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l " t e s t i s a spec-i a l mental a b i l i t y d i s t i n c t from the g e n e r a l "g" f a c t o r measured by v e r b a l i n t e l l i g e n c e t e s t s such as the " O t i s Q u i c k - S c o r i n g Mental A b i l i t y T e s t s " 1 8 ' 1 9 5. A b i l i t i e s (such as c r i t i c a l t h i n k i n g ) a c q u i r e d i n such a s u b j e c t as demonstrative geometry i f taught w i t h t h i s i n mind can t r a n s f e r i n t o s i t u a t i o n s out-side geometry. 1 7Goodwin Watson and Edward Maynard G l a s e r , "Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l " t e s t , World Book Co., New York, 1952. 1 8 A r t h u r S. O t i s , O t i s Q u i c k - S c o r i n g Mental A b i l i t y  T e s t s , Gamma Test, Form AM, World Book Co., New York, 1934. 1 9 S e e Chapter IV of t h i s t h e s i s p. 67. 11 6. Reasonably r e l i a b l e s t a t i s t i c a l data can be ob-t a i n e d from the use of two c l a s s e s comprising 30 p u p i l s each i f adequately matched i n age, grade, i n t e l l i g e n c e and c r i t i c a l t h i n k i n g a b i l i t y . IX LIMITATIONS OF THE STUDY Before any i n t e r p r e t a t i o n of the r e s u l t s of t h i s study can be made, the f o l l o w i n g l i m i t a t i o n s must be borne i n mind. 1. Inasmuch as the data obtained i n t h i s study were d e r i v e d from two p a r t i c u l a r groups of t h i r t y p u p i l s , each r e g i s t e r e d on a p a r t i c u l a r program at a par-t i c u l a r grade l e v e l i n a p a r t i c u l a r school i n a par-t i c u l a r area and taught by a p a r t i c u l a r teacher then any c o n c l u s i o n s based on these f i n d i n g s must-be l i m -i t e d to t h i s p a r t i c u l a r small sample p o p u l a t i o n . 2, The experimental design employing matched groups g e n e r a l l y r e q u i r e s that a l l the su b j e c t s be ranked and p a i r e d o f f on the b a s i s of the c o n t r o l v a r i a b l e s and that each member of these p a i r s be as s i g n e d on a random b a s i s to e i t h e r the c o n t r o l or experimental group. However, because of a d m i n i s t r a t i v e d i f f i c u l -t i e s , i t was i m p o s s i b l e to s e l e c t these groups on a random b a s i s , and hence the experimenter had to con-12 tent himself w i t h the c l a s s e s (groups) as set-up by the school a u t h o r i t i e s . T h i s random assignment of subj e c t s i s thought to be necessary i n order to pr e -vent a conscious or unconscious b i a s on the p a r t of the experimenter i n the assignment of s u b j e c t s to the two groups. In order to minimize t h i s b i a s , the a c t u a l p a i r s were s e l e c t e d by a second person who 2 0 d i d not know the s u b j e c t s . 3. The experimental design of t h i s study embodies the concept of a " s i n g l e v a r i a b l e " w i t h a l l other f a c -t o r s being h e l d constant. In the realms of s o c i a l s i t u a t i o n s i t i s very d i f f i c u l t to s a t i s f y the r e -quirements of such a concept. Thus Good and Scates s t a t e " . . . i t must be f r a n k l y r e c o g n i z e d t h a t the so-c a l l e d law of the s i n g l e v a r i a b l e i s a theory r a t h e r than an accomplished f a c t i n experimental s t u d i e s of e d u c a t i o n a l , p s y c h o l o g i c a l , and s o c i o l o g i c a l problems" ^ S e e page 76 f o r more d e t a i l s concerning the ass-ignment of s u b j e c t s . 21 C a r t e r V. Good, and Douglas E. Scates, Methods of  Research, A p p l e t o n - C e n t u r y - C r o f t s , Inc., New York, 1954, P.700 . 13 4. Since the measurable outcomes of t h i s study were to be evaluated i n terms of c r i t i c a l t h i n k i n g , i t was necessary to s e l e c t an instrument f o r measuring t h i s a b i l i t y . Because there has been very l i t t l e demand f o r t h i s type of t e s t , the q u a l i t y and s e l e c t i o n i s somewhat l i m i t e d . 5. Inasmuch as the data of t h i s study were obtained over a two month p e r i o d , i t i s d i f f i c u l t to p r e d i c t what the r e s u l t s would have been had t h i s experiment 2 2 been c a r r i e d on f o r a much longer p e r i o d of time. X DEFINITIONS OF TERMS USED Hypothes i s . Throughout t h i s study, the term hypothesis s h a l l be i n t e r p r e t e d i n the s c i e n t i f i c sense. In t h i s usage i t i s a t e n t a t i v e g e n e r a l i z a t i o n suggested by the a v a i l a b l e data which more c a r e f u l i n v e s t i g a t i o n may e i t h e r prove or d i s -prove. However, i t should be noted that t h i s term i s used i n another q u i t e d i f f e r e n t sense by the authors of many te x t s i n plane demonstrative geometry. In these t e x t s the ^ T h e normal time a l l o t m e n t g i v e n to the study of demonstrative geometry i n t h i s p a r t i c u l a r school i s two y e a r s . 14 term " h y p o t h e s i s " r e f e r s to some statements that are " g i v e n " or "assumed". The authors of many t e x t s r e p l a c e these terms wi t h others such as "giv e n data", or "assumed d a t a " . C r i t i c a l T h i n k i n g I t i s d i f f i c u l t to g i v e a comprehensive d e f i n i t i o n of t h i s term. However, f o r the purposes of t h i s study i t s h a l l be d e f i n e d i n terms of behaviour c h a r a c t e r i s t i c of a person doing c r i t i c a l t h i n k i n g and i n p a r t i c u l a r : 1. He w i l l s e l e c t the s i g n i f i c a n t words and phrases i n any statement t h a t i s important to him and ask that they be c a r e f u l l y d e f i n e d . 2. He w i l l r e q u i r e evidence i n support of any con-c l u s i o n he i s pressed to accept. 3. He w i l l analyze that evidence and d i s t i n g u i s h f a c t from assumption. 4. He w i l l r e c o g n i z e s t a t e d and unstated assumptions e s s e n t i a l to the c o n c l u s i o n s . 5. He w i l l evaluate these assumptions, a c c e p t i n g some and r e j e c t i n g o t h e r s . 6. He w i l l evaluate the argument, a c c e p t i n g or r e -j e c t i n g the c o n c l u s i o n . 7. He w i l l c o n s t a n t l y re-examine the assumptions which are behind h i s b e l i e f s and which guide h i s a c t i o n s . ^ 3 ^ H a r o l d P. Fawcett, The Nature of Proof, T h i r t e e n t h Yearbook, The N a t i o n a l C o u n c i l of Teachers of Mathematics, Bureau of P u b l i c a t i o n s , Teacher's C o l l e g e , Columbia Univer-s i t y , 1938, pp. 11-12. XI PREVIEW OF REMAINDER OF THESIS 15 Chapter I I i s devoted to a review of r e s e a r c h stud-i e s concerned w i t h the development of. c r i t i c a l t h i n k i n g by the study of demonstrative geometry. This review w i l l not only p o i n t out how t h i s study i s s i m i l a r to other s t u d i e s but a l s o how i t i s unique. Chapter I I I d e a l s w i t h a d e t a i l e d d e s c r i p t i o n of the methods and m a t e r i a l s employed i n te a c h i n g demonstrat-ive geometry to the c o n t r o l and experimental groups. Sam-p l e e x e r c i s e s and d e t a i l e d d e s c r i p t i o n of teaching tech -nique used w i l l be shown. Chapter IV i s a statement concerning the nature of c r i t i c a l t h i n k i n g . I t w i l l d e s c r i b e the v a r i o u s aspects of c r i t i c a l t h i n k i n g such as: i t s importance, v a r i o u s def-i n i t i o n s of i t , i t s r e l a t i o n ; ; to i n t e l l i g e n c e , e v a l u a t i o n of i t by teacher-made and commercial t e s t s , and a s t a t e -ment about the p a r t i c u l a r e v a l u a t i n g instrument used i n t h i s study. Chapter V i s devoted to a d e t a i l e d d e s c r i p t i o n of the d e s ign and a n a l y s i s of the experiment. This chapter w i l l g i v e not only d e t a i l e d account of p r e c a u t i o n s taken i n matching the c o n t r o l g.nd experimental group on the con-16 t r o l v a r i a b l e s but a l s o an a n a l y s i s of the d i f f e r e n c e i n performance on the c r i t e r i o n v a r i a b l e . Chapter VI concludes the study w i t h a .summary of the experiment, the c o n c l u s i o n s reached on the b a s i s of the s t a t i s t i c a l evidence and some suggestions f o r f u r t h e r study. * * # * CHAPTER II REVIEW OF RELATED RESEARCH This chapter i s devoted to a review of r e s e a r c h s t u d i e s that are concerned with the development of c r i t i c a l r easoning by the study of demonstrative plane geometry. I THE PARKER STUDY One of the e a r l i e s t s t u d i e s i n t h i s f i e l d was con-ducted by Parker"'' who set up a c o n t r o l l e d experiment i n an e f f o r t to answer the q u e s t i o n ; Can p u p i l s of geometry be taught to prove theorems more economically and e f f e c t i v e l y when t r a i n e d to use c o n s c i o u s l y a technique of l o g i c a l t h i n k i n g , and furthermore does such t r a i n i n g , more than the usual method i n c r e a s e the p u p i l ' s a b i l i t y to a n a l -yze and see r e l a t i o n s h i p s i n other, non-geometrical s i t u a t i o n s ? 2 In order to answer t h i s q u e s t i o n a c o n t r o l and ex-perimental group were set up and taught by the same t e a -cher. The c o n t r o l group s t r e s s e d geometric content and l i t t l e a t t e n t i o n was g i v e n to the thought processes i n v o l -ved i n p r o v i n g geometric e x e r c i s e s . In the experimental group a development of a technique i n reasoning about 1 E l s i e Parker, "Teaching P u p i l s the Conscious Use of a Technique of T h i n k i n g " , The Mathematics Teacher, V o l . 17, No. 4, pp. 191-201, 1924. 2 I b i d . , p. 191 18 geometric ideas was emphasized. Parker concludes; These data would seem, to o f f e r c o n c l u s i v e evidence ...that when p u p i l s are taught to use c o n s c i o u s l y a technique of l o g i c a l t h i n k i n g , they t r y more var-i e d methods of a t t a c k , r e j e c t erroneous suggestions more r e a d i l y , and without becoming discouraged main-t a i n an a t t i t u d e of suspended judgement u n t i l the method has been shown c o r r e c t . The data on the reasoning t e s t s ... i n d i c a t e t h a t . . . t r a i n i n g i n l o g -i c a l t h i n k i n g . . . tends to c a r r y over these methods of a t t a c k and a t t i t u d e to other problem s i t u a t i o n s . 3 I I THE PERRY STUDY Another experiment very s i m i l a r to the Parker Study was conducted by P e r r y 4 i n 1925. She attempted to answer two important q u e s t i o n s ; 1. Is i t p o s s i b l e to teach students so that they may a t t a c k the s o l u t i o n of geometry e x e r c i s e s w i t h assurance e i t h e r of s u c c e s s f u l outcomes or of the a b i l i t y to d e t e c t t h e i r own e r r o r s ? 2. Or must t h e i r a t t a c k s be haphazard and fumbling, l e a d i n g only by chance to s u c c e s s f u l outcomes, and a r o u s i n g d i s s a t i s f a c t i o n due to p e r p l e x i n g f a i l u r e s . ^ 3 I b i d . , p. 201. 4Winona Perry, "A Study i n the Psychology of Learn-ing i n Geometry", Bureau of P u b l i c a t i o n s Teachers C o l l e g e , Columbia U n i v e r s i t y , 1925, c i t e d i n Harry Lewis, An Exper-iment i n d e v e l o p i n g C r i t i c a l T h i n king Through the Teach-ings of Plane Demonstrative Geometry, unpublished D o c t o r a l t h e s i s , New York U n i v e r s i t y , 1950. 5 I b i d . , p. 1. 19 In order to answer these q u e s t i o n s , she set up one experimental and two c o n t r o l groups. She, h e r s e l f , taught one experimental and one c o n t r o l group and another teacher taught the second c o n t r o l group. In one of the c o n t r o l groups the book p r o p o s i t i o n s were emphasized, w h i l e i n the other, emphasis was p l a c e d upon p r o v i n g o r i g i n a l e x e r c i s e s . No emphasis i n e i t h e r c o n t r o l group was devoted to any par-t i c u l a r method of r e a s o n i n g . The experimental group was taught the techniques of reasoning such as a n a l y s i s of f a c t s i n t o t h e i r elements, and purposive t h i n k i n g when f o r m u l a t i n g and t e s t i n g p o s s i b l e s o l u t i o n s . Sample ques-t i o n s i n d i c a t i v e of t h i s technique were; Again, what r e l a t i o n i s to be proved? What r e -l a t i o n s are given? When are t r i a n g l e s equal? How many p a i r s of e q u a l i t i e s do we know? E q u a l i t i e s between what? Since two p a i r s of angles are equal, which of these sets of c o n d i t i o n s f o r e q u a l i t y of t r i a n g l e s i n c l u d e s t h i s f a c t ? ^ As a r e s u l t of t h i s experiment Perry concludes that : The experimental techniques i n reasoning was the means of d e c r e a s i n g a student's d i f f i c u l t i e s i n the s o l u t i o n of e x e r c i s e s i n geometry and i t a l s o developed h a b i t s which l e d to s u c c e s s f u l s o l u t i o n s . Even though the program of the experimental group d i d not i n c l u d e non-mathematical m a t e r i a l neverthe-l e s s t h e i r a b i l i t y to solve problems of non-mathem-a t i c a l c h a r a c t e r was markedly improved, f o l l o w i n g 6 I b i d . , p. 12. 2 0 the p e r i o d of t r a i n i n g i n the s o l u t i o n of e x e r c i s e s i n geometry. This i n c r e a s e d a b i l i t y was more not-i c e a b l e as r e s u l t i n g from those t e s t s more s i m i l a r to the type of reasoning emphasized i n demonstrative geometry i n form and c o n t e n t . 7 I t i s s i g n i f i c a t n t to note that the Perry and Par-ker s t u d i e s d i d not c o n s c i o u s l y teach f o r t r a n s f e r . That i s , they adhered to s t r i c t l y mathematical m a t e r i a l s f o r the i n s t r u c t i o n of the experimental and the c o n t r o l groups. Yet both r e p o r t a s i g n i f i c a n t t r a n s f e r of l o g i c a l t h i n k i n g a b i l i t i e s a c q u i r e d i n geometry c l a s s e s to s i t u a t i o n s out-side mathematics. This was e s p e c i a l l y true f o r the exper-imental groups where the emphasis was upon the methods of reasoning used i n geometry. I l l - THE FAWCETT STUDY The f i r s t important study having demonstrative g geometry taught f o r t r a n s f e r was conducted by Fawcett i n 1938. He i n v e s t i g a t e d three problems i 1. The problem of l e a d i n g p u p i l s to understand the nature of deductive proof through the study of geometric s i t u a t i o n s . ' I b i d . , pp. 36-37. 8 H a r o l d P. Fawcett, The Nature of Proof, T h i r t e e n t h Yearbook, The N a t i o n a l C o u n c i l of Teachers of Mathematics, Bureau of P u b l i c a t i o n s , Teachers C o l l e g e , Columbia Univer-s i t y , 1938 . 21 2. The problem of g e n e r a l i z i n g t h i s experience so that e f f e c t i v e t r a n s f e r w i l l r e s u l t . 3. The problem of e v a l u a t i n g the r e s u l t i n g change i n behaviour of the s t u d e n t . 9 His study i n v o l v e d two groups of twenty-five pup-i l s each. The c o n t r o l group was taught using a t r a d i t i o n a l approach w h i l e the other used an experimental method. Each group met f o r forty-minute p e r i o d s , four days a week over a two year p e r i o d . During f i r s t f o u r weeks the experimen-t a l group spent time i n d i s c u s s i n g undefined terms, d e f i n -i t i o n s , and assumptions p e r t a i n i n g to mathematics and non-mathematical s i t u a t i o n s . E d i t o r i a l s , advertisements, p o l -i t i c a l speeches, c o u r t evidence were analyzed f o r b a s i c assumptions and f o r the evidence o f f e r e d i n support of the given c o n c l u s i o n s . A f t e r t h i s p r e l i m i n a r y t r a i n i n g the t h i n k i n g of the p u p i l s was guided to a c o n s i d e r a t i o n of space "where ideas s t u d i e d are devoid of strong emotional content and the p u p i l s a b i l i t y to t h i n k i s not s t i f l e d by p r e j u d i c e or b i a s " . The students were encouraged to make t h e i r own assumptions and i m p l i c a t i o n s based on these. The major emphasis was not on the theorems proved, but on the method of proof and t h i s method was g e n e r a l i z e d and app-l i e d to non-mathematical s i t u a t i o n s . 9 I b i d . , pp. 13-14. 22 The r e s u l t s of Fawcett's study l e d him to the f o l -lowing c o n c l u s i o n s : 1. Mathematical methods i l l u s t r a t e d by a small num-ber of theorems y i e l d s a c o n t r o l of the s u b j e c t . matter of geometry at l e a s t equal to t h a t o b t a i n -ed from the usual formal course. (Determined by a d m i n i s t r a t i o n to the experimental and c o n t r o l groups of the "Every P u p i l Plane Geometry Test", p u b l i s h e d by the State Department of Educat i o n at Columbus, Ohio ) . 2. By f o l l o w i n g the ( c l a s s ) procedures ( d e s c r i b e d ) , i t i s p o s s i b l e to improve the r e f l e c t i v e t h i n k -ing of secondary school p u p i l s . 3. This improvement i n the p u p i l s ' a b i l i t y f o r r e -f l e c t i v e t h i n k i n g i s gen e r a l i n c h a r a c t e r and t r a n s f e r s to a v a r i e t y of s i t u a t i o n s . 4. The usual formal course i n demonstrative geom-e t r y does not improve the r e f l e c t i v e t h i n k i n g of pu p i l s . 1 0 A c a r e f u l study of Fawcett's r e s e a r c h r e v e a l s c e r -t a i n l i m i t a t i o n s . The f i r s t of these concerns the time con-sumed duri n g the experiment. He spent some two years cover-ing the same mathematical m a t e r i a l that i s normally covered i n one year by the t r a d i t i o n a l method. T h i s , of course, l i m i t s the use i n the average secondary school where the time f a c t o r has to be c o n s i d e r e d . The second l i m i t a t i o n i n v o l v e s the t e s t used to determine the growth i n the a b i l -i t y of students to analyze non-mathematical m a t e r i a l s . I b i d . , pp. 55-56. 23 Since t h i s t e s t r e q u i r e d s u b j e c t i v e s c o r i n g and " f o u r d i f f e r -ent people, one of whom was the w r i t e r (Fawcett), scored these t e s t s independently and from the r e s u l t s a composite 11 score was found f o r each p u p i l " , one wonders whether the r e s u l t s would have been d i f f e r e n t i f scored by four d i f f -erent people. N e v e r t h e l e s s , the study had a g r e a t impact on the methods of te a c h i n g geometry and many of the techniques used i n the experimental groups are c u r r e n t l y emphasized. IV THE ULMER STUDY Since Fawcett's study, many experiments have been conducted to demonstrate how non-mathematical reasoning m a t e r i a l combined w i t h the t e a c h i n g of demonstrative geom-e t r y can improve g e n e r a l reasoning a b i l i t y . One such study 1 2 was conducted by G i l b e r t Ulmer. He set out to answer the q u e s t i o n , as to whether teachers could expect a " l a r g e amount of t r a n s f e r of reasoning under o r d i n a r y class-room s i t u a t i o n s where demonstrative geometry i s taught, i f they 13 make a c o n s c i e n t i o u s attempt to teach f o r i t " . 11 I b i d . , p. 103. 1 2 G i l b e r t Ulmer, "The Teaching of Geometry to C u l -t i v a t e R e f l e c t i v e T h i n k i n g " , The J o u r n a l of Experimental  E d u c a t i o n , V o l . 8, Sept., 1939. l 3 I b i d . , p. 18. 24 In order to answer t h i s , he examined the records of 1,239 students i n seven d i f f e r e n t schools f o r the purpose of choosing h i s c o n t r o l and experimental groups. A f t e r he had equated h i s c o n t r o l and experimental groups he used only 990 students who were d i v i d e d i n t o the f o l l o w i n g groups. An experimental geometry group c o n s i s t i n g of twenty-one d i f f e r e n t classes.where the t e a c h i n g attempted to "improve the q u a l i t y of the p u p i l s ' t h i n k i n g by making use of the o p p o r t u n i t y o f f e r -ed i n geometry to study p r i n c i p l e s of r e f l e c t i v e t h i n k i n g " . A geometry c o n t r o l group c o n s i s t i n g of f i f t e e n c l a s s e s , " i n which no p a r t i c u l a r emphasis was p l a c e d upon methods of t h i n k i n g or upon the app-l i c a t i o n of the k i n d of t h i n k i n g done i n geom-e t r y to non-geometric s i t u a t i o n s " . A non-geometry c o n t r o l group c o n s i s t i n g of 575 " p u p i l s who were not e n r o l l e d i n geometry and who had never p r e v i o u s l y s t u d i e d geometry". 1 4 These groups were equated on the b a s i s of chronolog-i c a l age, i n t e l l i g e n c e q u o t i e n t , and the i n i t i a l t e s t scores on a reasoning t e s t p a t t e r n e d a f t e r those developed by-the P r o g r e s s i v e Education A s s o c i a t i o n as p a r t of t h e i r e v a l u a t i o n program i n the E i g h t Year Study. The exper-imental c l a s s e s s t r e s s e d the v a r i o u s aspects of r e f l e c t i v e t h i n k i n g such as: 1 4 I b i d . , pp. 18-19. 25 I f , then or p o s t u l a t i o n a l t h i n k i n g , The importance of d e f i n i n g key words and phrases, Reasoning by g e n e r a l i z a t i o n . Reasoning by analogy, D e t e c t i n g i m p l i c i t assumptions, Inverses and converses, I n d i r e c t p r o o f . Name c a l l i n g . 1^ As a r e s u l t of h i s experiment Ulmer concludes t h a t , . . . i t i s p o s s i b l e f o r high school t e a c h e r s , under normal class-room c o n d i t i o n s , to teach i n such a way as to c u l t i v a t e r e f l e c t i v e t h i n k i n g , that t h i s can be done without s a c r i f i c i n g an understanding of geometric r e l a t i o n s h i p s , and that p u p i l s at a l l I.Q. l e v e l s are capable of p r o f i t i n g from such i n -s t r u c t i o n . The r e s u l t s . . . i n d i c a t e that even what i s commonly r e p o r t e d as s u p e r i o r geometry has l i t -t l e e f f e c t upon a p u p i l ' s behaviour i n the d i r e c t -i o n of r e f l e c t i v e t h i n k i n g unless d e f i n i t e p r o v i s -ions are made to study methods of t h i n k i n g as an important end i n i t s e l f . 1 6 K e l l o g g p o i n t s out some r a t h e r i n t e r e s t i n g l i m i t -a t i o n s which may be a t t r i b u t e d to the Ulmer study, such as: P a r t i c i p a t i n g teachers were chosen on the b a s i s of i n t e r e s t and p r o x i m i t y , thus l i m i t i n g the g e n e r a l -i z a b i l i t y of the f i n d i n g s . This s e l e c t i o n of t e a -chers i n t u r n b i a s e d the choice of p u p i l s who par-t i c i p a t e d . C o n t r o l and experimental teachers were equated on s u b j e c t i v e c r i t e r i a . The assignment of teachers to the method was a r b i t r a r y r a t h e r than random. 1 5 i b i d . , p. 21. 1 6 I b i d . , p. 25. 26 F u r t h e r , no adjustments were made f o r i n i t i a l d i f f -ences among groups when the a n a l y s i s was completed. The s t u d i e s of Fawcett and Ulmer showed beyond doubt that r e f l e c t i v e t h i n k i n g ( c r i t i c a l t h i n k i n g ) of p u p i l s c o u l d be improved i n c o n j u n c t i o n w i t h the teaching of dem-o n s t r a t i v e geometry by the i n c l u s i o n of non-mathematical m a t e r i a l . However Ulmer's unique c o n t r i b u t i o n was to show, to a l i m i t e d degree, that t h i s r e f l e c t i v e t h i n k i n g c o u l d be taught i n the o r d i n a r y geometry class-room p e r i o d w i t h normal time a l l o t m e n t , i f teachers make a c o n s c i e n t i o u s e f f o r t to teach f o r i t . By way of c o n t r a s t , Fawcett's me-thod r e q u i r e d twice as long as Ulmer's to teach the same t r a d i t i o n a l course i n geometry. V THE GADSKE STUDY Another study on the improvement of c r i t i c a l t h i n k -ing by means of i n s t r u c t i o n i n demonstrative geometry was conducted by G a d s k e 1 8 i n 1940. He attempted to answer the ^'Theodore E. K e l l o g g , The R e l a t i v e E f f e c t s of  V a r i a t i o n s i n Pure and P h y s i c a l Approaches to the Teaching  E u c l i d e a n Geometry on P u p i l ' s Problem S o l v i n g , unpublished D o c t o r a l t h e s i s . U n i v e r s i t y of Minnesota, 1956, p. 12. Richard 1 Edward Gadske, "Demonstrative Geometry as a means f o r Improving C r i t i c a l T hinking, Summaries of  D o c t o r a l D i s s e r t a t i o n s , June-August 1940, Northwestern U n i v e r s i t y , V o l . V I I I , pp. 91-97. 27 f o l l o w i n g q u e s t i o n s : 1. Can demonstrative .geometry be used by mathem-a t i c s teachers as a means of developing more e f f e c t i v e c r i t i c a l t h i n k i n g a b i l i t i e s i n high school p u p i l s ? 2. Does the usual course i n demonistrative geometry accomplish t h i s purpose? 3. How do p u p i l s i n geometry c l a s s e s i n which c r i t -i c a l t h i n k i n g i s s t r e s s e d compare i n t h i s a b i l -i t y w i t h p u p i l s i n geometry c l a s s e s i n which c r i t i c a l t h i n k i n g i s not emphasized? 4. How do p u p i l s i n geometry c l a s s e s i n which c r i t -i c a l t h i n k i n g i s s t r e s s e d compare i n knowledge of usual s u b j e c t matter i n geometry w i t h . p u p i l s i n geometry c l a s s e s i n which t h i s o b j e c t i v e i s not e m phasized. 1 9 His experimental d e s i g n employed 659 tenth grade p u p i l s from s i x d i f f e r e n t p u b l i c s c h o o l s . The teachers who were s e l e c t e d to teach the students i n the experimental group were chosen on the b a s i s of i n t e r e s t . These were matched w i t h c o n t r o l teachers on the b a s i s of t e a c h i n g ab-i l i t y and experience. In t e a c h i n g the experimental groups, techniques were developed which, "fo c u s e d a t t e n t i o n of p u p i l s upon each of the ten elements of c r i t i c a l t h i n k i n g ; seeking motives, q u e s t i o n i n g the meaning of terms, d e t e c t i n g and q u e s t i o n i n g u n d e r l y i n g assumptions, s e a r c h i n g f o r more f a c t s , t e s t i n g f a c t s f o r p e r t i n e n c e , d i s c r i m -i n a t i n g between f a c t and assumption, e v a l u a t i n g f o r b i a s or p r e j u d i c e , t e s t i n g c o n c l u s i o n s f o r c o n s i s t e n c y w i t h assumptions, suspending judgement and c o n s i d e r i n g consequences" I b i d . , p. 93 . 20Ibid., p. 93. 28 The c o n t r o l group on the other hand, r e c e i v e d none of t h i s t r a i n i n g i n the elements of c r i t i c a l t h i n k i n g but f o l l o w e d the t r a d i t i o n a l course i n demonstrative geometry. As a r e s u l t of t h i s study, Gadske concluded t h a t : Demonstrative geometry may be used as a means of d e v e l o p i n g more e f f e c t i v e c r i t i c a l t h i n k i n g a b i l i t i e s . . . The usual course, i n demonstrative geometry does not accomplish these purposes as w e l l as the experimental course. C l a s s e s i n which c r i t i c a l t h i n k i n g was emphas-i z e d surpassed c l a s s e s i n t h i s a b i l i t y i n which c r i t i c a l t h i n k i n g was not s t r e s s e d . C l a s s e s i n which c r i t i c a l t h i n k i n g was s t r e s s e d compare f a v o r a b l y i n the knowledge of usual sub-j e c t matter of geometry w i t h c l a s s e s i n which c r i t i c a l t h i n k i n g was not emphasized.21 VI THE KOPPENHAVER STUDY Koppenhaver, i n 1943, repeated Fawcett's e a r l i e r study using more modern techniques f o r design and a n a l y s i s He randomly assigned f o r t y - f o u r students to the experimen-t a l and c o n t r o l groups. The experimental group f o l l o w e d 2 3 the procedure used by' Fawcett of not using a t e x t , and 21Ibid., p. 96. 2 2 C h e s t e r V. Koppenhaver, "A Comparative Study of the E f f e c t i v e n e s s of the Nature of Proof, and a C o v e n t i o n a l Method of Teaching Plane Geometry", unpublished D o c t o r a l t h e s i s , Temple U n i v e r s i t y , 1943. 23Fawcett, Nature of Proof, pp. 28-87. 29 having the students determine t h e i r own d e f i n i t i o n s , assum-p t i o n s and theorems. Great emphasis was p l a c e d upon non-mathematical reasoning m a t e r i a l . The c o n t r o l group f o l l o w e d a t y p i c a l t e x t , and d i d not d i s c u s s a p p l i c a t i o n s of reason-ing i n s i t u a t i o n s o u t s i d e of mathematics. Koppenhaver s t a t e s t h a t . The purpose of t h i s study i s to compare the e f f -e c t i v e n e s s i n terms of the measurable outcomes of the "Nature of Proof" w i t h a c o n v e n t i o n a l method of t e a c h i n g plane geometry. A second o b j e c t i v e of t h i s study, without which the f i r s t c o u l d not be achieved, i s the development of a course of study i n plane geometry based upon & s i m i l a r to the "Nature of Proof". 2 4 , 2 5 -As might be expected i n the l i g h t of the s t u d i e s by Fawcett and Gadske, Koppenhaver r e p o r t s : No s i g n i f i c a n t d i f f e r e n c e between the two methods r e l a t i v e to achievement i n f a c t u a l i n f o r m a t i o n and s k i l l s i n reasoning about geometric s i t u a t i o n s . The r e s u l t s a l s o i n d i c a t e w i t h a high degree of c e r -t a i n t y that there i s a r e a l d i f f e r e n c e w i t h r e s p e c t to the a b i l i t y to reason about and analyze s i t u a t -ions which are non-mathematical i n c h a r a c t e r . They (the r e s u l t s ] show that the a b i l i t y of students to do c r i t i c a l , r e f l e c t i v e t h i n k i n g can be c u l t i v a t e d when there i s a conscious attempt on the p a r t of the teacher to c u l t i v a t e t h i s type of t h i n k i n g . D "Nature of Proof" r e f e r s to m a t e r i a l s d e v e l -oped by H.P. Fawcett. ^Koppenhaver, op. c i t . , pp. 1-2. 2 6 I b i d . , pp. 148-149. VII THE LEWIS STUDY 30 S t i l l another study s i m i l a r to the Fawcett, Ulmer and Gadske s t u d i e s was one conducted by Lewis i n 1950 . 2 ^  The purpose of h i s study was: 1. To develop and p r e s e n t m a t e r i a l s which may be used i n the t e a c h i n g of demonstrative geometry so as to c u l t i v a t e w i t h i n the c h i l d the power to understand the nature of p r o o f . 2. To i l l u s t r a t e how mathematical reasoning mater-i a l taught i n elementary geometry can be a p p l i e d to some s i t u a t i o n s i n v o l v i n g c r i t i c a l t h i n k i n g that i s non-mathematical. 3. To a s c e r t a i n whether the techniques of s t r e s s -ing an understanding of the nature of proof i n plane geometry and i l l u s t r a t i n g how t h i s may be a p p l i e d to non-mathematical concepts w i l l l e a d to a g r e a t e r a b i l i t y to t h i n k c r i t i c a l l y about c u r r e n t a f f a i r s , s c i e n t i f i c i n v e s t i g a t i o n s , s t a t i s t i c a l data and l i k e , than i f the course were taught i n the t r a d i t i o n a l manner. 4. To compare t e s t scores achieved on a standard-i z e d t e s t i n E u c l i d e a n geometry by students who have been taught by the "ex p e r i m e n t a l " method w i t h those who have r e c e i v e d the usual t r a d i t -i o n a l course . 5. To determine the extent to which students apply t h e i r knowledge of c r i t i c a l a n a l y s i s when they are w i t h i n the c o n f i n e s of a class-room. 28 ^ H a r r y Lewis, An Experiment i n Developing C r i t i c a l  T h i n king Through the Teaching of Plane Demonstrative Geom-e t r y , unpublished D o c t o r a l t h e s i s , New York U n i v e r s i t y , 1950 . 2 8 I b i d . , pp. 2-3. 31 In order to answer these q u e s t i o n s Lewis set up an experimental group of 22 p u p i l s and two c o n t r o l groups of 35 and 21. The i n i t i a l measures i n c l u d e d the O t i s Quick Sc o r i n g Mental A b i l i t y T est, Form D, the Nelson Denny Reading Test, Form A, the Watson-Glaser Test of C r i t i c a l T hinking, and an I n t e r p r e t a t i o n of Data Test, 2.52 d e v i s e d by E.R. Smith and R.W. T y l e r . The c o n t r o l groups f o l l o w e d the t r a d i t i o n a l course i n demonstrative geometry which i n c l u d e d such u n i t s as " D e f i n i t i o n s and Assumptions, Congruent T r i a n g l e s , Para-l l e l L i n e s , P a r a l l e l o g r a m s , C i r c l e s , S i m i l a r T r i a n g l e s , & Areas of Polygons".^9 The experimental group d i s c u s s e d only those u n i t s which aided i n the development of c r i t i c a l t h i n k i n g . In a d d i t i o n the course was not d i v i d e d i n t o the t r a d i t i o n a l u n i t s such as congruent t r i a n g l e s , p a r a l l e l l i n e s , c i r c l e but was d i v i d e d i n t o the f o l l o w i n g c a t e g o r i e s . 1. D e f i n i t i o n s (a) Need f o r c l e a r d e f i n i t i o n s , (b) Need f o r s t i p u l a t i n g u ndefined terms, (c) Types of d e f i n i t i o n s , (d) A r i s t o t e l i a n or c o n n o t a t i v e d e f i n i t i o n , (e) E f f e c t upon the c o n c l u s i o n of an a l t e r -a t i o n i n d e f i n i t i o n , ( f ) C olored words and t h e i r e f f e c t upon i n d i v i d -u a l emotions. I b i d . , p. 8 9.. 32 2. Assumptions (a) Need f o r assumptions, (b) " A u t h o r i t a t i v e " b a s i s of an assumption, (c) E f f e c t upon c o n c l u s i o n by an a l t e r a t i o n i n an assumption. 3. D i r e c t Proof (a) P r o p o s i t i o n s ( i ) C a t e g o r i c a l ( i i ) H y p o t h e t i c a l (b) S y l l o g i s t i c r easoning ( i ) C a t e g o r i c a l s y l l o g i s m ( i i ) H y p o t h e t i c a l s y l l o g i s m (c) D i s c u s s i o n of words, " a l l " , "some", "no", ( i ) Reasoning from the converse, i n v e r s e , and, contropos i t i ve . 4. I n d i r e c t Proof (a) A r i s t o l e ' s Law of the Excluded Middle (b) D i f f e r e n c e between Contrary and C o n t r a d i c -t o r y Statements. (c) D i f f i c u l t i e s encountered i n a p p l i c a t i o n of i n d i r e c t p r o o f . (d) L i m i t a t i o n s of A r i s t o l e ' s Law. (e) Reasoning that may be s u b s t i t u t e d f o r t h i s law, Casual A n a l y s i s or "Post Hoc" r e a s o n i n g . 5. Proof by I n d u c t i o n (a) Wide use of incompLete i n d u c t i o n , (b) Meaning and value of e m p i r i c a l p r o o f s , (c) D i f f i c u l t y of a p p l y i n g complete mathematical induction". (d) I n t e r p r e t a t i o n of data w i t h r e f e r e n c e to r e c o g n i t i o n of t r e n d , e x t r a p o l a t i o n , i n t e r -p o lation," and sampling.30 SOi b i d . , pp. 92-93. 33 The f i n a l e v a l u a t i o n i n c l u d e d ; "Co-operative Plane Geometry T e s t " , "Watson-Glaser Test of C r i t i c a l T h i n k i n g " , and the " I n t e r p r e t a t i o n of Data Test", and as a r e s u l t of h i s study, Lewis concludes t h a t : 1. Demonstrative geometry taught by the experimen-t a l method d e s c r i b e d i n the study developed a c h i l d ' s a b i l i t y i n r e f l e c t i v e t h i n k i n g i n non-mathematical areas f a r g r e a t e r than e i t h e r t r a d -i t i o n a l course i n t h i s s u b j e c t or no exposure to t h i s s u b j e c t at a l l . 2. Learning demonstrative geometry through the ex-perimental method used i n t h i s study appeared to y i e l d as thorough an understanding of con-tent u s u a l l y a s s o c i a t e d w i t h t h i s s u b j e c t as d i d the t r a d i t i o n a l method.31 VII I SUMMARY AND CONCLUSIONS The s t u d i e s of Fawcett, Ulmer, Gadske, Koppenhaver, and Lewis i n d i c a t e t h a t when p u p i l s are exposed to the t r a d i t i o n a l course i n demonstrative plane geometry where the emphasis i s upon geometric content and very l i t t l e s t r e s s i s p l a c e d on a p p l y i n g c r i t i c a l reasoning to non-mathematical s i t u a t i o n s , the amount of t r a n s f e r of t h i s r e a s o n i n g to l i f e s i t u a t i o n s i s very s m a l l . F u r t h e r , when there i s a conscious e f f o r t to show the a p p l i c a t i o n s of these p r i n c i p l e s of c r i t i c a l r e a s o n i n g to non-mathematical s i t u a t i o n s , the t r a n s f e r of t h i s a b i l i t y to other s i t u a t -ions i s r e a l l y s i g n i f i c a n t . The f i n d i n g s are n e i t h e r I b i d . , p. 249. 34 unusual or unexpected. In f a c t , these r e s u l t s could have been p r e d i c t e d w i t h a f a i r l y h i g h degree of c e r t a i n t y w i t h -out performing the above experiments by j u s t examining the s t u d i e s which have been conducted on t r a n s f e r i n other 3 2 f i e l d s . But what i s unusual i s that the m a j o r i t y of authors of text-books i n demonstrative geometry have gen-e r a l l y i gnored the r e s u l t s of these s t u d i e s by g i v i n g very l i t t l e , i f any,, prominence to the i n c l u s i o n of non-mathem-a t i c a l ma t e r i a1s. Not only has there been very l i t t l e a t t e n t i o n g i v e n to the i n c l u s i o n of t h i s non-mathematical m a t e r i a l , but a l s o very l i t t l e a t t e n t i o n has been given by r e s e a r c h e r s or text-book w r i t e r s concerning changes i n geometric exer-c i s e s . In p a r t i c u l a r , most demonstrative geometric t e x t s i n c l u d e as a very important type of e x e r c i s e , the problem where the student i s s u p p l i e d w i t h data e i t h e r g i v e n or assumed and t o l d p r e c i s e l y what c o n c l u s i o n s he must d e r i v e from t h i s d a t a . Fawcett notes t h a t t h i s method of prese n -t a t i o n d e p r i v e s a student of a very important method of l e a r n i n g , namely; that of d i s c o v e r y and i n a d d i t i o n he has no experience i n checking the v a l i d i t y of statements that are not t r u e . Pedro T. Orata, "Recent Research S t u d i e s on Trans-f e r of T r a i n i n g w i t h I m p l i c a t i o n s f o r C u r r i c u l u m Guidance and Personnel Work" Harvard Review, V o l . I I , pp. 3S9-378, 1941 . 35 At no time does the student have experience i n checking the v a l i d i t y of a statement that i s not c o n s i s t e n t w i t h given data...Is it; not j u s t as im-p o r t a n t to know how to d i s p r o v e a hypothesis as i t i s to prove one No doubt Fawcett had t h i s i n mind when he conducted 3 4 h i s now well-known study of 1938 i n which he encouraged the students of the experimental group to make t h e i r own 3 5 d i s c o v e r i e s and to prove them d e d u c t i v e l y . However, i t i s d i f f i c u l t , i f not i m p o s s i b l e , to a s c e r t a i n what p o r t i o n of the g a i n i n c r i t i c a l reasoning was due to the r e v i s e d geometry e x e r c i s e s and what to the i n c l u s i o n of non-mathem-a t i c a l m a t e r i a l s . Thus, i t has been shown that some s t u d i e s (Fawcett and Koppenhaver) have attempted to r e v i s e the geometry ex-e r c i s e s but the e f f e c t s of these r e v i s i o n s have been ob-scured by the i n c l u s i o n of non-mathematical r e a s o n i n g . The w r i t e r of t h i s study proceeds w i t h the object of d e t e r -mining what the e f f e c t on c r i t i c a l reasoning a b i l i t y of students w i l l be, when the only v a r i a b l e i s the nature of the geometric e x e r c i s e s . 3 3 H a r o l d P. Fawcett, "Quod er a t Demonstrandum", The Mathematics Teacher, V o l . 49, Jan., 1956, p. 4. 3 4 H a r o l d P. Fawcett, The.Nature of Proof, 1938. 3 5 I b i d . , p. 91. 3 6 S e e p a g e H 9 of t h i s t h e s i s f o r samples of these r e v i s e d e x e r c i s e s . T h i s chapter has reviewed the r e s e a r c h s t u d i e s which were concerned w i t h the development of c r i t i c a l r easoning by the study of demonstrative plane geometry. * * * * CHAPTER I I I TEACHING PROCEDURES AND MATERIALS Th i s chapter i s devoted to a d e s c r i p t i o n of the methods and m a t e r i a l s employed i n t e a c h i n g demonstrative plane geometry to the c o n t r o l and experimental groups. I PRELIMINARY TRAINING The experimental and c o n t r o l groups r e c e i v e d approx-imately the same t r a i n i n g which i n c l u d e d the geometric ma-t e r i a l s c l a s s i f i e d below: (1) Experimental geometry which embraces simple c o n s t r u c t i o n s , d e f i n i t i o n s of geometric terms and the d i s -covery of c e r t a i n geometric r e l a t i o n s h i p s by experimental means. This n e c e s s i t a t e d e x t e n s i v e use of measuring de-v i c e s such as the r u l e r and p r o t r a c t o r . (2) Assumptions - axioms and p o s t u l a t e s . (3) Types of reasoning - i n d u c t i v e versus d e d u c t i v e . (4) . The t o p i c of congruent t r i a n g l e s was developed only to the p o i n t where students were r e q u i r e d to prove very elementary deductions by use of the p r i n c i p l e s of congruency. I t was at t h i s time that the use of t e x t 1 was d i s c o n t i n u e d F.M. Morgan, W.E. Breckenridge, Plane Geometry, Thomas Nelson & Sons, Toronto, O n t a r i o (Canada), 1954, pp. 1-94. 38 and i t s p l a c e was taken by two d i f f e r e n t workbooks espec-i a l l y designed f o r t h i s experiment by the i n v e s t i g a t o r . 2 P r i o r to using these workbooks, a s t a n d a r d i z e d t e s t i n c r i t i c a l t h i n k i n g was g i v e n . The g i v i n g of t h i s t e s t mar-ked the s t a r t of the experiment. The workbook 3 designed f o r the c o n t r o l group em-ployed the format of e x e r c i s e s which i s t y p i c a l of most demonstrative plane geometry t e x t s i n c u r r e n t h i g h school use, i n which the student i s t o l d p r e c i s e l y what to prove. On the other hand, the workbook^ designed f o r the exper-imental group employed the idea of not t e l l i n g the student s p e c i f i c a l l y what to prove, but r a t h e r of supplying him w i t h a l t e r n a t i v e s , which may or may not be p o s s i b l e to prove. That i s , the onus was p l a c e d on the student to de-termine which, i f any, of the a l t e r n a t i v e s could be proved on the b a s i s of the i n f o r m a t i o n g i v e n . The workbooks prepared f o r the c o n t r o l and the ex-perimental groups were d i s t r i b u t e d at the beginning of each p e r i o d and c o l l e c t e d at the end. oodwin Watson and Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l Test, New York, World Book Co., Form A, 1952. See page 123 of appendix. ^See page 116 of appendix. 39 A systematic check was made each p e r i o d to be sure that none of the workbooks l e f t the mathematics classroom. This check was deemed necessary f o r the f o l l o w i n g reasons: F i r s t , i f the workbooks had been taken home, then the amount of time spent by each student doing the e x e r c i s e s could not be c o n t r o l l e d i n both groups. Second, a s s i s t a n c e g i v e n the p u p i l s by parents and other would present another v a r i a b l e . T h i r d , the i n v e s t i g a t o r f e l t that i f the workbook l e f t the room,, some of the students i n the c o n t r o l group might s t a r t comparing t h e i r e x e r c i s e s w i t h those done by the exper-imental group and d i s c o v e r t h a t they were doing a d i f f e r -ent type of e x e r c i s e ^ . This was not deemed a d v i s a b l e be-cause, should the students f i n d out they were being t r e a t e d d i f f e r e n t l y i n both groups, then some of the more v o c a l students might c r e a t e a f e e l i n g of uneasiness i n the c l a s s . T h i s would a f f e c t the normal classroom atmosphere and pre-sent another v a r i a b l e . F i n a l l y , the experimental group, who had to s e l e c t the c o r r e c t hypotheses from those g i v e n , might r e c e i v e c l u e s from the c o n t r o l group who d i d the same exer-c i s e s but who were t o l d p r e c i s e l y what hypotheses to prove. N e i t h e r group was t o l d u n t i l the experiment was over that they were s u b j e c t s i n an experiment, where each group was doing a d i f f e r e n t type of e x e r c i s e . Upon care-f u l q u e s t i o n i n g • t h e i n v e s t i g a t o r was reasonably sure that no student was aware that he was p a r t i c i p a t i n g i n an exper-iment . 40 As a f u r t h e r check a g a i n s t the leakage of i n f o r m a t i o n from c o n t r o l to experimental group, the e x e r c i s e s i n both work-books were not i n i d e n t i c a l order, and the diagrams were a l t e r e d and l e t t e r e d d i f f e r e n t l y so as to appear t h a t they were not the same. A f u r t h e r p r e c a u t i o n to ensure that i n d i v i d u a l s of each group r e c e i v e d the same i n s t r u c t i o n s was the keeping of a d a i l y attendance r e c o r d . The students, who were ab-sent f o r any one day, were c a l l e d i n on t h e i r r e t u r n to r e c e i v e i n s t r u c t i o n i n those phases of the work t h a t they had missed. II THE TEACHING PROCEDURES AND MATERIALS USED IN CONTROL GROUP The c o n t r o l group s t a r t e d by reviewing the d e f i n -i t i o n s of various k i n d s of t r i a n g l e s and q u a d r i l a t e r a l s . ^ I t was s t r e s s e d that the diagrams used i n geometry should be as g e n e r a l as p o s s i b l e , and every e f f o r t should be made to a v o i d s p e c i a l c a s e s . For example, i f a student i s r e -q u i r e d to draw a t r i a n g l e and nothing e l s e i s s p e c i f i e d , he should draw one that i s n e i t h e r r i g h t angled, e q u i l a t e r a l nor i s o s c e l e s . See page 1 2 2 of appendix. 41 T h e r e a f t e r , very l i t t l e mention was made of g e n e r a l and s p e c i a l geometric f i g u r e s . 7 In f a c t , most of the diagrams accompanying the e x e r c i s e s i n the workbook s u p p l i e d the c o n t r o l group, were d e l i b e r a t e l y drawn to represent the most gene r a l case. That i s , the student r a r e l y concerned him-s e l f as to whether the diagrams were g e n e r a l or not. An e x e r c i s e t y p i c a l of t h a t encountered by the c o n t r o l group i s i l l u s t r a t e d below. 8 C a r e f u l examination of t h i s e x e r c i s e r e v e a l s the diagrams s u p p l i e d were very g e n e r a l , that i s t r i a n g l e RST i s n e i t h e r r i g h t - a n g l e d , e q u i l a t e r a l , or i s o s c e l e s . I t a l s o should be noted that the student i s t o l d p r e c i s e l y what to prove and he knows i n advance t h a t , that which he i s r e q u i r e d to prove, i s always t r u e . Thus, he i s never r e q u i r e d to prove any idea that i s f a l s e . In short, he knows the c o n c l u s i o n before he s t a r t s h i s p r o o f . Compare t h i s w i t h the extensive treatment g i v e n to the experimental group. See page: 116 of appendix. See pagel23 of appendix f o r more examples of t h i s type of e x e r c i s e . 42 This p r a c t i c e , of s u p p l y i n g the student w i t h a g e n e r a l i z e d diagram and r e q u i r i n g him to prove an idea which he knows i n advance (of p r o v i n g the e x e r c i s e ) to be t r u e , i s t y p i c a l of most t e x t books i n c u r r e n t use i n high schools today. q In f a c t , Fawcett i n d i c a t e s very few authors of t e x t books have attempted to develop t e x t s which do not supply the student w i t h the c o n c l u s i o n i n advance. However, he does mention that Rosskopf 1^ has developed a t e x t , i n which the student has to d i s c o v e r f o r h i m s e l f what he i s to prove. I l l THE TEACHING PROCEDURES AND MATERIALS USED IN EXPERIMENTAL GROUP The experimental group a l s o began by d e f i n i n g var-ious types of t r i a n g l e s and q u a d r i l a t e r a l s , but they r e -c e i v e d a more d e t a i l e d a n a l y s i s of these d e f i n i t i o n s than d i d the c o n t r o l group.1"'" For example, i t was p o i n t e d out that there are many kinds of q u a d r i l a t e r a l s . These, f o r q H a r o l d P. Fawcett, "Quod er a t Demonstrandum", The  Mathematics Teacher, V o l , 49, Jan, 1956, p. 3. 1 0 j 4 y r o n p m Rosskopf, Mathematics a Second Course, McGraw H i l l , New York, 1952. 1 1 S e e page 116 of appendix. 1 2 The term ' q u a d r i l a t e r a l ' i s used i n two senses. (1) As a general term to denote a f a m i l y which i n c l u d e s a l l four s i d e d polygons. (2) or to denote the most u n s p e c i a l i z e d member of t h i s fam-i l y , t h a t i s , one that has no angles or s i d e s equal. The word i s used here i n the former sense. 43 the sake of s i m p l i c i t y , can be thought of as be l o n g i n g to the q u a d r i l a t e r a l f a m i l y , which i n c l u d e s many s p e c i a l r e l -a t i v e s . The f a m i l y t r e e of the q u a d r i l a t e r a l s can be d i a -grammed as f o l l o w s : D FIGURE 1 THE QUADRILATERAL "FAMILY" The g u a d r i l a t e r a lis may be co n s i d e r e d here as the parent of a l a r g e f a m i l y of fo u r s i d e d f i g u r e s , which becomes more s p e c i a l i z e d as we proceed down, and each f i g u r e i s r e l a t e d to the previous one, which i n t u r n i s r e l a t e d to the o r i g -i n a l q u a d r i l a t e r a l . T h i s idea of r e l a t e d n e s s was f u r t h e r ^The term ' q u a d r i l a t e r a l * i s used here i n the sense of being the most u n s p e c i a l i z e d member of the quad-r i l a t e r a l f a m i l y . That i s , i t has no si d e s or angles e q u a l . 44 emphasized by the d e f i n i t i o n s s u p p l i e d f o r the va r i o u s kinds of q u a d r i l a t e r a l s . The f o l l o w i n g d e f i n i t i o n s were g i v e n : (1) Q u a d r i l a t e r a l i s a four s i d e d polygon (which has no angles or si d e s e q u a l ) . (2) P a r a l l e l o g r a m i s a q u a d r i l a t e r a l which has both p a i r s of opposite s i d e s p a r a l l e l . (3) Rectangle i s a p a r a l l e l o g r a m c o n t a i n i n g one r i g h t angle. (4) Square i s a e q u i l a t e r a l r e c t a n g l e . (5) Trapezium i s a q u a d r i l a t e r a l w i t h one p a i r of sides p a r a l l e l . (6) I s o s c e l e s Trapezium i s a trapezium i n which the n o n - p a r a l l e l s i d e s are eq u a l . (7) Rhombus i s an e q u i l a t e r a l p a r a l l e l o g r a m . The a t t e n t i o n of the c l a s s was drawn to the f a c t , that each f i g u r e was d e f i n e d i n terms of the one above i t i n the " f a m i l y t r e e " . I t was shown that t h i s method of d e f i n i t i o n had c e r t a i n advantages. F i r s t , i t made f o r a very con c i s e d e f i n i t i o n . Second, i t suggested c e r t a i n p r o p e r t i e s , which may be d i s c e r n e d from the d e f i n i t i o n . For example, s i n c e a p a r a l l e l o g r a m has i t s opposite s i d e s p a r a l l e l , then the r e c t a n g l e , square, and rhombus l i k e w i s e 45 have t h e i r opposite s i d e s p a r a l l e l , because they are spec-i a l cases of a p a r a l l e l o g r a m . The students p o i n t e d out, that they c o u l d c o n s i d e r a square as a s p e c i a l i z e d r e c t a n g l e . Then, one student suggested, that we v i o l a t e the above r u l e f o r the d e f i n i t i o n and d e f i n e a f i g u r e i n terms of another f i g u r e lower i n the f a m i l y t r e e " The example chosen was a " q u a d r i l a t e r a l i s a p a r a l l e l o g r a m " . The c l a s s soon r e a l -i z e d , that t h i s d e f i n i t i o n was i n c o n s i s t e n t , because i t im-p l i e d t h a t , t h a t which was true f o r a l l r e c t a n g l e s was a l s o true f o r a l l p a r a l l e l o g r a m s . Since a l l r e c t a n g l e s con-t a i n e d at l e a s t one r i g h t angle then a l l p a r a l l e l o g r a m s would c o n t a i n at l e a s t one r i g h t angle. T h i s , of course, i s not t r u e , because there are many p a r a l l e l o g r a m s , that do not c o n t a i n a r i g h t angle. This method of d e f i n i n g 14 terms was a l s o e x p l a i n e d by the use of a simple diagram. (See f i g u r e 2 page 46) In using t h i s d i a g r a m a t i c approach to d e f i n i t i o n s the most general c l a s s i f i c a t i o n i s i n d i c -ated by the o u t s i d e c i r c l e , which rep r e s e n t s a l l q u a d r i l a t -e r a l s . 1 ^  C i r c l e s were f i r s t used to analyze problems i n reasoning by Leonard E u l e r i n the e i g h t e e n t h century and are g e n e r a l l y r e f e r r e d to as " E u l e r ' s c i r c l e s " . 1 5Convex q u a d r i l a t e r a l s - v r e r e the only type c o n s i d -ered, that i s to say concave q u a d r i l a t e r a l s were not con-s i d e r e d i n t h i s course. FIGURE 2 CIRCULAR DIAGRAMS AIDS IN DEFINING TERMS 47 The next l a r g e s t c i r c l e encompasses " a l l p a r a l l e l o g r a m s " . The " a l l p a r a l l e l o g r a m s " c i r c l e c o ntains the c i r c l e of " a l l r e c t a n g l e s " and the " a l l r e c t a n g l e s " c i r c l e c o n t a i n s " a l l squares". Thus we see t h a t , as we proceed from the outer c i r c l e to the innermost c i r c l e , the f i g u r e s become more s p e c i a l i z e d . T h i s i m p l i e s that a square i s a s p e c i a l k i n d of r e c t a n g l e , which i n t u r n i s a s p e c i a l case of a p a r a l l e l o g r a m , and t h i s i n t u r n a s p e c i a l case of a quad-r i l a t e r a l . I t was p o i n t e d out to the students, that t h i s has important i m p l i c a t i o n s , when we are d e f i n i n g f i g u r e s . For example a square has four equal s i d e s , at l e a s t one r i g h t angle (because i t i s a s p e c i a l k i n d of a r e c t a n g l e ) , opp-o s i t e sides p a r a l l e l (because i t i s a s p e c i a l k i n d of p a r a -l l e l o g r a m ) and that i t i s a four s i d e d polygon (because i t i s a s p e c i a l k i n d of q u a d r i l a t e r a l ) . Not only d i d t h i s diagramming i n d i c a t e these p r o p e r t i e s of f i g u r e s , that r e -s u l t from the d e f i n i t i o n , but a l s o i t a s s i s t e d the p u p i l s i n determining which was the more gen e r a l f i g u r e . For example, which i s the. more general f i g u r e , the rhombus or the p a r a l l e l o g r a m ? The answer of course i s , t h a t the para-l l e l o g r a m i s , because, by d e f i n i t i o n , (and by diagramming) i t i n c l u d e s a l l rhombuses. With r e f e r e n c e to the w r i t t e n d e f i n i t i o n s and the c i r c l e diagrams, the f o l l o w i n g t y p i c a l q u e s t i o n s were posed: 1. Which i s a more gen e r a l f i g u r e , the r e c t a n g l e or the p a r a l l e l o g r a m ? 2. Could you c l a s s i f y a square as a s p e c i a l k i n d of p a r a l l e l o g r a m ? 3. Could you d e f i n e a p a r a l l e l o g r a m as a r e c -t a n g l e ? 4. Which i s more s p e c i a l i z e d , the square, or the rhombus? As i t was very important t h a t the student should draw as general a diagram as p o s s i b l e , he was exposed to the f o l l o w i n g type of e x e r c i s e s : 1. Pick out the f i g u r e i n the f o l l o w i n g that r e p r e s e n t s the most ge n e r a l case. 2. Draw a f i g u r e t h a t best r e p r e s e n t s the f o l l o w -(b) 1 3 m g : (a) A t r i a n g l e RST (b) An i s o s c e l e s t r i a n g l e ABC i n which AB i s the base. 49 3. In each of the f o l l o w i n g q u e s t i o n s redraw ( i f necessary) the f i g u r e to r e f l e c t more accur-a t e l y the g i v e n c o n d i t i o n s . R (a) (b) (c) A Given RST i n which IS = /_T G iven Q u a d r i l a t e r a l ABCD Given AC = BC D mid pt of AB AF _ B E 1 6 This t r a i n i n g , i n the i m p l i c a t i o n s of d e f i n i t i o n s , was very necessary f o r the experimental group, because i t prepared them f o r the experimental type of e x e r c i s e under study i n t h i s i n v e s t i g a t i o n . The f i n a l t r a i n i n g i n v o l v e d s e l e c t i n g from a number of hypotheses ' the one which, i n terms of the data, c o u l d be shown to be p o s s i b l e . With t h i s i n mind the f o l l o w i n g 16 For f u r t h e r examples of these e x e r c i s e s see page 116 i n the appendix. 'The term h y p o t h e s i s i s used here i n the s c i e n t i -f i c sense, that i s , a t e n t a t i v e theory to be t e s t e d r a t h e r than as the g i v e n or assumed data. 50 e x e r c i s e s were d e v i s e d . 18 In each of the f o l l o w i n g q u e s t i o n s s e l e c t the hy-p o t h e s i s , which can most l i k e l y be proved t r u e . In most cases t h i s can be determined by a c a r e f u l r e -drawing of the diagram to r e f l e c t more a c c u r a t e l y the g i v e n c o n d i t i o n s and by seeing whether the p a r t s ( s i d e s or angles) are c o r r e s p o n d i n g l y p l a c e d . Underline the c o r r e c t h y p o t h e s i s . (a) Given (1 = [2 BA = BC D C A Hypotheses (1) (2) (3) (4) (5) AB = AC U = U BC = AC IJ = 1&BC None of the above (b) B G i ven AD = CF AB = EF IJ /J Hypothe se s (1) (2) (3) (4 ]•, (5) IJ = U IJ = IJ AB — CE AD = EF None of the above aSee appendix page 117 for.more examples of the same type. 51 A f t e r t h i s p r e l i m i n a r y t r a i n i n g the p u p i l s s t a r t e d immediately on the experimental type of e x e r c i s e of which the f o l l o w i n g i s a t y p i c a l example: In the f o l l o w i n g q u e s t i o n s e l e c t the hypothesis which can most l i k e l y be proved true and c a r r y out the p r o o f . I t i s suggested that the diagram be redrawn to r e f l e c t more a c c u r a t e l y the g i v e n con-d i t i o n s . Given AD = DC U = U Hypothe se s (1) /_8 = /ADC (2) /_5 = /_11 (3) AD = BC (4) AB == BC B (5) None of the above A b r i e f examination of t h i s e x e r c i s e r e v e a l s some very marked d i f f e r e n c e s from the type a s s i g n e d to the con-t r o l g r o u p . 1 9 The most notable change was that the "to prove" step has been r e p l a c e d by the heading "hypotheses". I t was e x p l a i n e d to the student, t h a t he would no longer be t o l d e x a c t l y what to prove, but r a t h e r he would be sup-p l i e d w i t h a l t e r n a t i v e hypotheses of which one or none may of the exer-119for those See page 1 2 3 0 f appendix.for samples c i s e s assigned to the c o n t r o l group and page as s i g n e d to experimental group. 52 be proved to be t r u e . I t was to be h i s r e s p o n s i b i l i t y to s e l e c t the c o r r e c t hypothesis from those g i v e n ( i f there were some). As p r e v i o u s l y mentioned, the student was i n -formed, that the s e l e c t i o n of the best hypotheses c o u l d o f t e n be determined i n f o r m a l l y by redrawing the diagram to r e f l e c t more a c c u r a t e l y the gi v e n c o n d i t i o n s , or by c o n s i d -e r a t i o n of corresponding p a r t s . I t should be p o i n t e d out that the term hypothesis i s used here i n the sense of a p r o p o s i t i o n to be t e s t e d r a t h e r than the sense of "given 9 0 or assumed d a t a " . That i s to say, the term hypothesis i s used i n the sense that a s c i e n t i s t would use the term, namely; t e n t a t i v e ideas suggested'by the a v a i l a b l e data, which more c a r e f u l i n v e s t i g a t i o n may e i t h e r prove or d i s -prove. A c a r e f u l examination of the pr e v i o u s example r e -v e a l s , that the diagram s u p p l i e d to the student was r e a l l y not as gen e r a l as the data would suggest. From appearance i t looked l i k e a square, but the i n f o r m a t i o n s u p p l i e d d i d not suggest such a f i g u r e . As p r e v i o u s l y noted, the p u p i l was encouraged to redraw t h i s diagram i n very g e n e r a l terms Geometry t e x t s use t h i s term w i t h q u i t e a d i f f e r -ent meaning "as something assumed or conceded merely f o r the purposes of argument". 53 so that he c o u l d , by o b s e r v a t i o n , decide which hypotheses showed promise of being able to be proved. Such a r e v i s e d drawing might be as f o l l o w s : I t can be seen, by o b s e r v a t i o n , t h a t oh the b a s i s of the new and more g e n e r a l i z e d diagram, hypotheses num-bered (1), (2), and (3) show very l i t t l e promise. However, hypothesis (4) does look p r o m i s i n g . The next step would be to proceed to t e s t h y p o t h e s i s (4) by means of deductive p r o o f . The e x e r c i s e s were chosen so that t h i s redrawing of the diagram reduced the number of l i k e l y hypotheses to a small number ( u s u a l l y one or none) The q u e s t i o n may be now asked, as to why the exper-imenter chose to supply the experimental group w i t h exer-c i s e s t hat i n c l u d e d diagrams that were more s p e c i a l i z e d than the " g i v e n " (or data) would suggest. This was nec-essary because, had the student been s u p p l i e d w i t h a very g e n e r a l diagram, then each of the hypotheses would not have been e q u a l l y a t t r a c t i v e and, i n f a c t , i n most cases the 54 student c o u l d see t h a t many were not tenable by o b s e r v a t i o n and measurement. That i s to say, many of the hypotheses g i v e n would appear l e s s a t t r a c t i v e i f the diagram was very g e n e r a l . In f a c t , the very essence of t h i s study was to  see i f students developed t h e i r c r i t i c a l r easoning more  when they were not t o l d what to prove, but i n s t e a d , were  g i v e n • p o s s i b l e hypotheses which they had to t e s t f o r t h e i r  v a l i d i t y : or, to rephrase the problem, does the a d d i t i o n a l  experience of checking a statement, that i s not c o n s i s t e n t  w i t h the gi v e n data, a s s i s t a p u p i l i n developing h i s  reasoning? IV DESCRIPTION OF LOG BOOK A very necessary p a r t of t h i s experiment, were the 21 d a i l y e n t r i e s , made i n .a l o g book of the experiment. This book co n t a i n e d such items as the proposed l e s s o n p l a n f o r each p e r i o d , the extent of m a t e r i a l a c t u a l l y covered i n the p e r i o d , the students who were absent f o r that per-i o d , o b servations as regards a t t i t u d e of c l a s s , the names of those who l e f t the room or who were c a l l e d out of c l a s s , i n t e r r u p t i o n s w i t h p u b l i c address n o t i c e s or assembly of whole student body i n the auditorium, notes concerning 21see page 127of appendix f o r t y p i c a l sheet out of.1og book. 55 those who had to be c a l l e d i n a f t e r school f o r e x t r a i n s t r u c t i o n because they were absent, general notes r e -g a r d i n g f a c t o r s which might be c o n s i d e r e d to e f f e c t the r e s u l t s of the experiment (such as experimental group a l -ways having t h e i r l e s s o n before the c o n t r o l g r o u p ) . V FINAL TESTING A f t e r t h i s experiment was over, a s t a n d a r d i z e d t e s t 2 2 i n c r i t i c a l t h i n k i n g was g i v e n . This t e s t was an equated form of the t e s t which was a d m i n i s t e r e d at the s t a r t of the experiment. These equated forms served as instruments f o r measuring the gains or l o s s e s i n c r i t i c a l t h i n k i n g f o r the d u r a t i o n of the experiment. The d i f f e r e n c e of the gains made by the experimental and the c o n t r o l groups f u r n i s h e d a comparative measure of the e f f e c t i v e n e s s of the two methods. 2^ VI SUMMARY This chapter has d e s c r i b e d the methods and mater-i a l s which were used i n t e a c h i n g demonstrative plane geom-e t r y to the c o n t r o l and experimental groups. ^Goodwin Watson and Edward Maynard G l a s e r , C r i t i c a l  T h i n k ing A p p r a i s a l , Test, Form B, New York, World Book Co., 1952 . 23see chapter V f o r more d e t a i l e d r e s u l t s of t h i s experiment. CHAPTER IV NATURE OF CRITICAL THINKING Since the r e s u l t s of t h i s study are to be eval u a t e d i n terras of changes i n c r i t i c a l t h i n k i n g a b i l i t y , a more d e t a i l e d d e s c r i p t i o n of t h i s a b i l i t y i s d e s i r a b l e . In par-t i c u l a r , t h i s chapter w i l l be devoted to the va r i o u s as-pects of c r i t i c a l t h i n k i n g such as i t s importance, v a r i o u s d e f i n i t i o n s of i t , r e l a t i o n to such f a c t o r s as i n t e l l i g e n c e , age, and sex, e v a l u a t i o n of i t by commercial and teacher-made, t e s t s , j u s t i f i c a t i o n f o r using the Watson-Glaser t e s t i n t h i s study, and the l i m i t a t i o n s of t h i s t e s t . I THE IMPORTANCE OF CRITICAL THINKING The a b i l i t y to t h i n k c r i t i c a l l y about ideas i s im-por t a n t f o r e s t a b l i s h i n g an e f f e c t i v e democracy. I t has ofte n been s a i d t h at a democracy i s a p l a c e of c o n f l i c t i n g propaganda. The t r u t h of t h i s statement i n a democratic country can be r e a d i l y v e r i f i e d by examining newspaper a r t -i c l e s and e d i t o r i a l s , t e l e v i s i o n and magazine a d v e r t i s i n g . Thus, i t would seem necessary that the c i t i z e n s i n a democ-racy be able to reco g n i z e the more common f a l l a c i e s of r e a -soning and to evaluate d i f f e r e n t p o i n t s of view i n the l i g h t of f a c t s and not be swayed by personal p r e j u d i c e s . 57 There can be no q u e s t i o n t h a t t r a i n i n g i n c r i t i c a l t h i n k -ing i s very necessary. I t i s not s u r p r i s i n g to f i n d t h a t Brown"'" r e p o r t s , that i n a p o l l of 700 teachers s e l e c t e d at random from the N a t i o n a l C o u n c i l of the Teachers of Mathematics m a i l i n g l i s t , n e a r l y h a l f the teachers l i s t e d as the most important o b j e c t i v e of tea c h i n g demonstrative geometry, " t o develop a h a b i t of c l e a r t h i n k i n g and p r e c i s e e x p r e s s i o n " , and secondly, " t o gi v e a knowledge of f a c t s and p r i n c i p l e s of geometry". II DEFINITIONS OF CRITICAL THINKING Having agreed that a b i l i t y i n c r i t i c a l t h i n k i n g i s a worthwhile o b j e c t i v e to s t r i v e f o r , i n the tea c h i n g of mathematics, the q u e s t i o n remains as to how to d e f i n e t h i s a b i l i t y . The answer to t h i s q u e s t i o n i s made more d i f f i c -u l t by the f a c t that t h i s type of t h i n k i n g i s o f t e n des-c r i b e d by many a d j e c t i v e s other than " c r i t i c a l " . Although d i f f e r e n c e s i n meaning are not c l e a r l y apparent, the use of the word " c r i t i c a l " as an a d j e c t i v e i s slowly g a i n i n g precedence over the use of such d e s c r i p t i v e terms as " r e f l e c t i v e " , " e l a b o r a t i v e " , " s c i e n t i f i c " and " s t r a i g h t " . Other expressions r e l a t e d to c r i t i c a l t h i n k i n g Kenneth E. Brown, "Why Teach Geometry", The Math-ematics Teacher, March, 1950, V o l . 43, p. 105. 58 are "understanding", " s c i e n t i f i c method", and "problem s o l v i n g " 2 . Other phrases which have been used to d e s c r i b e t h i s a b i l i t y are " l o g i c a l t h i n k i n g " , "nature of proof", and " c l e a r t h i n k i n g " . Although there seems to be no complete agreement as to how c r i t i c a l t h i n k i n g should be d e f i n e d , neverthe-l e s s , there i s a good deal of o v e r l a p p i n g i n the v a r i o u s d e f i n i t i o n s . Many of the d e f i n i t i o n s suggested, d e f i n e t h i s type of t h i n k i n g i n terms of behaviour c h a r a c t e r i s t i c of a student doing c r i t i c a l t h i n k i n g . Thus, both Pingry° and Edwards 4 suggest that an adequate d e s c r i p t i o n of t h i s behaviour i s given by John Dewey's f i v e steps i n r e f l e c t i v e t h i n k i n g which are : 1. Becoming aware of a problem. A p e r p l e x i n g s i t u a t i o n has a r i s e n . The i n -d i v i d u a l i s aware that a problem e x i s t s . 2. D e f i n i n g the problem. The r a t h e r vague, p e r p l e x i n g s i t u a t i o n i s now made sharp and s p e c i f i c . The g o a l to be ach-i e v e d i s now known. AT. Bentley Edwards, "Measurement of Some Aspects of C r i t i c a l T h i n k i n g " , J o u r n a l of Experimental Education, V o l . 18, 1950, p. 263. 3 R o b e r t E . P i n g r y , " C r i t i c a l Thinking—What i s i t " , The Mathematics Teacher, V o l . 44, Nov, 1951, pp. 468-469 4Edwards, op. c i t . , p. 2 66. 5 9 3. Suggesting hypotheses f o r the s o l u t i o n of the problem. C o n j e c t u r e s , s u p p o s i t i o n s , guesses are made. The i n f e r e n c e i n v o l v e s a " l e a p " , "a jump", the p r o p r i e t y of which cannot be a b s o l u t e l y warr-anted i n advance. 4. Reasoning out i m p l i c a t i o n s of the suggested hypothese s . Tr a c i n g out the consequences of the v a r i o u s hypothe ses. 5. Experimental c o r r o b o r a t i o n . A t e s t of the hypothesis i s made a g a i n s t ex-per i e n c e . ^  Fawcett l i k e w i s e d e s c r i b e s the same type of t h i n k -ing when he r e f e r s to the behaviour e x h i b i t e d by a person who r e a l l y understands the "nature of p r o o f " . 1. He w i l l s e l e c t the s i g n i f i c a n t words and phrases i n any statement that are important to him and ask that they be c a r e f u l l y d e f i n e d . 2. He w i l l r e q u i r e evidence i n support of any con-c l u s i o n he i s pressed to accept. 3. He w i l l analyze that evidence and d i s t i n g u i s h f a c t from assumption. 4. He w i l l r e c o g n i z e s t a t e d and unstated assumptions e s s e n t i a l to the c o n c l u s i o n . 5. He w i l l e v aluate these assumptions, a c c e p t i n g some and r e j e c t i n g o t h e r s . 6. He w i l l evaluate the argument, a c c e p t i n g or r e -j e c t i n g the c o n c l u s i o n . 5 J o h n Dewey, How We Think, D.C. Heath Co., 1933, pp. 106-115. 60 7, He w i l l c o n s t a n t l y re-examine the assumptions which are behind h i s b e l i e f s and which guide h i s a c t i o n s . The authors of the t e s t , which was used i n t h i s study as the instrument f o r measuring c r i t i c a l t h i n k i n g suggest the f o l l o w i n g d e f i n i t i o n . A b i l i t y to t h i n k c r i t i c a l l y i n v o l v e s three t h i n g s ; (a) An a t t i t u d e of wanting to have supp o r t i n g e v i d -ence f o r opinions or c o n c l u s i o n s before assum-ing them to be t r u e . (b) A knowledge of the methods of l o g i c a l i n q u i r y which h e l p determine the weight of d i f f e r e n t '.kinds of evidence and which help one to reach warranted c o n c l u s i o n s . (c) S k i l l i n employing the above a t t i t u d e and know-ledge;'..^ In c o n c l u s i o n , Pingry, a f t e r c a r e f u l examination of the l i t e r a t u r e i n t h i s f i e l d , suggests most of the d e f i n -i t i o n s he has found tend to s t r e s s f i v e d i f f e r e n t aspects of c r i t i c a l t h i n k i n g , which a r e : 1. C r i t i c a l t h i n k i n g as c o l l e c t i n g data, o r g a n i z i n g data, and f o r m u l a t i n g hypotheses from d a t a . 6 H a r o l d P. Fawcett, The Nature of Proof, T h i r t e e n t h Yearbook, The N a t i o n a l C o u n c i l of Teachers of Mathematics, Bureau of P u b l i c a t i o n s , Teacher's C o l l e g e , Columbia Univer-s i t y , New York, 1952, pp. 11-12. 7 Goodwin Watson, Edward Maynard G l a s e r , " C r i t i c a l  T h i n k i n g A p p r a i s a l , " Manual f o r t e s t , World Book Co., New York, 1952, p. 8 . 61 2. C r i t i c a l t h i n k i n g as use of c o r r e c t p r i n c i p l e s of l o g i c and understanding the nature of p r o o f . 3. C r i t i c a l t h i n k i n g as c r i t i c i s m of t h i n k i n g . 4. C r i t i c a l t h i n k i n g as r e l a t e d to understanding of psychology of propaganda and a d v e r t i s i n g technique . 5. C r i t i c a l t h i n k i n g as synonymous wi t h problem s o l v i n g 8 . Even though there seems to be no agreement as to the s p e c i f i c aspects of c r i t i c a l t h i n k i n g , n e v e r t h e l e s s , there can be d i s c e r n e d i n these d e f i n i t i o n s a great deal of o v e r - l a p p i n g . In g e n e r a l , these d e f i n i t i o n s imply that c r i t i c a l t h i n k i n g i n v o l v e s more than the mere r e c a l l of f a c t u a l i n f o r m a t i o n . I t i n v o l v e s , among other t h i n g s , ex-amining p o s s i b l e e x p l a n a t i o n s and a l t e r n a t i v e courses of a c t i o n s which might be taken and an e v a l u a t i o n of the r e s u l t i n g c o n c l u s i o n s . I l l EVALUATION OF CRITICAL THINKING One of the most f r u i t f u l methods f o r g a i n i n g a f u r -ther understanding of t h i s type of t h i n k i n g , i s to examine some of the procedures used to evaluate i t . Some d e v i c e s which have been used to evaluate c r i t i c a l t h i n k i n g are, commercially-prepared t e s t s , teacher-made t e s t s , teacher o b s e r v a t i o n and judgement, parent and student o p i n i o n s Pingry, op. c i t . , pp. 466-467. 62 obtained through q u e s t i o n n a i r e s and i n t e r v i e w s , and the study of students' c r e a t i v e p r o d u c t s . As might be expected, the cre.ation of s i t u a t i o n s which g i v e a clue as to the q u a l i t y and q u a n t i t y of t h i s type of t h i n k i n g r e q u i r e s a g r e a t deal of i n g e n u i t y . And, as a r e s u l t , K i n s e l l a concludes: It i s r e l a t i v e l y easy f o r teachers to evaluate the a b i l i t y to r e c a l l i n f o r m a t i o n and to perform c e r -t a i n s k i l l s . I t i s not so easy, however, to assess the growth of concepts and development of under-st a n d i n g . I t i s s t i l l more d i f f i c u l t to gather evidence of the improvement i n a b i l i t y to apply what i s l e a r n e d to s i t u a t i o n s beyond those i n which the . l e a r n i n g took p l a c e . F i n a l l y , i t i s a r e a l c h a l -lenge to be able to judge whether students are g a i n -ing c e r t a i n a t t i t u d e s and a p p r e c i a t i o n s . Since the e v a l u a t i o n of t h i s c r i t i c a l t h i n k i n g r e -q u i r e s s k i l l , i n g e n u i t y and i s time-consuming, most t e a -chers have' g e n e r a l l y ignored t h i s type of t h i n k i n g . . . . f o r teachers of geometry r e a d i l y g i v e v e r b a l acceptance t h a t l o g i c a l or c r i t i c a l t h i n k i n g i s a primary o b j e c t i v e . Yet few teachers can i l l u s -t r a t e any methods used d i r e c t l y to teach t h i s obj.ec t i v e . 9John' K i n s e l l a , "The E v a l u a t i o n of Mathematical Learning", Emerging P r a c t i c e s i n Mathematics Education, Twenty-second Yearbook, N a t i o n a l C o u n c i l of Teachers of -Mathematics, Washington, D.C, 1954,- p. 339. 1 0 B j a r n e U l l s v i k , "An Attempt to Measure C r i t i c a l Judgement", School Science and Mathematics, V o l . 4 9, 1949, p. 446 . 63 Hence, i t i s not s u r p r i s i n g to note that the s i n g l e best source of i n f o r m a t i o n on t h i s type of e v a l u a t i o n i s not to be found i n teacher-made t e s t s but r a t h e r i n commer-c i a l l y - p r e p a r e d t e s t s . Since the demand f o r s t a n d a r d i z e d t e s t s i n c r i t i c a l t h i n k i n g would not be as great as that f o r i n t e l l i g e n c e t e s t s , i t i s only n a t u r a l to expect that the s e l e c t i o n and the q u a n t i t y of the former i s somewhat l i m i t e d by compar-i s o n w i t h that of the l a t t e r . U l l s v i k concludes t h a t , "there are but two t e s t s that a h i g h s c h o o l geometry t e a -cher may choose to secure a measure of student a b i l i t y to t h i n k c r i t i c a l l y i n non-geometric situations""'" 1. These "1 2 a r e : "The Co-operative Test of S o c i a l S t u d i e s " , and the "Watson-Glaser 1 3 t e s t s on c r i t i c a l t h i n k i n g " . An examin-a t i o n of these r e v e a l s more c l e a r l y what each author con-s i d e r s to be the v a r i o u s aspects of t h i s k i n d of t h i n k i n g . Probably the most g e n e r a l t e s t of the two mentioned i s the one d e v i s e d by Watson and G l a s e r . 1 ^ 1 1 I b i d . , p. 445. J.W. Wrightstone, 'Co-operative Test of S o c i a l  S t u d i e s A b i l i t e s , " C o-operative Test S e r v i c e , New York, 1936 13 G oodwin Watson and Edward Maynard G l a s e r , " C r i t i c a l  T h inking A p p r a i s a l " t e s t , World Book Co., New York,.1952. 1 4 S e e appendix page 128 f o r sample copy. 64 I t c o ntains f i v e s e c t i o n s which ar e : i n f e r e n c e , r e c o g n i t i o n of assumptions, deductions, i n t e r p r e t a t i o n , and e v a l u a t i o n of arguments. In the f i r s t s e c t i o n , i n f e r e n c e s from a given paragraph are to be c l a s s i f i e d as to degree of t r u t h or f a l s i t y . In the second s e c t i o n , the t e s t e e i s r e q u i r e d to i n d i c a t e which assumptions are and which are not i m p l i e d by a g i v e n statement. The t h i r d s e c t i o n d e a l s w i t h s y l l -o g i s t i c r e a s o n i n g . In the f o u r t h s e c t i o n , the examinee must i n d i c a t e which of the c o n c l u s i o n s does or does not f o l l o w from a given paragraph. The f i f t h s e c t i o n r e q u i r e s that the student d i s t i n g u i s h between arguments which are strong and important to the i s s u e and those which are un-important or i r r e l e v a n t . The second t e s t mentioned by U l l s v i k , the Co-oper-a t i v e Test of S o c i a l S t u d i e s , contains three p a r t s , which a r e : o b t a i n i n g f a c t s , drawing c o n c l u s i o n s from f a c t s and a p p l y i n g g e n e r a l f a c t s . In the f i r s t p a r t , the student i s r e q u i r e d to p i c k out c e r t a i n f a c t s a c c o r d i n g to p r e c i s e d i r e c t i o n s . Here, emphasis i s p l a c e d upon reading t a b l e s , reading graphs, where to l o c a t e f a c t s , and how to use an index. The second p a r t r e q u i r e s the student to compare one set of f a c t s w i t h another' and p i c k out those which correspond. The t h i r d p a r t p e r t a i n s to a p p l y i n g g e n e r a l f a c t s . 65 B r i e f mention should be made of another w e l l known s e r i e s of t e s t s f o r measuring c r i t i c a l t h i n k i n g which were produced under the guidance of the P r o g r e s s i v e Education A s s o c i a t i o n as pa r t of the e v a l u a t i o n program i n the. E i g h t Year S t u d y . 1 5 These t e s t s have the f o l l o w i n g t i t l e s : " I n t e r p r e t a t i o n of Data", " A p p l i c a t i o n of P r i n c i p l e s " , " A n a l y s i s of C o n t r o v e r s i a l W r i t i n g " , and "The Nature of Proof". These t e s t s are d i s t r i b u t e d by the Co-operative Test S e r v i c e . 1 6 A f i n a l example of a t e s t i n c r i t i c a l reasoning was 1 7 t h a t produced by Edwards. I t c o n s i s t e d of four t e s t s : j u d g i n g o p i n i o n s , matching f a c t s and p r i n c i p l e s , d e t e c t i n g good and bad arguments, and jud g i n g the worth of c o n c l u -sions based on f a c t s . There are many other commercially prepared t e s t s which have been designed to measure c r i t i c a l t h i n k i n g . These p a r t i c u l a r t e s t s were chosen not only because they were i l l u s t r a t i v e of the t r e n d i n items appearing c u r r e n t l y 1 5 E u g e n e R. Smith, Ralph W. T y l e r and E v a l u a t i o n S t a f f , " A p p r a i s i n g and Recording Student Progress, Harper Bros., New York, 1942, V o l . 2. 1 6 C o - o p e r a t i v e Test S e r v i c e , E d u c a t i o n a l T e s t i n g S e r v i c e , P r i n c e t o n , New J e r s e y . 1 7 T . Bently Edwards, Measurement of Some Aspects of C r i t i c a l T hinking, D o c t o r a l D i s s e r t a t i o n , U n i v e r s i t y of Cal-i f o r n i a , B e r k e l y , C a l i f o r n i a , 1949, r e p o r t e d i n Journal' of Experimental Education, V o l . 18, 1950, pp. 263-272. 66 on t h i s type of t e s t , but a l s o because they represent the instruments of measurement most commonly chosen by r e -searc h e r s i n t h i s f i e l d . The other methods of e v a l u a t i n g c r i t i c a l t h i n k i n g , such as teacher o b s e r v a t i o n and judgement wi t h anecdotal r e c o r d s , student and parent o p i n i o n s obtained through ques-t i o n n a i r e s and i n t e r v i e w s , and the study of the s t u d e n t s ' c r e a t i v e products, are open to the c r i t i c i s m that they can be scored only on a s u b j e c t i v e b a s i s . A second d i f f i c u l t y i s encountered when there i s an attempt to q u a n t i f y the r e s u l t s f o r sake of comparing s c o r e s . One important study that made extensive use of these methods f o r e v a l u a t i n g 18 c r i t i c a l t h i n k i n g was conducted by Fawcett. The n e c e s s i t y f o r having such measures of t h i s a b i l -i t y i s beyond q u e s t i o n . . At the present time, however, a f t e r examining the d e s c r i p t i o n of these t e s t s one can only conclude that " t h e r e i s very l i t t l e agreement on what items should be i n c l u d e d i n these t e s t s , and there i s some doubt about the comprehensiveness and v a l i d i t y of the r e s u l t s 1 9 obtained from them". 1 8 F a w c e t t , Nature of Proof, pp. 105-116. 1 9 D a v i d R u s s e l l , C h i l d r e n ' s T h i n k i n g , Ginn and Co., Boston, 1956, p. 291. 67 IV RELATIONSHIP BETWEEN INTELLIGENCE AND CRITICAL THINKING TESTS Another f r u i t f u l approach to a b e t t e r understanding of c r i t i c a l t h i n k i n g i s to compare t e s t s of i t w i t h var-ious t e s t s of i n t e l l i g e n c e . On the one hand, they do have many f e a t u r e s i n common. Both attempt to present r e l a t i v e -l y novel tasks to the t e s t e e so that mere r e c a l l i s minim-i z e d . They a l s o p r e s e n t tasks which r e q u i r e the students to determine new r e l a t i o n s h i p s from data s u p p l i e d . On the other hand, there are d i f f e r e n c e s between these t e s t s . Most of the t e s t s i n c r i t i c a l t h i n k i n g tend to be based upon m a t e r i a l drawn from a p a r t i c u l a r f i e l d , and hence, are somewhat s p e c i a l i z e d i n nature; whereas, t e s t s of i n -t e l l i g e n c e ((.scholastic a p t i t u d e ) u s u a l l y do not c o n t a i n m a t e r i a l of such a s p e c i a l i z e d nature. In f a c t , the i n -t e l l i g e n c e t e s t s are c o n s t r u c t e d to cover a wider f i e l d of knowledge i n order to reduce to a minimum the e f f e c t of d i f f e r e n c e s i n experiences, e s p e c i a l l y d i f f e r e n c e s a r i s i n g out of school l e a r n i n g . Since the t e s t s of i n t e l l i g e n c e and c r i t i c a l t h i n k -ing have many elements i n common, i t i s l o g i c a l to expect these t e s t s to be r e l a t e d , but not p e r f e c t l y , s i n c e they d i f f e r i n types of m a t e r i a l sampled. In f a c t , i f the co-e f f i c i e n t of c o r r e l a t i o n between these t e s t s were very high, 68 then one would be a good measure of the other and thus there would be no need f o r separate t e s t s f o r i n t e l l i g e n c e and c r i t i c a l t h i n k i n g a b i l i t y . S t udies of G l a s e r , 2 0 Edwards 2 1 and F u r s t 2 2 c o n f i r m that performance on i n t e l l i g e n c e t e s t s i s r e l a t e d , but not h i g h l y , to performance on c r i t i c a l t h i n k i n g t e s t s . Even though these three s t u d i e s used d i f f e r e n t t e s t s , which em-p h a s i z e d d i f f e r e n t aspects of c r i t i c a l t h i n k i n g , neverthe-l e s s , none of these showed a high c o r r e l a t i o n w i t h t e s t s of i n t e l l i g e n c e . Edwards found that the c o - e f f i c i e n t or c o r r e l a t i o n between h i s t e s t s of c r i t i c a l t h i n k i n g ° and 24 g e n e r a l measures of i n t e l l i g e n c e ranged from .00 to .17. F u r s t r e p o r t s that two-thirds of the c o r r e l a t i o n between the A.C.E. t e s t s of i n t e l l i g e n c e and a s p e c i a l t e s t i n 2 0 Goodwin Watson, and Edward Maynard Glaser,"Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l , " t e s t manual. World Book Co., New York, 1952, p. 9. T. Bentley Edwards, "Measurement of Some Aspects of C r i t i c a l T h i n k i n g " , D o c t o r a l D i s s e r t a t i o n , J o u r n a l of  Experimental Education, V o l . 18, 1950, pp. 269. 2 2Edward J . Furst,- " R e l a t i o n s h i p Between Tests of I n t e l l i g e n c e and Tests of C r i t i c a l T h i n k i n g " , J o u r n a l of  E d u c a t i o n a l Research, V o l . 43, 1950, pp. 614-625. 2 3 T h e s e t e s t s s t r e s s e d a p p l i c a t i o n of c r i t i c a l t h i n k i n g i n s c i e n c e . ^Edwards, op. c i t . , p. 269. 69 c r i t i c a l t h i n k i n g f e l l below .41 and that i n s t r u c t i o n over a two year p e r i o d d i d not seem to a f f e c t t h i s r e l a t i o n s h i p . G l a s e r found that c o - e f f i c i e n t s of c o r r e l a t i o n between h i s t e s t s of c r i t i c a l t h i n k i n g and v a r i o u s t e s t s of i n t e l l i g e n c 2 6 c l u s t e r around .45. The w r i t e r found a c o r r e l a t i o n of r = .463 between the Watson-Glaser t e s t s of c r i t i c a l t h i n k -ing and O t i s Quick S c o r i n g Mental A b i l i t y Tests, Gamma Test, Form A, (n = 60). . Since i t has been shown that these t e s t s of c r i t -i c a l t h i n k i n g are r e l a t e d to t e s t s of i n t e l l i g e n c e , the q u e s t i o n now may be asked as to whether they are a p t i t u d e 2 7 t e s t s . The s t u d i e s of Fawcett, Lewis, Koppenhaver, and F u r s t 2 8 i n d i c a t e that improvement i n c r i t i c a l t h i n k i n g i s p o s s i b l e and hence i t would appear that these are achieve-ment tests.. A n a s t a s i concludes: In e v a l u a t i o n s of any such t e s t s ( c r i t i c a l t h i n k -ing) ...a q u e s t i o n q u i t e n a t u r a l l y a r i s e s r e g a r d i n g the extent of o v e r l a p w i t h t e s t s of "general i n t e l l -i g ence" or of d i f f e r e n t i a l a p t i t u d e s . The d i s -t i n c t i o n between a p t i t u d e and achievement t e s t s be-comes e s p e c i a l l y tenuous when a p p l i e d to these t e s t s However, they are c u s t o m a r i l y regarded as a c h i e v e -ment t e s t s i n s o f a r as they were c o n s t r u c t e d to 2 5 F u r s t , op. c i t . , pp. 622-623 . G l a s e r , _op. c i t . , p. 9. 9 7 'See Chapter I I f o r d e t a i l s of these s t u d i e s , 2 8 F u r s t , op. c i t ., p. 624 . 70 measure progress towards some of the e x p l i c i t l y -s t a t e d e d u c a t i o n a l o b j e c t i v e s . The rapprochement between a p t i t u d e and achievement t e s t s , which these instruments i l l u s t r a t e , may r e f l e c t i n p a r t the changing viewpoint towards the concept of ap-t i t u d e s . There i s c e r t a i n l y a growing r e a l i z a t i o n t h a t many behaviour c h a r a c t e r i s t i c s which were once n a i v e l y regarded as f i x e d by h e r e d i t y are, i n f a c t , s u s c e p t i b l e to ed u c a t i o n . Consequently, a c h i e v e -ment t e s t s are now appearing i n many areas once r e s e r v e d f o r a p t i t u d e t e s t i n g . V JUSTIFICATION FOR USING THE WATSON—GLASER TEST Having d i s c u s s e d the nature of c r i t i c a l t h i n k i n g , i t i s now necessary to make some statement as to why the Watson-Glaser Test was chosen i n t h i s study as the measur-ing instrument f o r t h i s type of t h i n k i n g . The d e c i s i o n to use t h i s t e s t was l a r g e l y i n f l u -enced by the opinions of people, who had shown some l e a d e r -ship i n the e v a l u a t i o n of c r i t i c a l t h i n k i n g as evidenced by t h e i r a r t i c l e s i n var i o u s j o u r n a l s , and by n o t i n g that t h i s t e s t was a popular choice i n many of the more recent stud-i e s i n t h i s f i e l d . In many cases the suppo r t i n g evidence had to be obtained by pers o n a l correspondence w i t h the a u t h o r i t i e s i n t h i s f i e l d . Thus, Horrocks s t a t e s , "there are very few Co., Anne A n a s t a s i , 19 54, pp . 4 92. P s y c h o l o g i c a l T e s t i n g , Macmillan 71 p r i n t e d t e s t s l a b e l l e d c r i t i c a l t h i n k i n g and of the ones a v a i l a b l e I t h i n k that the Watson-Glaser i s the best one." Rosskopf i n commenting on t h i s t e s t s t a t e s ; Your choice of the Watson-Glaser t e s t of C r i t i c a l T h i n k i n g i s a l l r i g h t . I know of no other t e s t that might be used except the one that Dr. Fawcett worked on during the E i g h t Year Study of the Pro-g r e s s i v e Education A s s o c i a t i o n . . . It seems to me that the Watson-Glaser w i l l g i v e you a l a r g e r num-ber of items i n the t e s t and a b e t t e r coverage of p r i n c i p l e s than the C r i t i c a l Reasoning Test that Dr. Fawcett worked on. However, I myself, p r e f e r the one that he worked on.3-'-which Rosskopf recommends were withdrawn i n 1953 and hence are no longer a v a i l -The t e s t s from c i r c u l a t i o n a b l e . 3 2 Ennis suggests; The American C o u n c i l on Education has a t e s t c a l l e d "A Test of C r i t i c a l Thinking"., Form G, which I. would recommend, i f your students are mature enough A p r e l i m i n a r y manual has been prepared f o r t h i s t e s t , which was designed f o r c o l l e g e f r e s h m e n . 3 3 3 0 John E. Horrocks, ( P r o f e s s o r of Psychology, The Ohio State U n i v e r s i t y ) , l e t t e r to w r i t e r , 16 Feb., 1959. 31 Myron F. Rosskopf, ( P r o f e s s o r of Mathematics, Teacher's C o l l e g e , Columbia U n i v e r s i t y , New York), l e t t e r to w r i t e r , 9 May, 1956. 3 2 F o r a d e s c r i p t i o n of these t e s t s see page 65 of t h i s t h e s i s . 3 3 Robert H. Ennis, (School of E d u c a t i o n , C o r n e l l U n i v e r s i t y , Ithaca, New York), a l e t t e r to the w r i t e r , 18 Feb., 1959. 72 I t seemed to the w r i t e r that a t e s t designed prim-a r i l y f o r c o l l e g e freshmen would not be s u i t a b l e f o r use in t h i s study. He f u r t h e r notes that t h i s t e s t was used along w i t h the Watson-Glaser i n an important recent study This t e s t and the Watson-Glaser were used as c r i -t e r i o n instruments i n an experiment i n the teach-ing of c r i t i c a l t h i n k i n g i n high school * T h i s ex-periment was conducted by the C r i t i c a l T h i n king P r o j e c t of the I l l i n o i s C u r r i c u l u m Program ( C o l l -ege of Education, U n i v e r s i t y of I l l i n o i s , Urbana, I l l i n o i s ) . 3 4 / 3 5 -Other recent s t u d i e s which have used the Watson-3 7 G l a s e r t e s t were conducted by Lewis 0 and Massimiano. VI LIMITATION OF THE WATSON-GLASER Since the Watson-Glaser t e s t s of c r i t i c a l t h i n k i n g were developed i n the l a t e t h i r t i e s , they have undergone seven r e v i s i o n s i n order to overcome c e r t a i n d i f f i c u l t i e s encountered i n e a r l i e r forms. However, i t would appear that even i n the l a t e s t form, t h i s t e s t has some s h o r t -3 4 I b i d J t lNo r e p o r t of t h i s study at the U n i v e r s i t y of I l l -i n o i s has been made up to the time of w r i t i n g t h i s t h e s i s . 3 6 H a r r y Lewis, An Experiment i n Developing C r i t i c a l  T h i n k ing Through the Teaching of Plane Demonstrative Geom-e t r y , u n p ublished D o c t o r a l t h e s i s , New York, U n i v e r s i t y , New York, 1950. 3 7 Carmen C. Massimiano, The Inf l u e n c e of the Study  of Plane Geometry on C r i t i c a l T h i n k i n g , unpublished Doc-t o r a l t h e s i s . U n i v e r s i t y of Ottawa, Canada, 1955. comings. 73 A s p e c i a l d i f f i c u l t y encountered i n t h i s t e s t per-t a i n s to the c o r r e c t n e s s of the s c o r i n g key. The manual f o r t h i s t e s t s t a t e s t h a t : The key r e p r e s e n t s the "judgement" of t h i r t y - f i v e people s e l e c t e d f o r t h e i r advanced t r a i n i n g i n l o g i c and language meaning, plu s t h e i r demonstrated l e a d e r s h i p i n such f i e l d s as chemistry, b i o l o g y , p h y s i c s , psychology, education and business admin-i s t r a t i o n , who agreed unanimously that the key an-swers ( a f t e r many r e v i s i o n s and refinement of items) are l o g i c a l l y c o r r e c t . . . 3 8 A n a s t a s i , 3 9 T h o u l e s s 4 0 and E n n i s 4 1 agree " i t i s hard to b e l i e v e that any t h i r t y - f i v e persons c o u l d agree unan-imously on t h i s key, i f they c o n s i d e r e d the items c a r e -f u l l y . " 4 2 Ennis f u r t h e r suggests " i t would be i n t e r e s t i n g to know more about the c o n d i t i o n s under which t h i s agree-ment was reached. 38 G oodwin Watson and Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l , Test Manual, World Book Co., New York, 19 52, p. 8. 3 9Anne A n a s t a s i , P s y c h o l o g i c a l T e s t i n g , Macmillan Co., New York, 1954, p. 491. 40Rob e r t H. Thouless, Reader i n E d u c a t i o n a l Psych-ology, Cambridge U n i v e r s i t y , Cambridge, England, The T h i r d  Mental Measurement Yearbook, p. 544, E d i t e d by Oscar K. Buros, New Brunswick, New Je r s e y , Rutgers, U n i v e r s i t y Press, 1949. 4 i R o b e r t H. En n i s , "An App r a i s a l of the Watson-Glaser C r i t i c a l T h i n king A p p r a i s a l " , Journal- of E d u c a t i o n a l Re- search, V o l . 52, D e c , 1959, p. 158. 4 2.1b i d 4 3 I b i d , p. 155. 74 Ennis p o i n t s out another shortcoming of t h i s t e s t by n o t i n g that the " p a t h o l o g i c a l doubter" w i l l r e c e i v e too hig h a score . By " p a t h o l o g i c a l doubter" i s meant "a per-son who i s not j u s t c a u t i o u s , but who w i l l not accept any-t h i n g as proven, a person f o r whom "proof", " s u f f i c i e n t evidence" are I n a p p l i c a b l e i n a l l c o n c e i v a b l e s i t u a t i o n s . " 4 4 Ennis notes that t h i s " p a t h o l o g i c a l doubter", because of h i s very nature and not h i s a b i l i t y to t h i n k c r i t i c a l l y , c o u l d r e c e i v e a score of s i x t y - s e v e n on Form B of t h i s t e s t and t h i s would p l a c e him at the e i g h t y - s i x t h percen-t i l e i f he were i n high s c h o o l . On Form A he would o b t a i n a score of f i f t y - n i n e and t h i s would r a t e him at the s i x t y -n i n t h p e r c e n t i l e . VI SUMMARY This chapter was devoted to a c o n s i d e r a t i o n of c r i t i c a l t h i n k i n g w i t h r e s p e c t to i t s importance as an ed u c a t i o n a l o b j e c t i v e i n a democratic s o c i e t y , nature of the d i f f i c u l t i e s encountered when attempting to d e f i n e t h i s type of t h i n k i n g , a survey of some of the more important t e s t s i n t h i s f i e l d , the j u s t i f i c a t i o n f o r using the Watson-Gl a s e r t e s t i n t h i s study and f i n a l l y , the l i m i t a t i o n s of t h i s t e s t . 4 4 I b i d . , p. 156 CHAPTER V DESIGN AND ANALYSIS OF EXPERIMENT This chapter i n c l u d e s a d e s c r i p t i o n of s u b j e c t s , a d i s c u s s i o n of f a c t o r s i n f l u e n c i n g choice of experimental design, a d e s c r i p t i o n of the b a s i s of matching i n d i v i d u a l s i n the experimental and c o n t r o l groups, a d i s c u s s i o n of the degree of matching achieved, and an a n a l y s i s of the r e s u l t s on the c r i t e r i o n v a r i a b l e . I THE SUBJECTS The s u b j e c t s chosen f o r t h i s experiment c o n s i s t e d of e i g h t y three grade ten p u p i l s e n r o l l e d i n the U n i v e r s i t y Entrance program and t a k i n g the course d e s i g n a t e d as Math-ematics 20 1 at C omo Lake High School i n Coquitlam School D i s t r i c t No. 43. These p u p i l s were grouped i n t o two c l a s s e s on the b a s i s of whether or not they were t a k i n g French i n grade te n . Because of t h i s d i v i s i o n i t was i mpossible to s e l e c t the c o n t r o l and experimental groups on a random b a s i s and Province of B r i t i s h Columbia, Department of Educ-a t i o n , D i v i s i o n of C urriculum, J u n i o r and Senior High  School Mathematics 1958, V i c t o r i a , B.C., Queens P r i n t e r , 1958, pp. 35-38. 76 hence the w r i t e r had to content h i m s e l f w i t h the c l a s s e s (groups) as set up by the a d m i n i s t r a t i o n . This r e s t r i c t i o n f o r c e d the experimenter to f o l l o w a design employing p a i r e d o b s e r v a t i o n s . That i s , there were to be two groups i n which every i n d i v i d u a l i n the f i r s t group was p a i r e d on the b a s i s of the c o n t r o l v a r i a b l e s w i t h another i n the second group. The t o s s i n g of a c o i n determined which c l a s s was to be the experimental group, the other group to become the c o n t r o l . The experimental c l a s s contained f o r t y - t h r e e pup-i l s , the c o n t r o l , f o r t y . Because of the l a r g e range i n scores on the c o n t r o l v a r i a b l e s , and i n order to e f f e c t good matching, only t h i r t y i n each group were p a i r e d and c o n s i d -ered f o r the purposes of t h i s study. I t should be noted that the a c t u a l matching of t h e s e . p a i r s was determined a f t e r the experiment was over and by a second p e r s o n 2 , who was not employed i n t h i s d i s t r i c t , or acquainted w i t h the p u p i l s i n the study. The f i n a l c r i t e r i o n s cores were not r e v e a l e d to him u n t i l he had chosen the t h i r t y matched p a i r s on the b a s i s of the c o n t r o l v a r i a b l e s . 2E.N. E l l i s , Dept. of Research and S p e c i a l S e r v i c e s , School D i s t r i c t No. 39, Vancouver, B.C. ^Goodwin Watson and Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l Test, Form A, World Book Co., New York, 1952 and the Arthur S. O t i s , O t i s Quick  S c o r i n g Mental A b i l i t y Test, Gamma, Form Am, 1937 77 The matching was based p r i m a r i l y upon the c o n t r o l v a r i a b l e s of i n t e l l i g e n c e and c r i t i c a l t h i n k i n g a b i l i t y . 4 The l a t t e r v a r i a b l e was g i v e n p r i o r i t y , because the' measur-able outcomes of t h i s study were to be given i n terms of i t . Since the r e s u l t s of t h i s study were to be analyzed i n terms of l e v e l s of a b i l i t y , i t was necessary a l s o , that the p a i r -ing secure a r e p r e s e n t a t i v e sample over the e n t i r e range of a b i l i t y . This was mandatory, i n order to e f f e c t a good d i v -i s i o n , on the b a s i s of the c o n t r o l variables-, i n t o the three sub-groups of " s u p e r i o r " , "average" and " i n f e r i o r " . The f a c t o r s of sex and age were not considered'important i n the matching, because the former would be accounted f o r i n the computation of the i n t e l l i g e n c e q u o t i e n t , 5 and the l a t t e r was c o nsidered not s i g n i f i c a n t by the a u t h o r s 6 of the t e s t i n c r i t i c a l t h i n k i n g . 4See Table I p. 78 and Table I I p. 84. ^ I n t e l l i g e n c e q u o t i e n t — Mental Age  C h r o n o l o g i c a l Age Goodwin Watson, Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l , Manual f o r Test, World Book Co., New York, 1952, pp. 6 and 11. 78 TABLE I THE DEGREE OF MATCHING ACHIEVED IN CRITICAL REASONING SCORES a L e v e l A l ( C o n t r o l Group) A 2 (Exper. Group) Mean S.D. Var iance Mean S.D. Variance L i ( S u p e r i o r ) 67.1 5.43 29.49 67.4 5 . 06 25.60 L 2(Average) 58.4 1.50 2.25 58.1 1.44 2.07 L 3 ( I n f e r i o r ) 50.5 3 .88 15.05 50.4 5.37 28 .84 L o ( O v e r a l l ) 58.66 9.66 93 .32 58.63 8 .22 67.57 a Watson-Glaser Test of C r i t i c a l T h i n k i n g , Form A 79 II ANALYSIS OF THE PAIRED MATCHING The data w i t h regard to matching on c r i t i c a l t h i n k -ing a b i l i t y , as measured by the Watson-Glaser Test, are pre-sented i n Table I page 78. A curso r y examination of the means and standard d e v i a t i o n s f o r the c o n t r o l and exper-imental groups r e v e a l s that they approximate each other q u i t e c l o s e l y . The d i f f e r e n c e between the means was not more than t h r e e - t e n t h s of a p o i n t at the three s u b - l e v e l s and the o v e r a l l l e v e l of a b i l i t y . However, l a r g e r d i f f e r e n c e s i n standard d e v i a t i o n s were noted at the va r i o u s l e v e l s but they d i d not exceed 1.49 p o i n t s . The l a r g e s t d i f f e r e n c e i n stan-dard d e v i a t i o n was recorded at the " I n f e r i o r L e v e l " . Although the c o n t r o l and experimental groups appeared to be f a i r l y w e l l matched across the l e v e l s , n e v e r t h e l e s s , there are d i f f e r e n c e s . Since the design of t h i s experiment r e q u i r e s c l o s e matching of the c o n t r o l and experimental groups on the c o n t r o l v a r i a b l e s , i t i s necessary to prove s t a t i s t i c a l l y , that t h i s requirement i s s a t i s f i e d . This can be shown by a p p l y i n g a s e r i e s of " t " t e s t s of s i g n i f i c a n c e between the va r i o u s means. However, before " t " t e s t s can be a p p l i e d , a guarantee, that the v a r i a n c e s do not d i f f e r s i g -n i f i c a n t l y , i s r e q u i r e d . T h i s i s because a " s i g n i f i c a n t d i f f e r e n c e i n v a r i a n c e s may r e s u l t i n a somewhat l a r g e r 80 7 value of " t " than otherwise would be o b t a i n e d " . A g e n e r a l o v e r a l l t e s t , f o r the s i g n i f i c a n c e of d i f f e r e n c e s between g v a r i a n c e s f o r many sub-groups i s f u r n i s h e d by the B a r t l e t t t e s t of homogeneity of v a r i a n c e . 9 This t e s t w i l l r e v e a l whether the d i f f e r e n c e s i n v a r i a n c e s are s i g n i f i c a n t f o r not only the l e v e l s themselves, but a l s o between the l e v e l s . When the B a r t l e t t t e s t was a p p l i e d , a value of 24.47 f o r X was obtained. E n t e r i n g the t a b l e s of~^( 2 f o r f i v e degrees of freedom 1^, the value of 24.47 exceeds the t a b l e d value at the one percent l e v e l . Thus the hypothesis of homogeneous varian c e has to be r e j e c t e d . A study of the v a r i a n c e s i n Table I, page 78 r e v e a l s that the two v a r i a n c e s of 2.07 and 2.25 r e c o r d e d f o r the "average" l e v e l appear to approximate each other q u i t e c l o s e l y . Likewise the v a r i a n c e s of 29.49 and 25.60 f o r the " s u p e r i o r " l e v e l and those of 15.05 and 28.84 f o r the " i n -f e r i o r " l e v e l are q u i t e s i m i l a r . ' A l l e n L. Edwards, Experimental Design i n Psycholog-i c a l Research, Rinehart & Company, Inc. New. York, 1950 . p. 165 ^In t h i s study there are s i x sub-groups, that i s three each f o r the experimental and c o n t r o l groups. ^Edwards, o_p. c i t . , pp. 195-197 10 The degrees of freedom are obtained by the formula d . f . = r - l , and r r e f e r s to the number of sub-groups ( i n t h i s case there were s i x sub-groups) 81 However, the v a r i a n c e s , r e p o r t e d f o r "average" l e v e l , , appear very small by comparison to those of the " s u p e r i o r " and " i n -f e r i o r " l e v e l s . In f a c t , the v a r i a n c e s f o r the " s u p e r i o r " and " i n f e r i o r " l e v e l s are seven to f o u r t e e n times as l a r g e as the two recorded f o r the "average" l e v e l . Edwards r e -port s t h a t , " i f two samples each have ten or fewer cases, then one of the two v a r i a n c e s w i l l have to be approximately 4.5 times as l a r g e as the other i n order that the d i f f e r e n c e may be s i g n i f i c a n t at the f i v e percent l e v e l " . 1 1 Thus i t would appear that " t " t e s t , of s i g n i f i c a n c e d i f f e r e n c e s i n means at the v a r i o u s l e v e l s and a l s o between the " s u p e r i o r " and " i n f e r i o r " l e v e l s , can be made wit h the assurance of hom-ogeneity of v a r i a n c e . However, since the " s u p e r i o r " and " i n f e r i o r " l e v e l have v a r i a n c e s i n excess of 4.5 times the "average" l e v e l v a r i a n c e s , then any " t " t e s t f o r d i f f e r e n c e s of means i n v o l v i n g the "average" group, w i t h e i t h e r of the " s u p e r i o r " or " i n f e r i o r " , would be u n r e l i a b l e . Why were the two v a r i a n c e s f o r the "average" l e v e l so small compared w i t h the " s u p e r i o r " and " i n f e r i o r " l e v e l s ? Or, why d i d the scores tend to be more d i s p e r s e d at the " s u p e r i o r " and " i n f e r i o r " l e v e l s compared w i t h those at the "average" l e v e l ? T h i s can be p a r t i a l l y accounted f o r by the manner i n which the experimental and c o n t r o l groups were Edwards, op. c i t . , p. 162 82 p a i r e d and s t r a t i f i e d i n t o the three l e v e l s of a b i l i t y . In p a r t i c u l a r , the students making scores amongst the top ten, middle ten, and lowest ten, were assigned to the l e v e l s of " s u p e r i o r " , "average" and " i n f e r i o r " 1 2 r e s p e c t i v e l y . The remaining students were ignored f o r the purposes of t h i s study. On the assumption t h a t t h i s d i s t r i b u t i o n of scores would roughly tend to approximate a normal d i s t r i b u t i o n (or a skewed v e r s i o n of i t ) , then i t would appear l o g i c a l , t h a t most of the scores would tend to c l u s t e r near a cen-t r a l p o i n t , where the spread of the scores would be r e l a t -i v e l y s m a l l . Hence any sample taken from the middle por-t i o n would e x h i b i t a r e l a t i v e l y small v a r i a n c e . On the other hand, the top and lowest ten scores would tend to be spread out more and hence the variance would be g r e a t e r . As p r e v i o u s l y mentioned, the groups were matched on the b a s i s of two c o n t r o l v a r i a b l e s , 'namely, i n t e l l i g e n c e and c r i t i c a l t h i n k i n g . The l a t t e r v a r i a b l e was given p r i -o r i t y , because the measurable outcomes of t h i s study were to be g i v e n i n terms of i t . I n t e l l i g e n c e was used as the second matching v a r i a b l e , because there was good reason to b e l i e v e that a f a i r degree of c o r r e l a t i o n e x i s t e d between i t and c r i t i c a l t h i n k i n g a b i l i t y . ^ I n the be i g n o r e d . i n t e r e s t of matching, some scores had to 83 The authors of the t e s t i n c r i t i c a l t h i n k i n g , used i n t h i s study, r e p o r t a c o r r e l a t i o n w i t h " v a r i o u s i n t e l l i g e n c e t e s t s . . . t e n d to c l u s t e r around .45". 1 3 The w r i t e r found a 14 c o r r e l a t i o n of r=.463 between i n t e l l i g e n c e and c r i t i c a l t h i n k i n g a b i l i t y . " ^ A b r i e f examination of Table II r e v e a l s d i f f e r e n c e s i n means and v a r i a n c e s f o r the c o n t r o l v a r i a b l e of i n t e l l i g -ence. As i n the case of c r i t i c a l t h i n k i n g , i t was necessary to guarantee the homogeneity of v a r i a n c e s between groups, before " t " t e s t f o r the s i g n i f i c a n c e of d i f f e r e n c e s between the means i n i n t e l l i g e n c e c o u l d be a p p l i e d . Thus the B a r t -l e t t t e s t f o r homogeneity of va r i a n c e was a p p l i e d and a value of 8.569 was obtained fo rT • E n t e r i n g the t a b l e s f o r f i v e degrees of freedom, the value of 8.569 was l e s s than the t a b l e d value of 11.07 at the f i v e percent l e v e l . 13 G oodwin Watson, Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l , Manual f o r t e s t , World Book Co., New York, 1952, p. 9. l ^ T h i s c o r r e l a t i o n was computed by the use of the "product moment method"> n = 60. l ^ F o r a more d e t a i l e d r e p o r t on the r e l a t i o n of i n t e l l i g e n c e to c r i t i c a l t h i n k i n g , see pp. 67. 1 6 See p a g e l l 3 of appendix f o r d e t a i l s of the B a r t -l e t t t e s t . 84 TABLE II THE DEGREE OF MATCHING ACHIEVED IN INTELLIGENCE SCORES a Level A]_ ( C o n t r o l Group) A 2 (Exper. Group) Mean S.D. Var iance Mean S.D. Variance L-^  (Superior) 116.0 4.76 22 .66 116.4 5.57 31.02 L 2(Average) 109.4 3.17 10.05 108.7 4.04 16.32 L 3 ( I n f e r i o r ) 102.9 6 .84 46.79 103 . 7 7 .31 53 .44 L Q ( O v e r a l l ) 109.4 7.94 63 .04 109.6 7.81 61 .00 a O t i s Quick S c o r i n g Mental A b i l i t y Test, Gamma, Form A 85 Hence the hypo t h e s i s , of the homogeneity of v a r i a n c e s f o r l e v e l s and between l e v e l s , was accepted. Having e s t a b l i s h e d s t a t i s t i c a l l y , that there were no s i g n i f i c a n t d i f f e r e n c e s i n the v a r i a n c e s f o r the matching v a r i a b l e s of i n t e l l i g e n c e and c r i t i c a l t h i n k i n g , i t was now p o s s i b l e to t e s t the hy p o t h e s i s , that there i s no s i g n i f i c -ant d i f f e r e n c e i n means on c r i t i c a l t h i n k i n g among the groups. A study of Table I I I on page 86 r e v e a l s t h a t the " t " values, obtained f o r the various l e v e l s , were l e s s than the t a b l e d value at the f i v e percent l e v e l . Thus the hypo-t h e s i s , that there was no s i g n i f i c a n t d i f f e r e n c e i n means on c r i t i c a l t h i n k i n g , has to be accepted. Likewise the hy p o t h e s i s , t h a t there i s no s i g n i f i c -ant d i f f e r e n c e i n means on i n t e l l i g e n c e , has to be accepted, because Table IV page 87 i n d i c a t e s that the " t " values ob-t a i n e d f o r the d i f f e r e n c e s i n means f o r the va r i o u s l e v e l s i s l e s s than the t a b l e d values at the f i v e percent l e v e l . ' Thus i t has been e s t a b l i s h e d s t a t i s t i c a l l y , that there i s no s i g n i f i c a n t d i f f e r e n c e i n means on the c o n t r o l v a r i a b l e s of i n t e l l i g e n c e and c r i t i c a l t h i n k i n g w i t h r e f e r -ence to a l l the l e v e l s and between the " s u p e r i o r " and " i n -f e r i o r " l e v e l s . I 7 " t " t e s t s f o r d i f f e r e n c e s i n means i n v o l v i n g the "average" group wi t h e i t h e r the " s u p e r i o r " or " i n f e r i o r " were omitted because 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 s . Refer to page 81 . 86 TABLE I I I SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS FOR CRITICAL THINKING Le v e l Source of d i f f . of means D i f f . i n Means d . f . t t .05 t .01 L]_ ( S u p e r i o r ) MIE a MlC .3 9 .71 2 .262 3 .250 L£(Average) M2E - .3 9 1 .43 2 .262 3 .250 L 3 ( I n f e r i o r ) - M3C .1 9 .12 2 .262 3 .250 L 0 ( O v e r a l l ) MOE b .03 29 .098 2 .045 2 .756 L]_ & Lg (Int e r a c t i o n (MlE ) ( M 3 E c Mic) -M 3 C) .2 18 .0069 2 .101 2 .878 a) M 1 E r e f e r s to the mean f o r f i r s t l e v e l ("superior") of experimental group. b) MQE r e f e r s to the mean f o r the experimental group. c) (M^E - Mic) - ( M 3 E - M 3 C ) w i l l be used i n computing i n t e r a c t i o n between f i r s t ( s u p e r i o r ) and t h i r d ( i n f e r i o r ) l e v e l . 87 TABLE IV SIGNIFICANCE OF DIFFERENCE BETWEEN MEANS FOR INTELLIGENCE L e v e l Source of d i f f . of means D i f f . i n Means d.f . t t .05 t.01 Lj( S u p e r l o r ) M 1 E a M1C .40 9 .69 2 .262 3 .250 L 2(Average) M2E - M2C .70 9 .78 2 .262 3 .250 L 3 ( I n f e r i or) M 3E - M 3 C .80 9 .99 2 .262 3 .250 L 0 ( O v e r a l l ) MOE b Hoc .20 29 .41 2 .045 2 .756 L l & L 3 ( I n t e r a c t i o n (MIE ) ( M 3 E c Mic) -M 3c) - .40 18 .11 2 .101 2 .878 a) Mi£ r e f e r s to the mean f o r f i r s t l e v e l ("superior") of experimental group. b) MQ£ r e f e r s to o v e r a l l mean f o r experimental group. c) (MIE - Mic) - ( M 3 E - M 3 C ) w i l l be used i n computing the i n t e r a c t i o n between f i r s t and t h i r d l e v e l s . 88 I I I NATURE OF CRITERION VARIABLE 1 Q A f t e r the experiment was over on March 24, 1958 x o, 19 the Watson-Glaser t e s t of c r i t i c a l t h i n k i n g form B ( c r i t e r i o n v a r i a b l e ) was a d m i n i s t e r e d to both the c o n t r o l and experimental groups. This t e s t was a p a r a l l e l from of 2 0 the t e s t t h at was used as one of the c o n t r o l v a r i a b l e s . As might be expected, there e x i s t e d a f a i r degree of c o r r -e l a t i o n between both forms. The extent of the c o r r e l a t i o n i s g i v e n by t h e . r e p o r t e d " r e l i a b i l i t y c o e f f i c i e n t of average 2 1 scores on both forms" which range from .88 to .95 . G u i l -f o r d p o i n t s out that the use of p a r a l l e l forms which are c o r r e l a t e d has d i s t i n c t advantages. ... i t pays to match samples only on v a r i a b l e s that are c o r r e l a t e d w i t h the measured v a r i a b l e . . . I t i s l o g i c a l i f we t r y to keep s u c c e s s i v e samples con-s t a n t w i t h r e s p e c t to the mean on. some v a r i a b l e pos-i t i v e l y c o r r e l a t e d w i t h the experimental v a r i a b l e the means on the l a t t e r w i l l a l s o be kept more con-s t a n t , depending upon the extent of the c o r r e l a t i o n . The standard e r r o r mean should be sm a l l e r under t h i s 18 The experiment s t a r t e d on January 21, 1958. 1 9 Goodwin Watson and Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l Test, Form B, World Book Co., New York, 1952. 2 0 Form A was used as one of the c o n t r o l v a r i a b l e s . 21 Goodwin Watson, Edward Maynard G l a s e r , Watson-G l a s e r C r i t i c a l T h i n k i n g A p p r a i s a l , Manual f o r t e s t , World Book Co., New York, 1952, p. 9. 89 r e s t r i c t i o n . The g e n e r a l formula i s £T, = ^ /l-r^mx where rmx i s the c o r r e l a t i o n between matching 9 9 v a r i a b l e and experimental v a r i a b l e . The l a r g e r value of mx and the r e s u l t i n g smaller standard e r r o r of mean (^yj) would i n c r e a s e the s i z e of " t " (the t e s t of s i g n i f i c a n c e ) a c c o r d i n g to the formula t = - M2 • M Thus i t seemed d e s i r a b l e to c a p i t a l i z e on t h i s advantage a f f o r d e d by the use of p a r a l l e l forms. IV ANALYSIS OF RESULTS Since i t has been e s t a b l i s h e d s t a t i s t i c a l l y , t h a t there i s no s i g n i f i c a n t d i f f e r e n c e i n means on the c o n t r o l v a r i a b l e s of i n t e l l i g e n c e and c r i t i c a l t h i n k i n g , i t i s now p o s s i b l e to t e s t the two f i n a l hypotheses concerning the c r i t e r i o n v a r i a b l e of c r i t i c a l t h i n k i n g . The f i r s t hypo-t h e s i s i s , that there i s no s i g n i f i c a n t d i f f e r e n c e i n means f o r each l e v e l of a b i l i t y . Table V shows that the " t " values f o r the s i g n i f i c a n c e of d i f f e r e n c e of means at the v a r i o u s l e v e l s ("superior", "average", " i n f e r i o r " and "over-a l l " ) were l e s s than the r e q u i r e d t a b l e d value at the f i v e percent l e v e l . Thus the h y p o t h e s i s , t h a t there i s no s i g -n i f i c a n t d i f f e r e n c e i n means on c r i t i c a l t h i n k i n g w i t h J.P. G u i l f o r d , Fundamental S t a t i s t i c s i n Psychology  and Education, McGraw-Hill Co., New York, 1956, pp. 195-196. 90 TABLE V DIFFERENCE IN MEAN SCORES ON CRITERION VARIABLE OF CRITICAL THINKING L e v e l Source d i f f . of of means D i f f . i n Means d . f . t t .05 L j ( S u p e r i o r ) M 1 E a M1C 2.6 9 1 .29 2 .262 3 .250 L 2(Average) - 3.2 9 1 .13 2 .262 3 .250 Lg ( I n f e r i o r ) M 3 E - M3C -1.1 9 0 .33 2 .262 3 .250 b L o ( O v e r a l l ) MoE — MOC 1.56 29 0 .97 2 .045 2.756 L i & L 3 (MlE c Mic) - 3 .7 18 0 .31 2 .101 2 .878 ( I n t e r a c t i o n ) (M3E M3C ) a) M]_E r e f e r s to the mean f o r f i r s t l e v e l ("superior") of experimental group b) MQE r e f e r s to the o v e r a l l mean f o r experimental group. c) (MlE - Mic) - (M3E - M3C) w i l l be used i n computing the i n t e r a c t i o n between f i r s t and t h i r d l e v e l s . 91 r e s p e c t to the va r i o u s l e v e l s of a b i l i t y , has to be accepted, The second hypothesis to be i n v e s t i g a t e d i s that there i s no s i g n i f i c a n t d i f f e r e n c e i n means from one l e v e l to another. In other words, we wish to t e s t the hypothesis that there i s no s i g n i f i c a n t d i f f e r e n c e i n means between the_ v a r i a b l e s of method of i n s t r u c t i o n and the l e v e l of a b i l i t y . In p a r t i c u l a r , the d i f f e r e n c e , of the d i f f e r e n c e of means at two l e v e l s , w i l l be i n v e s t i g a t e d . A t y p i c a l formula r e p r e s e n t i n g the d i f f e r e n c e to be t e s t e d f o r s i g n i f i c a n c e i s (M]_E - MIQ) - ( M 3 E - M 3 C ) , where Mic r e f e r s to the mean f o r the c o n t r o l group at the f i r s t l e v e l ( s u p e r i o r ) . This i s o f t e n r e f e r r e d to as the " i n t e r a c t i o n " of l e v e l s w i t h methods. In t h i s study only the i n t e r a c t i o n of the super-i o r and i n f e r i o r groups was c o n s i d e r e d . ^ Table V r e v e a l s , that the " t " values f o r the " i n t e r -a c t i o n " between " s u p e r i o r " and " i n f e r i o r " l e v e l s i s l e s s than the t a b l e d value r e q u i r e d at the f i v e percent l e v e l . Thus the second h y p o t h e s i s of no s i g n i f i c a n t d i f f e r e n c e from one l e v e l to another has to be accepted. 23 The" average" l e v e l c o u l d not be used f o r study of i n t e r a c t i o n because of l a r g e d i f f e r e n c e i n varia n c e between i t and the " s u p e r i o r " and " i n f e r i o r " l e v e l s . See page 81 . 92 However, even though there were no s t a t i s t i c a l l y s i g -n i f i c a n t d i f f e r e n c e s i n means between the experimental and c o n t r o l groups, n e v e r t h e l e s s some r a t h e r i n t e r e s t i n g trends can be seen by examining the r e s u l t s recorded i n Table V page 90 and Table VI page 93. Table V r e v e a l s an a n a l y s i s of the d i f f e r e n c e s i n means on the c r i t e r i o n v a r i a b l e of c r i t i c a l t h i n k i n g . Trends which are observed, i n t h i s t a b l e are : 1. The l a r g e s t " t " value f o r s i g n i f i c a n c e of d i f f e r -ence i n means was recorded at the " s u p e r i o r " l e v e l and the l e a s t at the " i n f e r i o r " l e v e l . That i s , whatever d i f f e r -ence i n e f f e c t e x i s t e d between c o n t r o l and experimental me-thod, i t was manifested most at the " s u p e r i o r " l e v e l of ab-i l i t y and l e a s t at the " i n f e r i o r " l e v e l . 2. At the "average" and " s u p e r i o r " l e v e l s , the ex-peri m e n t a l groups had higher mean scores on the c r i t e r i o n than the c o n t r o l groups. At the " i n f e r i o r " l e v e l , the con-t r o l group had the high e r mean s c o r e s . Table VI shows the d i s t r i b u t i o n of gains i n c r i t i c a l t h i n k i n g scores f o r the d u r a t i o n of the experiment. The data of t h i s t a b l e i n d i c a t e s the f o l l o w i n g t r e n d s : 1. A l l the a b i l i t y groups, f o r both the experimental and c o n t r o l groups, showed p o s i t i v e mean gains ranging from 93 TABLE VI MEAN GAINS IN CRITICAL THINKING SCORES a L e v e l A l ( C o n t r o l Group Means) A2(Exper, G r oup Means) Form A Form B Gain i n mean Form A Form B Gain i n mean L i (Superior) 67.1 65.7 -1 .4 67.4 68 .3 40.2 L 2(Average) 58 .4 59.9 41 .5 58.1 63.1 45.0 L 3 ( I n f e r i o r ) 50.5 5 9,1 •/8.6 50.4 58.0 47.6 L Q ( O v e r a l l ) 58.66 61.57 42 . 91 58 .63 63 .13 1 44: .5 a) Watson-Glaser C r i t i c a l T h i n k i n g T e s t . 94 .9 to 8.6 wit h the one exception o c c u r r i n g at the " s u p e r i o r " l e v e l f o r the c o n t r o l group who recorded a mean l o s s of 1.4 2. The l a r g e s t mean gains of 8.6 and 7.6 were r e -corded f o r the " i n f e r i o r " l e v e l of the c o n t r o l and exper-imental group r e s p e c t i v e l y . The s m a l l e s t mean g a i n was noted at the " s u p e r i o r " l e v e l of the experimental group. 3 . The l a r g e s t d i f f e r e n c e i n mean g a i n s between the experimental and c o n t r o l group was recorded at the "aver-age" l e v e l . 4. The l a r g e s t o v e r a l l g a i n i n mean scores was achieved by the experimental group. The r e s u l t s of t h i s study, even though they were not s i g n i f i c a n t , do suggest trends that may have important im-p l i c a t i o n s which should be i n v e s t i g a t e d by f u r t h e r r e s e a r c h . This w i l l be a m p l i f i e d f u r t h e r i n the l a s t chapter. This chapter has d i s c u s s e d ; s u b j e c t s and the match-ing of them on the c o n t r o l v a r i a b l e s of i n t e l l i g e n c e and c r i t i c a l t h i n k i n g , the nature of the c r i t e r i o n v a r i a b l e , and the a n a l y s i s of the r e s u l t s o b t a i n e d . CHAPTER VI SUMMARY AND CONCLUSIONS This chapter w i l l be devoted to the importance of c r i t i c a l t h i n k i n g , the purpose and nature of t h i s study, the p r i n c i p a l f i n d i n g s , the c o n c l u s i o n s based on these r e s u l t s and, some suggestions of problems that m e r i t f u r -ther study. I THE IMPORTANCE OF CRITICAL THINKING Competent c i t i z e n s h i p i n a democracy c a l l s f o r a good deal more than the a b i l i t y to read and w r i t e . I t has o f t e n been s a i d that a democracy i s a p l a c e of c o n f l i c t i n g propaganda. This can be r e a d i l y seen i n a democratic country by examining; t h e i r newspaper a r t i c l e s and e d i t o r -i a l s , commercial advertisements and p o l i t i c a l speeches. Thus i t would seem necessary that the populace of a dem-ocracy be able to r e c o g n i z e ; the more common f a l l a c i e s of reasoning, d i f f e r e n t p o i n t s of view, and to evaluate them i n the l i g h t of facts, not p e r s o n a l p r e j u d i c e . Hence there can be no q u e s t i o n that c r i t i c a l t h i n k i n g i s a necessary p a r t of the t r a i n i n g f o r the c i t i z e n r y of a democracy. 96 II THE PURPOSE AND NATURE OF THIS STUDY To meet t h i s need demonstrative geometry has been r e t a i n e d i n the t e n t h and e l e v e n t h year of the secondary program p a r t l y because some c u r r i c u l u m planners b e l i e v e that the c r i t i c a l r e asoning a b i l i t i e s a c q u i r e d i n the study of t h i s subject w i l l t r a n s f e r to l i f e s i t u a t i o n s . However, 1 2 most of the r e s e a r c h s t u d i e s (Fawcett , Gadske ) i n t h i s area seem to i n d i c a t e that very l i t t l e of t h i s a b i l i t y a c q u i r e d i n the us u a l demonstrative geometry course t r a n s -f e r s to non-mathematical s i t u a t i o n s . The usual course i n mathematics g e n e r a l l y employs a t e x t which i n c l u d e s , as a very important type of e x e r c i s e , the problem where the student i s s u p p l i e d w i t h data, e i t h e r g i v e n or assumed and t o l d p r e c i s e l y what c o n c l u s i o n s he must d e r i v e from t h i s d a t a . I t i s thought by some that, t h i s type of e x e r c i s e d e p r i v e s a student of a very important l e a r n i n g experience, namely, that of d i s c o v e r y and checking the v a l -i d i t y of ' statements that are not c o n s i s t e n t w i t h g i v e n data. Needless to say, t h i s s i t u a t i o n of knowing the c o r r e c t con-c l u s i o n i n advance of s o l v i n g a problem and not being exposed See page 20 of t h i s t h e s i s . See page 26 of t h i s t h e s i s . 97 to statements that are i n c o n s i s t e n t w i t h the data i s h i g h l y a r t i f i c i a l and not very l i k e l y to be found i n l i f e s i t -u a t i o n s . The w r i t e r of t h i s study proceeded to i n v e s t i g a t e what would be the e f f e c t on the c r i t i c a l reasoning a b i l i t y off the student who was exposed to a s p e c i a l type of exer-c i s e i n which he was not t o l d what c o n c l u s i o n s he must de-r i v e from the given data, but r a t h e r he was s u p p l i e d w i t h a l t e r n a t i v e s of which some might not be v a l i d i n terms of the g i v e n data. That i s , the onus was p l a c e d on the stud-ent f o r determining which a l t e r n a t i v e , i f any, was a v a l i d c o n c l u s i o n w i t h r e s p e c t to the g i v e n d a t a . I l l DESIGN OF EXPERIMENT In order to study, the e f f e c t on p u p i l s of t h i s r e -v i s e d type of e x e r c i s e , an experiment was conducted i n which two groups of p u p i l s were matched on the c o n t r o l v a r i a b l e s of c r i t i c a l t h i n k i n g and i n t e l l i g e n c e . Each of these two groups was su b d i v i d e d , a c c o r d i n g to a b i l i t y as demonstrated on the c o n t r o l v a r i a b l e s , i n t o three l e v e l s which were des-i g n a t e d as " s u p e r i o r " , "average", and " i n f e r i o r " . One group which was designated as the c o n t r o l group s t u d i e d e x e r c i s e s which were c h a r a c t e r i s t i c of the usual course i n geometry. The second became the experimental group who were exposed 98 to e x e r c i s e s i n which the students were not t o l d what to prove, but i n s t e a d were given p o s s i b l e hypotheses which they had to t e s t f o r t h e i r v a l i d i t y . In order to determine the gains i n c r i t i c a l t h i n k -ing f o r the d u r a t i o n of the experiment, a second t e s t ( c r i t e r i o n v a r i a b l e ) was administered a f t e r the experiment was over. The r e s u l t s on the c r i t e r i o n v a r i a b l e were a n a l -yzed to see i f there were any s i g n i f i c a n t d i f f e r e n c e s i n means between the c o n t r o l and experimental groups. IV PRINCIPAL FINDINGS 1. As there were no s i g n i f i c a n t d i f f e r e n c e s at the va r i o u s l e v e l s , i t would appear t h a t the experimental and c o n t r o l type of e x e r c i s e s were e q u a l l y e f f e c t i v e i n pro-moting c r i t i c a l t h i n k i n g at the d i f f e r e n t l e v e l s of a b i l i t y . 2. Since there were no s i g n i f i c a n t d i f f e r e n c e s i n o v e r a l l means,-then i t would seem that the experimental and c o n t r o l type of e x e r c i s e s were e q u a l l y e f f e c t i v e i n dev e l o p i n g c r i t i c a l t h i n k i n g when a l l l e v e l s of a b i l i t y were lumped together and c o n s i d e r e d as a s i n g l e u n i t . 3. Since there was no s i g n i f i c a n t d i f f e r e n c e be-tween the d i f f e r e n c e s i n means at the " s u p e r i o r " l e v e l and " i n f e r i o r " leve.l, i t would appear that each type of exer-c i s e i s j u s t as e f f e c t i v e at the " s u p e r i o r " as at the " i n -f e r i o r " l e v e l r e g a r d l e s s of type of e x e r c i s e . 9 9 4. Any d i f f e r e n c e i n means was g e n e r a l l y a t t r i b u t -able to the experimental group having a l a r g e r mean than that of the c o n t r o l group. 5. The " s u p e r i o r " , "average" and " i n f e r i o r " l e v e l s f o r both the experimental and the c o n t r o l groups showed p o s i t i v e gains i n c r i t i c a l t h i n k i n g f o r the d u r a t i o n of the experiment with the exception of the " s u p e r i o r " l e v e l i n the c o n t r o l group. 6. The l a r g e s t gains i n c r i t i c a l t h i n k i n g f o r the d u r a t i o n of the experiment were noted at the " i n f e r i o r " l e v e l of a b i l i t y f o r both the experimental and c o n t r o l groups. V CONCLUSIONS Inasmuch as the r e s u l t s of t h i s study were d e r i v e d from two groups of t h i r t y p u p i l s , each r e g i s t e r e d at the grade ten l e v e l on the U n i v e r s i t y Program, i n a s p e c i f i c school l o c a t e d i n a s p e c i f i c area, and taught by a s p e c i f i c teacher, any c o n c l u s i o n s based on the f i n d i n g s , must be l i m -i t e d to t h i s " s p e c i f i c p o p u l a t i o n " . Any e x t r a p o l a t i o n of these r e s u l t s to other p o p u l a t i o n s should be made conser-v a t i v e l y . The f o l l o w i n g c o n c l u s i o n s are sub j e c t to the l i m i t a t i o n s s t a t e d above : 1. Students of " s u p e r i o r " a b i l i t y who were exposed to geometric e x e r c i s e s r e q u i r i n g the a d d i t i o n a l experience 100 of checking statements that were not c o n s i s t e n t w i t h g i v e n data,•improved i n c r i t i c a l t h i n k i n g a b i l i t y j u s t as much as those who d i d not have t h i s e x perience. 2. Students of "average" a b i l i t y who were exposed to geometric e x e r c i s e s r e q u i r i n g the a d d i t i o n a l experience of checking statements that were not c o n s i s t e n t w i t h the give n data, improved i n c r i t i c a l t h i n k i n g a b i l i t y j u s t as much as those who d i d not have t h i s e x p e r i e n c e . 3. Students of " i n f e r i o r " a b i l i t y who were exposed to geometric e x e r c i s e s r e q u i r i n g the a d d i t i o n a l experience of checking statements that were not c o n s i s t e n t w i t h g i v e n data, improved i n c r i t i c a l t h i n k i n g a b i l i t y j u s t as much as those who d i d not have t h i s e x p e r i e n c e . 4. Students comprising a composite of the three l e v e l s who were exposed to geometric e x e r c i s e s r e q u i r i n g the a d d i t i o n a l experience of checking statements t h a t were not c o n s i s t e n t w i t h g i v e n data, improved i n c r i t i c a l t h i n k -ing a b i l i t y j u s t as much as those who d i d not have t h i s e xperience. 5. Students r e g a r d l e s s of whether they were of " s u p e r i o r " or " i n f e r i o r " a b i l i t y who were exposed to geo-me t r i c e x e r c i s e s r e q u i r i n g the a d d i t i o n a l experience of checking statements that were not c o n s i s t e n t w i t h g i v e n data, improved i n c r i t i c a l t h i n k i n g a b i l i t y , j u s t as much as those who d i d not have t h i s e x perience. 101 VI PROBLEMS FOR FURTHER STUDY 1 . Inasmuch as the gains i n c r i t i c a l t h i n k i n g f o r such a short p e r i o d of time were g e n e r a l l y i n fav o r of the experimental group, i t would seem d e s i r a b l e to repeat t h i s experiment f o r a longer p e r i o d w i t h a l a r g e r group of sub-j e c t s . 2. Since the l a r g e s t gains i n c r i t i c a l t h i n k i n g were made by the group of " i n f e r i o r " a b i l i t y and the smal-l e s t by the " s u p e r i o r " a b i l i t y group, i t would appear t h a t t h i s may.have some r a t h e r important i m p l i c a t i o n s f o r cur-r i c u l u m p l a n n i n g and may merit f u r t h e r study. 3. A necessary step f o r f u r t h e r s t u d i e s i n the area of c r i t i c a l t h i n k i n g i s the development of more v a l i d and more r e l i a b l e instruments f o r e v a l u a t i n g t h i s a b i l i t y . * * * * 102 B I B L I O G R A P H Y 103 BIBLIOGRAPHY A. BOOKS A n a s t a s i , Anne. P s y c h o l o g i c a l T e s t i n g , New York: Macmillan Co., 1954. Department of Education, Province of B r i t i s h Columbia, Jun-i o r and Senior High School Mathematics 1958, V i c t o r i a , B.C.: P r i n t e r to Queen, 1958. Province of B r i t i s h Columbia, Programme of S t u d i e s f o r the J u n i o r High Schools, V i c t o r i a , B.C.: P r i n t e r to Queen, 1939. Dewy, John, How We Think, Boston: D.C. Heath Co., 1933. Edwards, A l l e n L. Experimental Design i n P s y c h o l o g i c a l  Re search. New York: Rinehart and Co., Inc., 1950 Fawcett, H a r o l d P. The Nature of Proof, T h i r t e e n t h Yearbook, The N a t i o n a l C o u n c i l of Teachers of Mathematics, Bureau of P u b l i c a t i o n s , Teacher's C o l l e g e Columbia U n i v e r s i t y , New York, 1952. Gadske, R i c h a r d Edward. "Demonstrative Geometry as a Means f o r Improving C r i t i c a l T h i n k i n g " , Summaries of D o c t o r a l  D i s s e r t a t i o n s June - Aug. 1940, V o l . 8: 91-97, North-western U n i v e r s i t y , Chicago and Evanston, 1940. G l a s e r , E.M. An Experiment i n the Development of C r i t i c a l T h i n k i n g , New York, C o n t r i b u t i o n s to Education No. 843, Bureau of P u b l i c a t i o n s , Teacher's C o l l e g e , Columbia U n i v e r s i t y , 1941. Good, C a r t e r V. and Douglas E. S c a t e s . Methods of Research New York: A p p l e t o n - C e n t u r y - C r o f t s , Inc., 1954. G u i l f o r d , J.P. Fundamental S t a t i s t i c s i n Psychology and  E d u c a t i o n . New York: McGraw-Hill, 1956. Harvard U n i v e r s i t y . Committee on the O b j e c t i v e s of a General Education i n a Free S o c i e t y . General Education i n a  Free S o c i e t y , Cambridge Mass; Harvard Press, 1945 Hutchins, R.M. Higher Learning i n Yale U n i v e r s i t y Press, 1936. Amer i c a . New Haven, Conn; 104 K i n s e l l a , John. "The E v a l u a t i o n of Mathematical Learning", Emerging P r a c t i c e s i n Mathematics Education, Twenty-Second Yearbook, N a t i o n a l C o u n c i l of Teachers of Math-ematics, Washington, D.C., 1954. L i n d q u i s t , E.F. S t a t i s t i c a l A n a l y s i s i n E d u c a t i o n a l Research. New York: H a u g h t o n - M i f f l i n Co., 1950. Morgan, F.M., and W.E. Breckenridge. Plane Geometry. Toronto: Thomas Nelson and Sons, 1954. Perry, Winona. A Study i n the Psychology of Learning i n Geometry, New York, Bureau of P u b l i c a t i o n s , Teacher's C o l l e g e , Columbia U n i v e r s i t y , 1925. Rosskopf, Myron F. Mathematics a Second Course. New York: McGraw-Hill, 1950 R u s s e l l , David H. C h i l d r e n ' s T h i n k i n g . Boston: Ginn and Co., 1956 . Smith, Eugene R.S., Ralph W. T y l e r , and E v a l u a t i o n S t a f f . A p p r a i s i n g and Recording Student P r o g r e s s . New York: Harper Bros, Vol I I , 1942 Thouless, Robert H. "Watson G l a s e r Tests of C r i t i c a l Think-i n g " . p. 544 of The T h i r d Mental Measurements Yearbook, E d i t e d by Oscar K. Buros, New Brunswick, New J e r s e y : Rutgers U n i v e r s i t y Press, 1949. B" PERIODICAL REFERENCES Be a t l y , Ralph. "The T h i r d Report of the Committee, on Geom-e t r y " , The Mathematics Teacher, 28: 329-379, 401-450, 1935 . Brown, Kenneth E. "Why Teach Geometry," The Mathematics  Teacher, 43: 103-105, March, 1950. Edwards, T. B e n t l e y . "Measurement of Some Aspects of C r i t -i c a l T h i n k i n g " , J o u r n a l of Experimental Education, 18: 263-278, March, 1950 . Ennis, Robert H. "An A p p r a i s a l of the Watson-Glaser C r i t -i c a l T h i n king A p p r a i s a l " , J o u r n a l of E d u c a t i o n a l Re- search, 52 : 155-158, D e c , 19581. 105 Fawcett, Harold P. "Quod er a t demonstrandum", The Mathem-a t i c s Teacher, 49: 2-6, Jan., 1956. F u r s t , Edward J . " R e l a t i o n s h i p Between Tests of I n t e l l i g -ence and Tests of C r i t i c a l T h i n k i n g " , J o u r n a l of Educ-a t i o n a l Research, 43: 614-625, 1950. Orata, Pedro T. "Recent Research S t u d i e s on T r a n s f e r of T r a i n i n g w i t h I m p l i c a t i o n s f o r Curriculum, Guidance and Personnel Work", Harvard Review, 11: 359-378, 1941. Parker, E l s i e . "Teaching P u p i l s the Conscious use of a Technique of T h i n k i n g " , The Mathematics Teacher, 17: 191-201, 1924 . Pingry, Robert E. " C r i t i c a l T h i n k i n g — What i s i t " , The  Mathematics Teacher, 44: 466-470, Nov., 1951. Ulmer, G i l b e r t , "The Teaching of Geometry to C u l t i v a t e R e f l e c t i v e T h i n k i n g " , The J o u r n a l of Experimental  Education, 8: 18-25, Sept., 1939 U l l s v i k , B j a r n e . "An attempt to Measure C r i t i c a l Judgement", School Science and Mathematics, 49: 445-452, 1949. C. UNPUBLISHED MATERIALS Ennis, Robert H. ( C o r n e l l U n i v e r s i t y , I t h i c a , N.Y.), a l e t t e r to w r i t e r , 18 Feb., 1959. Horrocks, John E. (The Ohio State U n i v e r s i t y , Columbus, Ohio), a l e t t e r to w r i t e r , 16 Feb., 1959. K e l l o g g , Theodore E. "The R e l a t i v e E f f e c t s of V a r i a t i o n s i n Pure and P h y s i c a l Approaches to the Teaching of E u c l i d e a n Geometry on P u p i l ' s Problem S o l v i n g A b i l i t y " . Unpublished D o c t o r a l t h e s i s , U n i v e r s i t y of Minnesota, 1956 . Koppenhaver, Chester V. "A Comparative Study of the E f f e c -t i v e n e s s of the 'Nature of Proof' and a Conventional Method of Teaching Plane Geometry", Unpublished D o c t o r a l t h e s i s , Teacher's C o l l e g e , Temple U n i v e r s i t y , 1943 . 106 Lewis, Harry. "An Experiment i n Developing C r i t i c a l Think-in g Through the Teaching of Plane Demonstrative Geom-e t r y " . Unpublished D o c t o r a l t h e s i s , New York U n i v e r s i t y , 1950. Massimiano, Carmen C. "The I n f l u e n c e of the Study of Plane Geometry on C r i t i c a l T h i n k i n g " , Unpublished D o c t o r a l t h e s i s , U n i v e r s i t y of Ottawa, Canada, 1955. Rosskopf, Myron.F. (Columbia U n i v e r s i t y , New York) a l e t t e r to w r i t e r , 9 May, 1956. * * * * 107 A P P E N D I C E S 108 APPENDIX A RAW SCORE DATA TABLE VII AGE, SEX, INTELLIGENCE QUOTIENTS AND CRITICAL THINKING SCORES OF THIRTY MATCHED PAIRS OF . PUPILS CONSIDERED IN THIS STUDY Le v e l A G E S E X I. Q. C.T.A. Test C.T.A. Test of Form A Form B A b i l i t y Exp . Cont. Exp . Cont. Exp. Cont . Exp. Cont. Exp. Cont. 1 15-1 16-2 M M 127 124 77 78 74 78 2 15-10 16-2 M M 117 117 73 73 69 64 3 15-1 15-5 F M 121 121 73 71 71 66 4 15-3 15-6 M M 11.6 114 70 71 73 62 5 16-2 15-4 M M 108 108 64 65 68 59 6 15-7 15-3 F M 109 109 64 64 64 60 7 15-1 16-0 F M 120 1'2 0 64 63 65 69 8 14-8 16-0 F M 114 115 63 63 64 62 '9 16-7 16-4 M M 112 115 64 61 64 73 10 15-6 15-2 F M 120 117 62 62 71 64 continued next page. TABLE VII(CONTINUED) Level A G E s "E: .X I . Q. C.T.A. Test C.T.A. Test of Form A Form B A b i l i t y Exp. Cont. Exp . Cont. Exp . Cont. Exp. Cont . Exp. Cont . 11 16-1 15-2 M F 109 I l l 60 61 68 70 12 15-10 15-11 F M 112 112 60 61 65 63 13 16-6 15-4 F M 107 110 60 59 51 70 14 15-6 15-11 F M 106 107 58 58 69 65 15 14-8 . 15-5 F F 112 112 58 58 62 58 16 15-9 16-8 F F 106 107 58 58 59 45 17 14-8 15-4 F F 108 109 58 58 66 57 18 15-7 15-8 F M 106 103 57 58 61 56 19 15-3 15-3 F M 103 109 56 57 55 50 20 17-0 15-6 M M 118 114 56 56 75 65 continued on next page. TABLE VII(CONTINUED) a b Le v e l A G E S E X I. Q. C . T « A a Test C.T.A. Test of Form A Form B A b i l i t y Exp . Cont. Exp. Cont. Exp. Cont. Exp . Cont . Exp . Cont 21 15-2 14-11 F F 109 109 55 55 59 61 22 16-0 16-8 M M 102 98 56 54 66 56 23 16-2 15-4 F F 104 104 54 55 63 61 24 15-1 16-6 F M 100 99 55 54 59 60 25 15-0 15-6 F F 121 120 56 52 53 64 26 16-6 16-11 F M 94 98 49 50 48 51 27 15-1 15-8 F M 104 99 49 49 46 61 28 16-2 15-7 M F 104 99 45 45 68 58 29 15-4 15-1 F M 105 106 45 45 52 68 30 16-4 16-7 M M 94 97 40 46 66 51 a As determined, O t i s Quick S c o r i n g Mental A b i l i t y Test, Gamma Form A, World Book Co., New York, 1937. b Watson-Glaser C r i t i c a l T h i n k i n g A p p r a i s a l , Forms A & B,. World Book Co., New York, 1952. 112 APPENDIX B A SAMPLE CALCULATION OF BARTLETT'S TEST FOR HOMOGENEITY OF VARIANCE 113 T A B L E A U I A SAMPLE CALCULATION OF BARTLETT'S TEST FOR HOMOGENEITY OF VARIANCE. S Group b n d . f .c ' £ x 2 d ' 2 e Log. S 2 a L ^ 10 9 310.4 34.49 . 1.53769 L1C 10 9 226.0 25 .11 1 .39985 L 2 E 10 9 166.1 18 .46 1.26623 L 2 C 10 9 90 .4 10 .04 1 .00173 L3E 10 9 534.1 59.34 . 1 . 77335 L 3 C 10 9 468.9 5 2 . TO 1 .71684 SUM 199 .54 8.69569 a. Refers to " s u p e r i o r " l e v e l of experimental group. b. Number of s u b j e c t s i n each group. c . Degrees of freedom d. r 2 r Sum of squares w i t h i n groups, cx = cx 2 - ( £ x ) 2 n e . Variance f . r — number of groups g. A l l e n L. Edwards, Experimental Design i n Psycholog-i c a l Research, Rinehart & Co., New York, 1950, p. 196. continued on next page. 114 TABLE (CONTINUED) VII I Computations: 1. 2 2 £ S = 199.54 = 33.26; Log £S = 8.69569 = 1.52192 Log, £S — r _ 6 r 6 2 = ( 6 ) (1 . 52192 )= 9 .131 ,.52 3 . D i f f = r Log6S' r - £Logs = 9.13152-8.69569= .43583 4. K 2 = (2 .3026 ) ( n - 1 ) ( d i f f ) = 2 .3026( 9 ) ( .43583 )= 9 .0318 5. C o r r e c t i o n 1 4 r 4 1 = 1 4 & 4 1 = 1 4 7= 1.0432 3( r ) ( n - 1 ) 3(6 ) (9 ) 16 2 6. C o r r e c t e d "X 9 .0318 = 8 .659 1.0432 Tabled value of "X 2 at ( 5% l e v e l = 16.919 ( 17a l e v e l = 21.66 2 Hence obtained value for"X of 8 .659 i s not s i g n i f i c a n t . APPENDIX C EXERCISES OF EXPERIMENTAL GROUP EXERCISES Pick out the f i g u r e In the f o l l o w i n g  t h a t r e p r e s e n t s the most g e n e r a l case (Place an (a) b e s i d e i t ) 116 Given Z^RSI i n which RQ b i s e c t s /TRS (b) ( c ) Given AB = AD a = tt Draw a f i g u r e which w i l l best rep-resent the f o l l o w i n g ? ( i e a v o i d  s p e c i a l c a s e s ) . (a) A t r i a n g l e ABC i n which M i s mid p t . of AB (b) A t r i a n g l e RST (c) A q u a d r i l a t e r a l RSTQ (d) An i s o s c e l e s t r i a n g l e DEF, i n which DE i s the base (e) A r e c t a n g l e ABCD (f ) A t r i a n g l e ABC i n which BD b i s e c t s j_B (g) A q u a d r i l a t e r a l i n which the v e r t i c e s are A,B, C & D and /A=/C, £B=(D (h) A q u a d r i l a t e r a l QRST i n which RT b i s e c t s (R In each of the f o l l o w i n g p a r t s  (a) to (o) redraw ( i f necessary  the f i g u r e on your paper i n such way as to r e f l e c t more a c c u r a t e l y ( f ) Given QRST i s a square (g) Given Q u a d r i l a t e r a l ABCD /B='/C= / D= [k= 90° (h) Given AABC the g i v e n c o n d i t i o n s . (a) Given ARST i n which ( b ) l (c) 'given q u a d r i l a t e r a l ABCD M mid pt of AB CA = CB Li = tt AB = AC AE = AD Q u a d r i l a t e r a l ABCD AO = OC DO = BO ABC BD _ L CA AE i CB (1) Given AC = BC D mid pt of AB AE = BF AB = BC AD = DC (j ) Given Given (n) C Given AD = BC AB = CD G mid pt of BD DEF i s any l i n e through G (o) ,g Given AD = BE D- = tt BC = EF 117 I n e a c h o f t h e f o l l o w i n g q u e s t i o n s s e l e c t t h e h y p o t h e s e s w h i c h c a n m o s t l i k e l y be p r o v e d t r u e . I n m o s t c a s e s t h i s c a n be d e t e r m i n e d b y a c a r e f u l r e d r a w i n g o f t h e d i a g r a m t o r e f l e c t more a c c u r a t e l y t h e g i v e n c o n d i t i o n s a n d by s e e i n g w h e t h e r t h e p a r t s ( s i d e s o r a n g l e s ) a r e c o r r e s p o n d i n g l y p l a c e d U n d e r l i n e t h e c o r r e c t h y p o t h e s i s . ^ G i v e n [1=L2 BA=BC ( e ) G i v e n AB=AD /_3=/4 H y p o t h e s e s (1) AB=DCT (2) /3=/5 (3) 74 = 76 (4) BC=DC (5) None o f t h e a b o T B ( f ) G i v e n AD=CF AB=EF H y p o t h e s e s e ( 1 1 / 3 - / 4 /_8=[2 (b) ( c ) H y p o t h e s e s (1) AB=AC~~ (2) £3=/_4 (3) BC=AC (4) [3=/ABC (5) None o f t h e a b o v e * G l v e n QR | RS MS . RS R3t=ST 5 H y p o t h e s e s ( 1 ) RQ=ST ( 2 ) [4=16 (3) R l ^ M S ( 4 ) QR=MS (5) None o f t h e a b o v e G i v e n . fcl=[5 AB=BC H y p o t h e s e s (IT Zi=/_6 ( 2 ) AB=BE (2) /_l=/_6 (3) AB=CE (4) AD=EF (5) None o f t h e a b o v e ( g ) G i v e n ND & BM a r e s t r a i g h t l i n e s C(3) £2=/_5 ( 4 ) DA=BE (5) None o f t h e above, G i v e n RS=RQ /_2=L3 H y p o t h e s e s (1) RS=ST (2) ( 3 ) ( 4 ) ST=QT (5) None o f t h e a b o v e /6=/3 /l=/2 > H y p o t h e s e s (1) /_3=15 (2') AB=BC (3) AB=CD (4) AB=AD (5) None o f t h e a b o v e G i v e n BA=AD BC=DE writ':' ( 2 ) r2=/j 3) BC=AD £4) AD=DE None of t h e a b o v e ( i ) G i v e n A B = B C , AD=CD H y p o t h e s e s (1) AB=CD 6 7 C (2) /_8=/4 (3 ) /_BAD=/BCD ( 4 ) £_ABC=/BAD (5) None o f t h e a b o v e 10 , 118 I n t h e f o l l o w i n g q u e s t i o n s s e l e c t t h e  h y p o t h e s i s w h i c h c a n m o s t l i k e l y b e  p r o v e d t r u e a n d c a r r y o u t t h e p r o o f .  R e d r a w d i a g r a m t o r e f l e c t m o r e a c c u r -a t e l y t h e g i v e n c o n d i t i o n s G i v e n RS=QR /_5=£6 •^-Hypotheses ( 1 ) ST=( G i v e n /_7=/8 AE=CD o t h e s e s H y p  (1)' A D = i QT ( 2 ) ( 8 ) ST=TRS ( 4 ) [3^(6 (5) N o n e o f t h e a b o v e 11, G i v e n D E = E F o t h e s e s DE=FG /B=/J DG=EF ( 5 ) N o n e o f t h e a b o v e G i v e n AB & CD 3 b i s e c t e a c h o t h e r a t 0 H y p o t h e s e s ( 1 ) CO=OB ( 2 ) DB=AO ( 3 ) BD=AC ( 4 ) AC=D0 ( 5 ) N o n e o f t h e a b o v e G i v e n DB=BE AB=BC fo t h e s e s 12= U ( 2 ) DB=EC ( 8 ) [S=,U ( 4 ) BE=AD ( 5 ) N o n e o f t h e a b o v e A CE ( 2 ) AE=DB ( 8 ) CG=*AG ( 4 ) AC=AB (5) N o n e o f t h e a b o v e G i v e n ABCDE i s a f i g u r e w i t h 6 e q u a l s i d e s a n d 6 e q u a l a n g l e s H y p o t h e s e s ( 1 ) EA=FA ( 2 ) EA=BD ( 8 ) [1=12 ( 4 ) AE=AD (5) N o n e o f t h e a b o v e G i v e n AD=DC IJ=U H y p o t h e s e s f t n e s (1) /J=L6 ( 2 ) [ S = I J ( 3 ) AD=BC ( 4 ) CD=AB ( 5 ) N o n e o f t h e a b o v e T e l l w h e t h e r t h e f o l l o w i n g a u x i l -i a r y l i n e s ( i e : d o t t e d l i n e s ) a r e  l e g a l o r n o t a n d g i v e r e a s o n . ( c ) R B G i v e n A D = C F , C B = D E , (_3=L5  H y p o t h e s e s f> TIT"AC=CD F ( 2 ) [3=\2 ( 8 ) DF=AB ( 4 ) A B = E F ( 5 ) N o n e o f t h e a b o v e G i v e n A R S T RS=RT H y p o t h e s e s ( 1 ) 7_R=[S ( 2 ) RS=ST V{3) 13=[T ' ( 4 ) RT=ST ( 5 ) None o f t h e a b o v e G i v e n D M i d p t o f AB BC=AC AE=BF p o t h e s e s ( 1 ) DE=DF DF=FC DB=FC None o f t h e a b o v e 119 2 0 . T h e b i s e c t o r s o f t h e b a s e a n g l e s f o r i s o s c e l e s t r i a n g e s a r e H y p o t h e se s TT) n o t e q u a l ( 2 ) b i s e c t t h e e q u a l s i d e s (3 ) a r e e q u a l / (4_) a r e p e r p S n d i c u l a r t o t h e e q u a l s i d e s . G i v e n AB=BC AD=CD h y p o t h e s e s ( 1 ) £DCB=/DAB AB=CD /_l=/4 BD=AD None o f t h e a b o v e ( 2 ) ( 3 ) (4) (5) ( 2 ) ( 3 ) ( 4 ) ( 5 ) G i v e n AC=BA DB=EC H y p o t h e s e s ? 1 ) [2=/_ 5 ( 2 ) (8=/_9 ( 3 ) AC=BC ( 4 ) [i= [5 ( 5 ) None o f t h e a b o v e G i v e n BD=BE AD=EC H y p o t h e s e s AB=BE BE=BA BA=BC N o n e o f G i v e n A ABC i s e q u i l a t e r a l FC=EB=AD ^ H y p o t h e s e s ( 1 ) A A F D i s e q u i l a t e r a l ( 2 ) A B E D i s i s o s c e l e s A C F E i s e q u i l a t e r a l A DFE i s e q u i l a t e r a l (5) A N o n e o f t h e a b o v e G i v e n RS=ST=QT=RQ TH y p o t h e s e s (1) £_5=L6 ( 2 ) RT=SQ ( 3 ) MS=MT ( 4 ) SQ _j_ RT ( 5 ) None o f t h e a b o v e t h e a b o v e G i v e n A R S T i s i s o s c e l e s RS=RT 5 QT & MS a r e m e d i a n s H y p o t h e s e s TITTJFZF ( 2 ) QT=SM ( 3 ) [7=[B ( 4 ) RT=ST (5) None o f t h e a b o v e G i v e n RS=RT MS=MT H y p o t h e s e s ( 1 ) RM=MS £1=L2 RM=MQ R Q j _ S T N o n e o f t h e a b o v e 25 . AC=AB AE=AD H y p o t h e s e s ) None o f t h e ( 1 ) ( 2 ) ( 3 ) ( 4 ) a b o v e L5=L6 AE=EC 13= L2 DE=EC 26 , ABCD i s a q u a d r i l a t e r a l i n w h i c h A B = C D , A D = C B , BD i s a d i a g o n a l H y p o t h e s e s ( l i 12=13 ( 2 ) [k=lC ( 3 ) AB=BC ( 4 ) BD B i s e c t s /ADC (5) None o f t h e a b o v e R e q u i r e s two o r m o r e p a i r s o f  t r i a n g l e s I n o r d e r t o p r o v e  t h e v a r i o u s p a r t s e q u a l . 120 g G i v e n BE=AB ED=AC BD=CB Q. H y p o t h e s e s (1) EG=AF D (2) AB=BG (3) IJ=(J (4) BD=BE (5) None o f t h e a b o v e G i v e n RQ=RS At MS=MG RTM i s a s t r a i g h t l i n e H y p o t h e s e s (1) R T = T M (2) /R=/S (3) QT=TS (4) U=[5 (5) None o f t h e a b o v e 32 • G i v e n DH=BK U= I & AD=BC H y p o t h e s e s (1) AD=DC BK=KC AB=CD /3=/_8 None o f (2) (3) (4) (5) % D 33 • G i v e n GD=EF GF=DE H y p o t h e se s t h e a b o v e (2) * ( 3 ) (4) (5) DK=KF G£=DK GEj_DF None o f t h e a b o v e G 1 v e n AB=CD, AD=BC, DQ=QB H y p o t h e s e s (1) AD=AB (2) RQ=SQ (3) 11=12 (4) AB=BC (5) None o f t h e a b o v e G i v e n R9=HE, ST=HK M e d i a n RQ = M e d i a n H y p o t h e s e s EN 1) 16-IS 2) h-t* (3) o=L4 (4) RS=HR (5) None o f t h e a b o v e G i v e n DE=DF B=U> H y p o t h e s e s (1) GK=HK (2) DF=EF 3) IJ=[3 (4) (5) HFj_DF None o f t h e a b o v e G i v e n DE=DF A D E F i s i s o s c e l e s EH=HK H y p o t h e s e s _ (1) DE=EF r (2) DG=GH (3) (_3=U> (4) DH E F (5) None o f t h e a b o v e G i v e n DG=DE, /_l=/_7 H y p o t h e s e s ( l i 12= iS (2) 13=U (3) DG=GH H) DH=*HF (5) None of t h e a b o v e 34 . S e t up i n d i r e c t p r o o f s f o r t h e f o l l o w i n g . Ta) The V a n c o u v e r P o l i c e a r r e s t e d a man f o r 39. a r s o n . A t t h e t r i a l he p r o d u c e d a summon^ f o r i l l e g a l p a r k i n g i n t h e c i t y o f H a l i f a x , d a t e d t h e d a y o f t h e f i r e . I f y o u w e r e h i s l a w y e r how w o u l d y o u h a v e a r g u e d h i s c a s e . (b) When J o h n was s i c k , h i s m o t h e r t e l e p h o n e d t h e d o c t o r who s a i d , " I t m u s t be m e a s l e s o r s c a r l e t f e v e r . B u t s c a r l e t f e v e r p a t i e n t s 40 a l w a y s s t a r t b y b e i n g s i c k t o t h e i r s t o m a c h . P H a s J o h n b e e n s i c k t o h i s s t o m a c h ? " What was t h e d o c t o r ' s d i a g n o s i s i f t h e a n s w e r t o h i s q u e s t i o n was " n o " . G i v e n 121 QM // ST RS // MP RQ = TP . H y p o t h e s e s  M ( 1) QM = MP (2) B = 11 (3) RQ = QT (4) ST = QM P (5) None o f t h e a b o v e G i v e n AD // BC CD // AD 35 , 36 . I f AB // CD & [1=140 f i n d t h e s i z e o f „ 12. = *— U = £4 -£5 = _ £6 = T L2 = £8 = " 4 1 . T H y p o t h e s e s ( 1 ) u = £6 (2) /_3 = £4 {3) AD = AB (4) £1 = £3 (5) None o f t h e a b o v e G i v e n RS // QT — — i GH i s a t r a n s v e r s a l H y p o t h e s e s (l) £1 = £2 _LiJ £4 = Le H ( A £1 = i i (4) GH JL QT (5) None of t h e a b o v e N o t e : The a b o v e when p r o v e d c a n be u s e d h e r e a f t e r as a t h e o r e m . 4 2 , G i v e n ED = FG " ' ED // FG H y p o t h e s e s c ^ ( 1 ) DE = EF (2) £4 = £6 (3) J} - £7 (4) EF J _ F G (5) None o f t h e a b o v e 3 7 . 38 , N o t e : G i v e n DA = BC DA // BC AK = EC /\ H y p o t h e s e s i (1) DC = AD B (2) BE = DK (3) AK = KE (4) BE j . AC (5) None o f t h e abo i ' S G i v e n AB I CD EF i s a t r a n s v e r s a l , H y p o t h e s e s I (1) f6 4 /4 = 1 8 0 ° ( 2 ) 73 = I i (3) £5 = £3 (4) EF j _ A B (5) None of t h e a b o v e When p r o v e d c a n be h e r e a f t e r u s e d a s a t h e o r e m G i v e n /R = £B RS // AB RS - AB G i v e n TQ // RS L1 = IJ H y p o t h e s e s (1) SA = AT (2) RS = ST (3 ) ST = AC G i v e n AC = BC (4) £_5=/_6 (5) None o f t h e a b o v e RT H y p o t h e s e s ^ ni Li = 5 (2) TQ , ( 3 ) (1 7 £3=£6 (4) RT j _ RS (5) None o f t h e a b o v e H y p o t h e s e s w j l ] AC=AB (3) /4=£6 (4) 7j=£6 (2) £2-/£5=18 0 (5) None o f t h e a b o v e G i v e n RS// QT EF i s a t r a n s v e r s a l (4) £8-/£2=180° (5) N one o f t h e a b o v e H y p o t h e s e s ( i T - ^ = L 5 (2) /3= £4 (3) £8=£2 APPENDIX D EXERCISES OF CONTROL GROUP 122 A GENERAL NOTES Polygon " i s a c l o s e d broken l i n e i n a p l a n e " The segments are c a l l e d the s i d e s . A. Types of p o l y g o n s ; (1) T r i a n g l e i s a p o l y g o n of t h r e e s i d e s . (2) Q u a d r i l a t e r a l i s a p o l y g o n of f o u r s i d e s . (3) Pentagon i s a p o l y g o n of f i v e s i d e s . (4) Hexagon i s a pol y g o n of s i x s i d e s . B. Regular p o l y g o n i s a p o l y g o n w i t h a l l of i t s s i d e s and a n g l e s e q u a l . eg: A T h i s i s r e g u l a r s i d e s . an example of a p o l y g o n w i t h t h r e e eg: A 5 • i s a r e g u l a r q u a d r i l a t e r a l C. T r i a n g l e (1) Types of T r i a n g l e s ; (a) S c a l e n e - no two s i d e s or a n g l e s e q u a l . (b) I s o s c e l e s - two s i d e s e q u a l . (c) E q u i l a t e r a l - a l l t h r e e s i d e s e q u a l . (d) Obtuse t r i a n g l e - c o n t a i n s an obtuse angle, (e) A c u t a t r i a n g l e - a l l a n g l e s a c u t e ( f ) R i g h t t r i a n g l e - c o n t a i n s a r i g h t a n g l e . D. Q u a d r i l a t e r a l (1) Types of q u a d r i l a t e r a l s (a) q u a d r i l a t e r a l - " i s a p o l y g o n of f o u r s i d e s ' no s i d e s or a n g l e s e q u a l " (b) p a r a l l e l o g r a m - " i s a q u a d r i l a t e r a l i n which o p p o s i t e s i d e s are p a r a l l e l " (c) t r a p e z i u m - " i s a q u a d r i l a t e r a l i n which one p a i r of s i d e s a r e p a r a l l e l " (d) r e c t a n g l e - " i s a p a r a l l e l o g r a m c o n t a i n i n g one r i g h t a n g l e " (e) square - " i s an e q u i l a t e r a l r e c t a n g l e " . G i v e n QRSTUW i s a h e x a g o n ^ T w i t h a l l a n g l e s & s i d e s e q u a l . T o p r o v e QU = RT ST -= QT IJ = IJ 9/7 T ^ ^ o p r o v e /_S = [Q AE = AD AC = AB 7 2 = /3 AB = AD 12 = /3 o p r o v e BC = CD 123 9. I n d i c a t e w h e t h e r t h e f o l l o w i n g a u x i l i a r y l i n e s ( i e : d o t t e d l i n e s ) , a r e l e g a l o r n o t . G i v ^ r e a s o n f o r a n s w e r G i v e n RS = RQ /_1 = [2 e S T = QR G i v e n [1 = [2 RQ = MS RM = QS G i v e n MN & RT b i s e c t e a c h o t h e r a t S To p r o v e RN = MT 12 . T o p r o v e PT = QS RT = QM J = RS = PM AR = CS RT = ST RB = B S T o p r o v e AB = BC G i v e n AB = AC To p r o v e /_B = jC ( H i n t - j o i n A t o m i d p t o f BC) N o t e : T h i s e x e r c i s e c a n be u s e d h e r e a f t e r a s a t h e o r e m G i v e n RT = TS RQ = MS To p r o v e /_6 = / 8 - s GI- RD = E S DT = E T To p r o v e RT = ST G i v e n AC = BC BD & AE a r e m e d i a n s T o p r o v e A E = BD G i v e n RQ =RM RS=RT \ M To p r o v e /MQT = /SMQ G i v e n RS=RQ ST=QT p r o v e /_RST = /RQT ^ S G i v e n A RST i s e q u i l a t e r a l QT=KR=MS ; To p r o v e A Q M K i s e q u i l a t e r a l G i v e n AB=AD BC=CD To p r o v e AC | BD G i v e n BC=AB CE=EA To p r o v e 5 BD j AC The b i s e c t o r s o f t h e b a s e a n g l e s o f a n i s o s c e l e s t r i a n g l e a r e e q u a l , I n a q u a d r i l a t e r a l QRST QT=RS TS=QR RT i s a d i a g o n a l P r o v e /Q=/S C G i v e n CD=BC AD=AB AEC i s a s t r . l i n e To p r o v e DE=BE QR=RS >S /_8=/_9 To p r o v e / 7 = / 4 G i v e n A R S T i s i s o s SQ=QT To p r o v e R M j _ S T T T G i v e n QT=RS QR=ST A i s m i d p t o f To p r o v e AB=AC V G i v e n AB=DE BO=EF "jc; M e d i a n AM= "/vi g M e d i a n DR To p r o v e / 3 = / 4 G i v e n QT=RS QR-=ST To p r o v e WK=kT RT=ST To p r o v e ME=MF 125 31 ( a ) S e t u p I n d i r e c t f o 11 ow i n g : p r o o f s f o r t h e ( b ) T h e V a n c o u v e r p o l i c e a r r e s t e d a m a n f o r a r s o n . A t t h e t r i a l h e p r o d u c e d a s u m m o n s f o r i l l e g a l p a r k i n g i n t h e c i t y o f H a l i f a x , d a t e d t h e d a y o f t h e f i r e . I f y o u w e r e h i s l a w y e r , how w o u l d y o u h a v e a r g u e d h i s c a s e ? W h e n J o h n w a s s i c k , h i s m o t h e r t e l e p h o n e d t h e d o c t o r w h o s a i d , " I t m u s t b e m e a s l e s o r s c a r l e t f e v e r . B u t s c a r l e t f e v e r p a t i e n t s a l w a y s s t a r t b y b e i n g s i c k t o t h e i r s t o m a c h . H a s J o h n b e e n s i c k t o h i s s t o m a c h ? " W h a t w a s t h e d o c t o r ' s d i a g n o s i s i f t h e a n s w e r t o h i s q u e s t i o n w a s " n o " ? G i v e n A D = C F A B //EF BC//DE e B C = D E AB=CD AB/yCD A E = F C e B E = F D AB//CD a t r a n s v e r s a l N o t e : t h e a b o v e h e r e a f t e r b e w h e n u s e d A B / / CD = 1 4 0 ° t h e a n d — G i v e n s i z e Tj o f p r o v e d c a n a s a t h e o r e m . R S ^ Q T a t r a n s v e r s a l 7 4 - = 1 8 0 ° N o t e : T h e a b o v e w h e n p r o v e d c a n h e r e a f t e r b e u s e d a s a t h e o r e m G i v e n G i v e n b i s e c t s // A B M AB //DE AB=DE B C = E F BD b i s e c t s AM//BD T o p r o v e /_ABC L3 = U G i v e n AB //CD E F i s a t r a n s v e r s a l T o p r o v e / I 4 IJ = i8tr APPENDIX E SAMPLE OF DAILY 127 LOG OF ii.is^micm ;^>erimental Group (Block G). Control Group (Block A). lo Lesson Plan 2„ Work Covered 3o Observations Students Absent 5o General Notes 128 APPENDIX F STANDARDIZED TESTS 1 . " O t i s Quick S c o r i n g Mental A b i l i t y T e s t s " , Form Gamma, AM 2. Watson-Glaser C r i t i c a l T h i n k i n g A p p r a i s a l Test Manual 3. Watson-Glaser C r i t i c a l T h i n k i n g A p p r a i s a l , T e s t , Form A. 4. Watson-Glaser C r i t i c a l T h i n k i n g A p p r a i s a l , Test, Form B. OTIS QUICK-SCORING MENTAL ABILITY TESTS By AR T H U R S. OTIS, PH.D. Gamma Formerly Development Specialist with Advisory Board, General Staff, United States War Department / % G A M M A T E S T : F O R M AM ^ IQ For Senior High Schools and Colleges Score Read this page. Do what it tells you to do. Do not open this booklet, or turn it over, until you are told to do so. Fill these blanks, giving your name, age, birthday, etc. Write plainly. Name Age last birthday years F i r s t n a m e , i n i t i a l , a n d last n a m e Birthday Teacher Date .19 Month Day Grade School City. This is a test to see how well you can think. It contains questions of different kinds. Here are three sample questions. Five answers are given under each question. Read each question and decide which of the five answers below it is the right answer. Sample a: Which one of the five things below is soft? 1 1 2 3 4 6 © glass © stone 0 cotton 0 iron © ice I The right answer, of course, is cotton; so the word cotton is underlined. And the word cotton is No. 3; so a heavy mark has been put in the space under the 3 at the right. This is the way you are to answer the questions. Try the next sample question yourself. Do not write the answer; just draw a line under it and then put a heavy mark in the space under the right number. Sample b: A robin is a kind o f — « 7 s 9 10-© plant ® bird © worm © fish ® flower.... The answer is bird; so you should have drawn a line under the word bird, and bird is No. 7; so you should have put a heavy mark in the space under the 7. Try this one: Sample c: Which one of the five numbers below is larger than 55 ? « 12 13 M IS @ 63 @ 48 @ 29 © 57 ©16 :....!! II The answer, of course, is 57; so you should have drawn a line under 57, and that is No. 14; so you should have put a heavy mark in the space under the 14. The test contains 80 questions. You are not expected to be able to answer all of them, but do the best you can. You will be allowed half an hour after the examiner tells you to begin. Try to get as many right as possible. Be careful not to go so fast that you make mistakes. Do not spend too much time on any one question. No questions about the test will be answered by the examiner after the test begins. Lay your pencil down. Do not turn this booklet until you are told to begin. Published b y W o r l d Book C o m p a n y , Y«nkers-on-Hudson, N e w Y o r k , and Chicago, Illinois Copyright 1937 b y W o r l d Book Company. Copyright in Great B r i t a i n . All rights reserved FEINTED IN U.S.A. GAMMA: AM- 34 ' This test is copyrighted. The reproduction of any part of it by mimeograph, hectograph, or in any other way, whether the reproductions are sold or are furnished free for use, is a violation of the copyright law. Page 6 60 67 68 69 70 64 71 72 73 74 78 65 76 77 78 79 80 66 1 2 8 4 6 I! ii ii ii ii « 7 8 9 10 68 11 12 13 14 15 69 16 17 18 19 20 70 21 22 23 24 25 71 26 27 28 29 30 72 81 32 ' 33 34 73 j ! 86 37 38 74 41 42 43 44 75 46 47 48 49 SO 76 81 82 63 84 85 77 66 67 68 69 60 78 !! 64 68 79 66 67 68 69 70 80 li ANSWER SHEET Page 5 66 67 68 69 70 46 71 72 73 74 75 47 76 77 78 79 80 48 81 82 83 84 85 49 86 87 88 89 50 51 52 53 1 2 3 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 54 21 22 23 24 25 55 26 27 28 66 31 32 33 34 35 67 36 37 38 39 40 68 41 42 43 44 45 69 46 47 48 49 60 60 ii ii 61 52 83 64 61 66 67 68 69 62 61 62 63 64 ' 65 «3 ii ii ii ii ii NOTE. This Answer Sheet is not intended for machine scoring. [ 2 ] P a g e ^ 26 27 28 29 30 22 31 32 33 34 35 23 36 37 38 39 40 24 41 42 43 26 46 47 48 49 60 26 61 62 63 64 65 27 66 67 68 69 60 28 61 62 63 64 65 29 66 67 68 69 70 30 71 72 73 74 75 31 76 77 78 79 80 32 33 34 35 36 1 2 3 4 6 7 8 9 10 11 12 13 14 16 17 18 19 20 37 26 27 28 29 30 38 31 32 33 34 35 39 ii ii ii ii ii 36 37 38 39 40 40 ii ii ii ii- ii 41 42 43 44 45 41 ii ii 46 47 48 49 60 42 ii N ii ii ii 51 62 63 43 66 57 58 44 61 62 63 64 65 45 Otis Quick-Scoring: Gamma: AM Page 3 1 2 0 4 8 6 7 8 9 10 11 12 13 14 IS 16 17 13 19 20 21 22 23 24 25 •5 I; !{ ii ii i ; 26 27 28 29 30 6 ii . ii ii ii ii 31 32 33 34 35 7 36 37- 38 3? 41 42 43 44 46 46 47 48 49 SO 10 61 62 63 54 58 11 66 67 58 69 60 12 61 62 63 64 66 13 14 67 68 69 70 71 72 73 74 75 15 76- 77 78 79 80 16 17 1 2 3 4 6 6 7 8 9 10 18 i i 11 12 13 14 19 n ii ii ii 16 17 18 19 20 20 ii ii ii ii ii 21 22 23 24 25 2i ii Otis Quick-Scoring: Gamma: AM Page 1. The opposite of hate is — © e n e m y © f e a r © l o v e © f r i e n d © j o y 2. If 2 pencils cost 5 cents, how many pencils can be bought for 50 cents? © 100 © 10 © 20 © 25 © 6 3. A dog does not always have — @ eyes © bones © a nose @ a collar © lungs 4. A recollection that is indefinite and uncertain may be said to be — • © forgotten @ secure © vague © imminent © fond . 5. Which of these words would come first in the dictionary ? @ more © pile @ mist @ pick © mine 6. A fox most resembles a — © pig © goat © wolf © tiger © cat . 7. Gold is more costly than silver because it is — © heavier © s c a r c e r © yellower © harder © prettier 8. The first drawing below is related to the second in the same way that the third one is to one of the remaining four. Which one? . This is to this as this is t o — < » r^Q] w. 3 9.' A radio is related to a telephone in the same way that (?) is to a railroad train. © a highway @ an airplane © gasoline © speed © noise 10. The opposite of wasteful is — © wealthy @ quiet © stingy © economical © extravagant 11. A debate always involves — © an audience © judges © a prize © a controversy - © an auditorium 12. A party consisted of a man and his wife, his two sons and their wives, and four children in each son's family. How many were there in the party ? © 7 . © 8 © 1 2 © 1 3 , ® 14 13. One number is wrong in the following series. 1 5 . 2 . 6 - 3 - 7 _ 4 > 9 ( 5 ' 9 What should that number be? ' j © 9 " © 7 © 8 © 10 © 5 14. A school is most likely to have — © maps © books ® a janitor © a teacher © a blackboard 15. What letter in the word W A S H I N G T O N is the same number in the word (counting from the beginning) as it is in the alphabet ? ' © A © N © G © T © O 16. Which word makes the truest sentence? Fathers are (?) w e^er than their sons. . @ always © usually @ much @ rarely © never 17. Four of these five things are alike in some way. Which one is not like the other four ? © nut © turnip ® rose © apple © potatoes 18. The opposite of frequently is — 1 © occasionally © seldom © never © periodically © often. ; ^ ^ a s this is to 19. This—-—vis to this 20. At a dinner there is always — © soup © wine © food 55) waiters 20) dishes 21. If 10 boxes full of apples weigh 400 pounds, and each box when empty weighs 4 pounds, how many pounds db all the apples weigh? © 40 © 360 © 396 © 400 © 404 Copyright 1937 by World Book Company T 3 1 Copyright in Great Britain. All rights reserved I «5 J (Go right on to the next page.) Otis Quick-Scoring: Gamma: An Page 64. A statement the meaning of which is not definite is said to be — © erroneous © doubtful © ambiguous ® distorted @ hypothetical. 65. Evolution is to revolution as crawl is to — ® baby © floor © stand © run © hands and knees 66. Coming is to came as now is to — @ today © some time @ tomorrow © before now © hereafter 67. One number is wrong in the following series. 1 ' 2 4 8 16 32 64 96 What should that number be ? © 3 © 6 © 12 © 4 8 © 128 6 68. If George can ride a bicycle 60 feet while Frank runs 40 feet, how many feet can George ride while Frank runs 30 feet ? © 50 © 10 © 45 © 20 © 70 69. What letter is the fourth letter to the left of the letter which is midway between D and I in the word R E P R O D U C T I O N ? © C © R © O © N © D 70. Which of the five things following is most like-these three: ivory, snow, and milk? ©butter © rain ,@ cold © cotton © water.. 71. A hotel serves a mixture of 2 parts cream and 3 parts milk. How many pints of milk will it take to make 25 pints of the mixture? © 25 © 16| © 16 © 12£ © 10 72. A man who spends his money lavishly for non-essentials is considered.to be — ' @ fortunate @ thrifty @ extravagant © generous 73. This is to this J as this is to — (F economical. 74. If the first two statements following are true, the third is (?). One cannot become a good violinist without much practice. Charles practices much on the violin. Charles will become a good violinist. @ true ©, false © not certain , , 75. Which of these expressions is most unlike the other three? © small to tiny © pretty to beautiful © warm to hot @ excellent to good. 76. If the words below were rearranged to.make a good sentence, the fifth word in the sentence would begin with what letter? life friends valuable to The make asset in a is •© 1 © f @ v © t © a ability 77. What number is in the space that is in the rectangle and in the triangle but not in the circle ? © 1 © 2 © 3 © 4 © 5 78. What number is in the same geometrical figure or figures (and no others) as the number 6 ? © 1 © 2 © 3 © 4 © 5 79. How many numbers are there eachof which is in two geometrical figures but only two ? © 1 © 2 © 3 © 4 © 5 80. If a wire 40 inches long is to be cut so that one piece is § as long as the other piece, how long must the shorter piece be? © 26f in. © 3 9 £ in. © 18 in. © 24 in. © 16 in. [ 6 ] Otis.Quick-Scoring: Gamma: AH Page 22. If a boy can run at the rate of 5 feet i n \ of a second, how many feet c a n he . run in 10 seconds? © 1 © 50 (§) 250 © 2 © 25 23. A thermometer is related to temperature as a speedometer is to — © fast © automobile © velocity @ time ' © heat 24. "State of changing place", is a good definition for — • \ • @ advancement ' ® retardation ® rotation © motion @ revision 25. If the first two statements following are true, the third is (?). -All residents in this block are Republicans. Smith is not a Republican. Smith resides in this block. j ^ - © true • © false @ not certain 26. If the words below were arranged to make a good sentence, with what letter . would the second word of the sentence begin? same means big large the as © a © b @ m © s © t 27. Sunlight i s to darkness as (?) is to stillness. @ quiet @ sound © dark @ loud © moonlight. 28. A grandmother is always (?) than her granddaughter. © smarter © more quiet © older © smaller @ slower 29. Such things as looks, dress, likes, and dislikes indicate one's — . © character © wisdom ® personality © gossip © reputation . . . 30. A tree always has — © leaves © fruit © buds © roots @ a shadow 31. In general it is safest to judge a man's character by his — @ voice © clothes @ deeds @ wealth @ face 32. Which of these words is related to many as exceptional is to ordinary ? @ none © each @ more © much © few o o op <jK> np P-Q 33. T h i s O - O i s t o t l u s D l J a s t h i s C H D i s t o — © C K J © Ut2 © C H - l © 34. What i s related to a cube in the same way .that a circle is related to a square? © circumference © corners ® sphere ® solid © thickness 35. Which o n e of these pairs of words is most unlike the other three ? ©run — fast ©large — big ©loan — lend ©buy — purchase 36. The opposite of awkward is — © strong .© pretty ©graceful © short © swift 37. The two words superfluous and requisite mean — © the same © the opposite @ neither same nor opposite 38. Of the five words below, four are alike in a certain way. Which one is not like these four ? © push © hold ©lift © drag © pull 39. The idea that the earth is, fiat is — ' © absurd ® misleading @ improbable @ unfair © wicked., 40. The opposite of loyal is — © treacherous © enemy © thief © coward © jealous 41. The moon is related to the earth as the earth is to —• . @ Mars ©the sun @ clouds @ stars @ the universe 42. The o p p o s i t e o f sorrow is — , • ' @ fun @ success © joy @ prosperity © hope 43. If the first two statements are true, the third is (?). ^ Frank is older than George. James is older than Frank. \ 1 > F> G<S .,' George i s younger than James. © true @ false @ not certain 44. If 2£ yards of cloth cost 30 c nts, what will 10 yards cost ? © $1.20 © 750 © 400 © $3.00 © 37£0 5 Congest means t  bring together, condole means to grieve together. Therefo e con means— © to bring © together  to grieve © to bring or grieve together..— [ 4 ] (Go righ  on lo the next pa> Otis Quick-Scoring: Gamma: Ax Page 5 46. The law of gravitation is — © obsolete "© absolute 47. Oil is to toil as (?) is to hate. © love @ work © boil 48. If yards of cloth cost 90 cents, what will 3£ yards cost? ® $3.16 © SS%i @ 10r © 89£ © approximate © conditional ©constitutional @ ate © hat © 35£ 49. Which number in this series appears a second time nearest the beginning? 6 4 5 3 7 8 0 9 5 9 8 8 6 5 4 7 3 0 8 9 1 : © 9 © 0 © 8 © 6 ©6... 60. This is to this as this < 0 > i s t o — ® < ^ > ® <0 > ®<^^. 61. If the first two statements following are true, the third is (?). Some of our citizens are Methodists. Some of our citizens are doctors. Some of our citizens are Methodist doctors. ©true ©false ® not certain.. 52. Which one of the five words below is most unlike the other four ? ® fast © agile © run © quick © speedy... 63. One who says things he knows to be wrong is said to be — © careless © misled © conceited © untruthful 54. If the words below were arranged to make the best sentence, with what letter would the last word of the sentence end ? sincerity traits courtesy character of desirable © r © y @s © e @d... © prejudiced. and are 55. If a strip of cloth 36 inches long will shrink to 33 inches when washed, how many inches long will a 48-inch strip be after shrinking ? © 4 7 © 44 @ 45 © 46 56. Which of these expressions is most unlike the other three? 46J-. © draw pictures clean house come home © work problems. 57. If the following words were seen on a wall by looking at a mirror on the opposite wall, • which word would appear exactly the same as if seen directly ? © MEET ® ROTOR © MAMA © DEED © TOOT 68. Find the two letters in the word A C T O R which have just as many letters between them in the word as in the alphabet. Which one of these two letters comes first in the alphabet ? 69. 60. A © C © T A. surface is related to a line as a line is to a — © solid © plane One number is wrong in the following series. 1 2 4 7 11 16 23 What should that number be? © 3 © 6 © 10 © O M3) curve © R. @ point @ string. © 1 6 • © 22. is to this ^t^L as this is to- ®/^\ ®/^K 61. This 62. How many of the following words can be made fromi the letters in the word S T R A N G L E , using any letter any number of times? greatest, tangle, garage, stresses, related, grease, nearest, reeling © 7 © 6 © 3 © 4 _®5 63. Which of the following is a trait of character ? © reputation © wealth © influence is] © © fickleness © strength. (Go right on to the next page.) W A T S O N - G L A S E R C R I T I C A L T H I N K I N G APPRAISAL by G O O D W I N W A T S O N and E D W A R D M A Y N A R D G L A S E R Professor of Education, Teachers College, Columbia University Consulting Psychologist, Rohrer, Hibler, and Replogle, Los Angeles Manual C O N T E N T S Description of the Test . 1 Uses for Educational Purposes . : 2 .Uses for Personnel Purposes . . . . . . . . 3 General Directions to the Examiner ' 3 Directions for Administering 4 Directions for Scoring S Conversion to Percentiles . 5 Interpreting the Test Results . . . . . . . 5 Reliability . . . . . . . . . . . . . . 8 Validity 8 The Authors' Concept of Critical Thinking . . 8 Critical Thinking and Creative Thinking . . . 8 Critical Thinking and Intelligence 9 Construction and Technical Characteristics of the Test and Norms 9 References 12 Description of the Test • The Critical Thinking Appraisal is designed to provide problems and situations which require the application of some of the important abilities involved in critical thinking. It can serve both as a test to measure several of the major factors involved in ability to think critically and as a tool to aid in developing that ability. Its items are mostly of a realistic type, involving problems, statements, arguments, and interpretation of data similar to those which a citizen in a democracy might encounter in his daily life as he works, reads the newspaper, hears speeches, participates in discus-sions on various issues, et cetera. The test is available in two carefully equated forms, AM and BM, each consisting of five subtests designed to measure different factors related to the total concept of critical thinking. Each form contains 99 items and can be completed in less than 40 minutes by most persons with the equivalent of a ninth-grade education, although there is no time limit. The subtests of the Critical Thinking Appraisal are as follows: TEST 1. Inference. (Twenty items.) Designed to sample ability to discriminate among degrees of truth or falsity or probability of certain infer-ences drawn from given facts or data.' TEST 2. Recognition of Assumptions. (Sixteen items.) Designed to sample ability to recognize unstated assumptions in given .assertions or'•propositions. TEST 3. Deduction. (Twenty-five items.) Designed.to sample ability to reason deductively from given premises; to.recognize the relation of implication between propositions; to determine whether what seems an implication or necessary inference between one proposition and another is indeed such. TEST 4. Interpretation. (Twenty-four items.) 'Designed to sample ability to weigh evidence and to dis-tinguish between unwarranted generalizations and probable inferences which, though not con-clusive or necessary, are warranted beyond a reasonable doubt. TEST 5. Evaluation of Arguments. (Fourteen items.) Designed to sample ability to distinguish be-tween arguments which are strong and important to the question at issue and those which are weak and unimportant or irrelevant. Each item in the subtests of the Critical Thinking Appraisal requires critical thinking about one of two different kinds of subject matter. In some items, the testee is asked to think critically about problems involving "neutral" subject matter such as the weather, scientific facts or experiments, and other things concerning which people generally do not seem to have strong emotional feelings or prejudices. Other items are approximately parallel in logical structure, but Published by World Book Company, Yonkers-on-Hudson, New York, and Chicago, Illinois. Copyright 1952 by World Book Company Copyright in Great Britain. All rights reserved PRINTED IN U.S.A. W-GCTAIM-2 fl Watson-Glaser Critical Thinking Appraisal 2 pertain to subject matter involving political, economic, social, and racial issues toward which people are apt to have emotional feelings, biases, or prejudices. It is recognized that all the items will not have the same emotional impact for different individuals, but the inclusion of materials from various areas of common prejudice or controversy should generally provide a partial sample of an individual's think-ing about issues regarding which he is apt to have personal biases. Thus, any testee's total critical thinking score is likely to be reduced by any lack of objectivity in his thinking about the problems posed. The subtests of the Watson-Glaser Critical Thinking Ap- v' praisal were selected, from a larger number of subtests in-cluded in earlier editions, because empirical and logical con-siderations showed them to be most generally useful and practical. Due to the identity of the thought processes in-volved in answering the two sets of items, the total score on this test should correlate highly with the total score on the original Watson-Glaser Tests of Critical Thinking. How-ever, the Watson-Glaser Critical Thinking Appraisal is the result of extensive additional experimentation and analysis, and it is characterized by much simpler administration and scoring than the original. Additional information about the development of the test is given in the last section of this Manual. Uses for Educational Purposes Perhaps the most important broad uses of the Critical Thinking Appraisal are as an evaluation instrument and as a teaching tool to help students and trainees develop reliable techniques for logical reasoning that will guide them in their daily life situations. Abilitv_to think critically is tied closely to the citizenship attitudes and skills needed to preserve and strengthen our democratic state~ One hundred and sixty years of public education in the United States have resulted in an electorate who can read and write on at least an elementary level. Our public edu-cation has not resulted, however, in the development 'of a sufficient proportion of citizens who can evaluate critically what they'read. Over 18,000,000 adults in our population today cannot read a newspaper understandingly. Compe-tent citizenship in a democracy calls for • that degree of social understanding and critical-mindedness necessary to make intelligent judgments about public issues. There are numerous specific ways in which the Watson-Glaser Critical Thinking Appraisal can be of service and edu-cational value in the functioning of the teacher and admin-istrator and to the student who is contemplating or entering one of the occupations or courses of study which require a high degree of critical thinking ability. Some of the more common educational uses are summarized below: 1 , (1) The test offers a means for determining with the de-sired precision the relative level of a person's ability to think critically with regard to problems involving recogni-' tion of logical implication, interpretation of data, discrimi-nation between strong and weak arguments, recognition of 1 For instructional materials and units designed to develop the abil-ity to think critically, see pages 94-104 of reference 12. unstated assumptions in reasoning, discrimination among degrees of probable inference, and other aspects of critical thinking. (2) The test results may be useful in evaluating a highly significant portion of the total local curriculum. The ability to think critically has long been recognized as a desirable educational objective — in fact, a major goal of instruction. If the* local course of study aims to provide for educational experiences which will develop the ability to think critically, then the test may furnish some objective evidence as to the extent of the desired growth on the part of the students.2 (3) The test results may be useful in evaluating the rela-tive efficacy of different methods of instruction which are-in-tended to develop the ability to think critically. The test can be used as a research instrument to measure extent of improvement among equated groups who were instructed by different methods. For this kind of investigation, how-ever, the teacher or investigator would need" some degree oi "research competence" and understanding of statistical meth-ods in order to determine the reliability and significance of the results. . • (4) The tests may be useful for predicting academic suc-cess in special subjects and curricula, such as engineering, law, science, market analysis, logic, and debating. A num-ber of unpublished studies have explored the value of the tests for such purposes, and, although the number of cases have been small, correlations have been significantly positive. (5) When,one form of the test has served its purpose as an evaluation instrument, it may occasionally be used di-rectly as source material for instruction in situations where familiarity with the test content and correct answers would not affect adversely its use with subsequent groups. That is, in certain situations test items can be gone over in class, the principles of reasoning involved can be analyzed, and the how and why of the key answer discussed and explained. However, the same objectives can be attained, possibly even more effectively, by using similar items and practice mate-rials devised by the instructor or class. (6) The test will be a useful component of batteries used for individual guidance and for planning remedial teach-ing. A comparison can be made for each student, between his score on each subtest of the battery and the correspond-ing average scores of the class. Remedial help may be given in connection with those critical thinking factors in which the student shows extremely low achievement relative to his own over-all rank. Due to the comparatively low statistical reliability of such part scores, small differences should be ignored. (7) The test can provide cues as to the types of prob-lems on which the group tends to be most ineffective. The percentage of the group missing each item can be determined and compared with the percentage of the item-analysis population that missed each item. It will be revealing to determine the characteristics of the items which a particular I - Gains of a point or so may be found on retesting a group after a brief interval, due simply to greater familiarity with the test. In a study involving 671 eleventh- and twelfth-grade students in one county, the average practice effect was 0.6 point when retested within a week. Manual 3 group tended to miss most frequently. In evaluating a stu-dent, a judgment should not, be based on the results from any one item. ' (8) The test can be used to provide considerable insight into a student's' thinking processes' and the bases of "his deficiencies. First, note the characteristics of the items missed by the individual student and then ask him to explain how he arrived at incorrect answers. For example, some students tend to miss a disproportionately large amount of the emotionally toned items. Sometimes one of the basic difficulties contributing to low scores on these tests is inability to read adequately, or to comprehend language discriminatingly. Remedial in-struction and guided practice in. reading comprehension often are very helpful, therefore, in connection with efforts to improve a' student's ability to think critically. It also has been found that students who have good study habits and skill in outlining, abstracting, and summarizing do betr ter on the critical thinking tests than students, equated for age, grade, and intelligence test scores, who are relatively poor in these skills. The specific remedial exercises to be used will depend upon the needs of the individual student. Often it is helpful to give the student some problems similar to those in the tests and ask him to explain how he arrived at each answer or conclusion. There are many different routes to erroneous conclusions, and remedial work can perhaps best be undertaken from the starting point of how the problem 'appears from the viewpoint of the particular individual who is to be given help. Supplemental reading on methods for ' "straight thinking" may be helpful. A selected group of such readings are identified by asterisks in the references listed at the end of this Manual.-Uses for Personnel Purposes The Critical Thinking Appraisal is by no means limited to use with students. It may be used with adults in busi-ness and industry and public service in the following ways: .. ( 1 ) The test can function as one tool in the process of evaluating and developing significant components of execu-tive ability. "Ability to think analytically and comprehen-sively, to size up a situation and decide," is one of the most important factors which have been found by Starch (JJ^-' and other investigators to- distinguish good executives from poor ones. •j (2) Several Civil Service Commissions and Personnel (Directors have used all or parts of the critical thinking/tests 'as a part of examinations. Burton and Joel (^ )~'of the '.California State Personnel Board have stated: "Among v people engaged in personnel selection, the lack of suitable tests for measuring administrative ability has been widely : recognized. If critical thinking is an important ingredient in administrative ability, the Watson-Glaser tests should be of interest to those who are trying to select personnel for profes-sional and administrative positions." In C. F. Bridges' unpublished investigation of the predic-tion of success of Position Classification Analysts and other professional personnel employees, the critical thinking tests were found to provide the most valid single measure, having a corrected rank-order correlation with < a pairedTcomparisons rating, which attempted to hold experience constant,' of .70 ± .10. ' - - • (3) The tests have been used effectively to introduce the topic of "Practical Thinking" or "Straight Thinking" in conference sessions devoted to executive and supervisory development. (4) Instructors of adult evening classes as well as col-lege classes in Citizenship Problems, Psychology, Logic and Scientific Method, English, Science Survey, Human Rela-tions, Executive Functions, and Business Organization and Management have found the tests useful and interesting for evaluation of the students before and'after instruction and for practical introduction of the subjects of analytical think-ing,, critical reading, propaganda analysis, scientific method, and. problem solving. ., • • . General Directions to the Examiner Preparation for testing. The Watson-Glaser Critical Thinking Appraisal can be given without any extensive pre-vious training. If it is given to a large group, approxi-mately one proctor should be provided for each 25 persons. Prior to administering the test, the examiner should become thoroughly familiar with the test, what has to be done by those taking it, and the problems that are likely to arise while administering it. One of the best ways to do this is to take the test oneself. The usual conditions for op-timum testing — i.e., good ventilation, adequate lighting and desk space, and quiet — should prevail. All answers will . be recorded on separate answer sheets. The tests may be scored rapidly and accurately either by hand or by a test-scoring machine. Testing materials. Each person taking the test will need a test booklet, an answer sheet, two soft-lead pencils (or an electrographic'pencil if tests are to be machine-scored), and a good eraser. , Time schedule. The maximum working time usually re-quired for this test is 44 minutes. However, the total time for the battery and the. times for the subtests are suggested ~~ only as guides. Each group should be allowed, to work_until 95_per cent_haye,Gompleted the entire test booklet. Approx -. imately 95 per cent of the students in an average high school class will complete the test in 38 minutes, and approximately 95 per cent of adults or college groups will complete it in 35 minutes. Time can be called when all but one or two of a group of 30 h a v e completed all the tests. IL_any_ indi-viduals h a v e r n o t finished when time is called-, this fact should be re.cj3xde.d-on_their_papers. To the working time must be added approximately six miiu^ tes for the examiner—to_distribute and collect testing materials, and for the stu^ ent.s„to^ filLiiiI,theJidentifying in-- f ornm.ti.on onjhe answ^sheet^. In order to insure that even the slowest students attempt most of the items in each sub-test, the examiner may wish to note the starting time, add the time for each test successively, and when each of these 4 Watson-Glaser Critical Thinking Appraisal times arrives, say to the group: "If you are still working bn Test . . -1 now, stop and go to Test . . You, may go back if you finish the other tests before time is called." Care should be taken that the group does not feel under pressure, since this is a power test, not a speed test^ What is desired is each person's best response to each item in the test. r T A B L E 1. ESTIMATED MAXIMUM WORKING TIME TIME IN TEST MINUTES 1. Inference 13, 2. Recognition of Assumptions • 6, 3. Deduction 10 4. Interpretation 9 5. Evaluation of Arguments 6 -Total 44 Directions for Administering Be sure that each examinee has all the necessary materials. Then say: "May I have your attention, please? Each of you has been given a test booklet, (a special pencil,2) and a separate answer sheet. Do not open the booklet or make any marks on the answer sheet until I tell you to do so. "This booklet contains five tests designed to find out how logically and analytically you can think. "Each test is preceded by its own specific directions. When I tell you to begin, you will read the directions for the first test and study the sample questions until you know what you are to do. If you cannot readily deter-mine what the directions mean, raise your hand and I will explain them to you. Do not ask questions about a test after you start to answer it. Help will not be given on any test you have already started to answer. Make absolutely no.marks on the test booklet. "For each question, decide what you think is the best' answer. Then record your choice by making a black mark between the appropriate pair of dotted lines on the answer sheet. Do not make any other marks of any kind on the answer sheet. If you change your mind about an answer, be sure to erase the first mark completely. You may answer a question even when you are not perfectly sure that your answer is correct, but you should avoid wild guessing. Do not spend too much time on any one item. When you finish a page, go right on to the next one. If you finish all of the tests before time is up, go back and check your answers. Work as rapidly and as accurately as you can. "In marking your answers, always be sure that the answer space is numbered the same as the question in the test booklet. ("These^sts—arerHo^be^scWe^electrically, so failure to follow jhese^iyut^^ Be sure to use onlythejspecwl^pen ) 1 Insert the appropriate number or name. 2 Omit sections in italics if the test is to be hand-scored. "Now fill in your name and the other information called for on the left-hand side of the answer sheet. Be sure to fill in all the information accurately. The date of testing is . . -1 Be sure to record your birth date. The form of test you will be taking is Form^ i^jfc ; so circle the^j^^fon your answer sheet." Allow sufficient time for each student to fill in the required data. When all information has been filled in on the answer sheet, say: "You will be allowed 13 minutes for the first test. This is ample time for all of you to answer every ques-tion without hurrying if you do not take too long on any one question. When you finish Test 1, go right on to Test 2 without waiting. "So that you will have a guide in spacing your time, I am going to stop any of you who have not finished each test in the usual time and start you on the next test. Those who run a bit short of time on some tests may have time left at the end. When you finish Test 5, the last test, you can go back, answer any questions that were skipped, and check your answers to the other questions. If you finish a test before time is called, go right ahead to the next test. "Remember you are to start reading the directions when I tell you to start and continue working on the successive tests until I tell you to stop. After you have finished checking your answers, you may . . ,3 "Remember, if you wish to change an answer, erase completely, and make no marks on the test booklet. Are there any questions before we begin? "All right now, open your booklets and begin." Record_the starting time; add the appropriate number of minutes to determine the stopping time for each test. Allow -all the group to continue working until more than 95 per cent of them (all but one or two in a group of 30) have finished. In a few unusual groups, this may require allowing more than the estimated time. This additional time would be added on to the time allowed for the last test. When less than S per cent of the group .are working on any of the test, have them write "Test not completed in minutes" on the upper left-hand corner of the answer sheet underneath the word "Percentile," and turn in their papers. A few seconds devoted to seeing that the answer sheets are turned in with the name of the test on the same side will save many minutes of scoring time. During the test move about the room, making sure that each person is marking the answer sheets properly. Collect all the test materials supplied the group, includ-ing used scratch paper. Count booklets, answer sheets, and (if furnished) the electrographic pencils to make sure that all are returned. // the test is being administered to an individual or to a superior "test wise" group, give the examinee or group the materials, request that the blanks be filled in on the answer sheet, and say something like this: "This booklet contains tests designed to measure five aspects of your ability to think logically and analytically. Each test is preceded 3 Fill in with the desired action but see that the booklets are closed and, when turned in, that the answer sheets are all face up. Manual 5 by its own specific instructions. If you cannot readily determine what the directions mean or why the samples are marked as they are, tell me and I will explain them. Work as rapidly as you wish and let me know when you have finished." Timing is not necessary, but experience has shown that most persons who spend more than 44 minutes on the test are not likely to increase their score appreciably in the additional time. Shortly after work is begun on Test 1, check to be sure the instructions are being followed correctly. Directions for Scoring This test is arranged so that the Critical Thinking Score can be obtained with minimum effort and maximum accu-racy by the use of either hand- or machine-scoring methods. ' As a separate operation prior to the scoring process, each answer sheet should be carefully scanned and prepared for scoring. On any items for which two or more answer spaces have been filled in, both responses should be erased, or, if the tests are to be hand-scored, a horizontal Colored line may be drawn through both responses instead. On any item in which a second response was made but the first response has been partly erased, so that the item might be incor-rectly counted as correct, the partial erasure should be com-pleted. Taking these precautions will increase the speed and accuracy of the scoring and, of even greater importance, will increase the reliability of the measures obtained from the test. Either hand-scoring or machine-scoring is accomplished accurately and rapidly by means of the same perforated scoring stencil (key). To score an answer sheet by hand, proceed as follows: 1. Cut out the window on the key as indicated. This makes it possible to record the score on the answer sheet without having to remove the key. 2. Place the scoring key over the answer sheet so that the two heavy black arrows on the key are point to point with the arrows on the answer sheet, thus: . If necessary, adjust the key with a slight rotary motion so that the answer spaces on the answer sheet show through the openings on the key. 3. - Count the number of marks appearing through the holes punched in the stencil and record in the score box of the answer sheet the total number of items correctly answered. Do not count multiple-marked items as right even though the right answer is one of those marked. Con-sider multiple-marked items as omitted. To machine-score the answer, sheets, punch appropriate field holes in the scoring stencil provided and then proceed as usual, recording the total number right. Suggested allo-cation of the fields and switch settings are presented in Table 2. It may sometimes be desirable to obtain certain special scores in addition to the total raw score on the test, especially if both forms are given. Although the reliability coefficients for the subtest scores are not sufficiently high to warrant their use for an individual, subtests 3 and 4 do have sufficient reliability to warrant their use in studying further the thinking characteristics of • T A B L E 2. SUGGESTED FIELD ALLOCATION AND SWITCH SETTINGS FOR MACHINE SCORING TEST NO. 1 2 3 4 5 . Field C Rights C Rights A Rights B Rights C Rights Set at A A Rights A A groups. When subtest scores are to be used, they may be ob-tained readily at the same time that the total score is being ob-tained. Several different special scores might be obtained which would yield some indication of the extent to which each individual taking the test exhibited personal tendencies in thinking about the state-ments presented. However, these can most appropriately be considered as aids to analyzing, diagnosing, and .interpreting the results for a given individual. Hence they are discussed on page 7 of this Manual. Conversion to Percentiles When the raw score (the number right) for a paper has been determined, it must be converted into a percentile equiv-alent, or other norm, before attempting to interpret it.' First, determine the group with which it is desired to compare the individual; then select the appropriate table of norms in this Manual. For most college or high school groups and for many adult groups, Table 3 will be used. In it, any given raw score will be found in the middle column and the per-1 centile value for the score will be adjacent. For example, a high school student who has a raw score of 67 has, accord-ing to Table 3, a percentile rank of 86 on the test. Or, a s another example, according to Table 3 a college student with a score of 55 has a percentile value of 7, which is to say that he can think critically about the materials presented in the test as well as or better than seven per cent of the col-lege standardization population. The percentile equivalent should be entered in the designated space in the scoring box in the upper left corner of the answer sheet, preferably i ^ a different color from the raw score. It is desirable to check all transfers of score in order to insure accuracy. Interpreting the Test Results The raw scores obtained for this or any other test have little or no interpretive significance. When the raw scores for any test have been obtained, two questions usually arise: first, "What does this score mean?" and, second, "What should be done about it?" Possible uses of the results are discussed on pages 2-3 of this Manual and ways of developing critical thinking abilities are discussed in references 12, 21, 25, 26, 32, and 40. As mentioned previously (see page 5), a well-chosen set of norms is the essential background against which one evaluates the score of a given individual. A raw score (the number right on this test) is most commonly converted into meaningful units by determining its/position in the distribution of the scores made by some appropriate group; 6 Watson-Glaser Critical Thinking Appraisal i.e., by comparing it with the scores of a group in sueh a way as to show how it ranks within that group. For many purposes this reference group most appropriately is a local : one — a company's employee relations interns, a Problems of Democracy or other class. However, for several uses it is desirable to evaluate an individual's critical thinking score by comparing it with the scores of a" larger or more general group, such as a sample from the national population of high school students. For this purpose, the most appro-priate norms should be selected from the accompanying Tables 3 and 4, according to the school or job classification which is most pertinent. ' • • '. These percentiles provide a meaningful way of showing how an individual's achievement on the Critical Thinking Appraisal ranks in the distribution of achievement of the total group with which he is being compared. In inter-preting percentile ranks it is important not to confuse them with the per cent marks sometimes used in schools, which represent the per cent of test questions answered correctly. The percentile rank corresponding to a particular score in-dicates the per cent of individuals in the standardization group that are equaled or surpassed by individuals making that score. To group individuals according to a commonly used five-' level classification, percentiles of 94 and above may be considered as "Level I: Very High," of 70-93 as "Level II: High," of 32 -69"as "Level III: Average," of 8-31 as "Level IV: Low," and of 1 through 7 as "Level V : Very Low," in comparison with the standardization population. The senior high school norms given in Table 3 are based upon the distribution of scores for 5476 eleventh- and twelfth-grade students, from 53 different schools in 24 states and all the geographic divisions of the nation. This sample's mean IQ on the Terman-McNemar Test of Mental Ability was approximately one point below the probable mean of the national population of eleventh- and twelfth-grade students. The college norms were obtained from the distribution of scores of the freshmen in a large Eastern university who applied for classification as sophomores in 1951. Although data were obtained from several college groups, the com-bined distribution of scores was somewhat similar to that in the above-mentioned large "Presophomore" population for which considerable additional data were available. Since these additional data made it possible to define various other pertinent characteristics of the standardization group, the college norms are based upon this one population. Norms for neither high school nor college students are pre-sented separately by grade or sex, since the evidence from all comparisons thus far indicates that the differences between the distributions of score for these groups usually are not of practical significance. (See Tables 12-14.) .Additional normative data are presented in Table 4. Per-tinent supplementary data, which define further significant characteristics of the groups upon which these norms are based, are presented in the last section of the Manual. The test user can readily prepare another table that will permit interpretation of results with reference to a given school, school system, or other local group. To make such T A B L E 3. ' PERCENTILE NORMS FOR HIGH SCHOOL COLLEGE STUDENTS (Forms AM and BM) PERCENTILES CRITICAL PERCENTILES HIGH SCHOOL THINKING COLLEGE STUDENTS APPRAISAL STUDENTS SCORE 99+ 87 99+ 99+ 86 99 99+ 85 98 99+ 84 97 99+ 83 96' 99 82 95 99 81 93 99 80 91 99 79 88 98 78 84 98 77 80 97 76 76 96 •' 7 5 71 95 74 66 93 - 73 61 92 72 . 57 91 71 ' 53 90 70 49 89 69 45 88 68 •• 41 86 67 37 85 66 33 83 65 30 81 .64 26 79 63 ' 23 77 62 20 74 61 , 17 . 72 60 ., 15 69 59 13 66 58 11 63 57 9 60 56 8 56 55 7 53 54 6 49 53 5 45. 52 4 42 51 4 39 > 50 3 35 49 3 32 48 3 29 • 47 2 26 46 2 22 45 2 19 44 2 16 43 . 1 13 42 1 11 • 41 1 9 40 1 7 39 1 6 38 1 5 37 1 4 36 1 3 35 1 2 34 i_ 1 33 1 — 1 32 1 — 1 - 31 1 -5476 Number of Cases' 1940 53.3 Median 70.5 54.3 Mean 69.3 10.9 Stan. Deviation 9.5 Manual '7 a table, it is necessary merely to prepare the distribution of total1 scores of the group and: then find Lhe median (50th percentile) and quartiles (25th and 75th-percentiles), using the procedure outlined on the Class Record and presented in detail in any elementary statistics book. Listing these three dividing scores.makes it easy to classify each individual's score in the top quarter, second quarter, etc., of his class or group.-If the test results are to be'interpreted in terms of prob-ability of success in some pertinent activity, as when select-ing individuals for admission to certain curricula, graduate schools or special courses, or when hiring and upgrading personnel for technical, executive, professional, and admin-istrative positions, the appropriate cutting scores must be determined by local research. In situations where there is not adequate evidence of any .relationship between scores pnthe Critical Thinking Appraisal and. prediction of success in a particular field or course, research would need to be TABLE 4. MEDIAN AND RANGE OF SCORES FOR SPECIAL GROUPS - W-G CTA TOTAL SCORE (Unless otherwise GROUP indicated) LOW • MEDIAN HIGH SCORE SCORE SCORE 140-Ninth-Grade Students1 ' 28 52 80 5476 Eleventh- and Twelfth-Grade Students 2 23 53 • , 87 135 Freshmen Scholarship Applicants3 34 62.4 83 1940 College Freshmen Applying for Sophomore Status4 ' 25 . 70.6 88 447 School of Education Students, Mostly Juniors Working for Teachers' Certifi-cates6 •• 3.1 69.3 88 ' 24 Senior College Students 6 -Critical Thinking Total ' 38 68 , 83 Age in Years 21 22 50 21 Senior College English Students 7 - ,53 69.0 84 - 16 Graduate Students, Candidates for - _ Ph.D. in English8 Critical Thinking Total 59 76.5 88 Miller Analogies, Form H •38'" 65.5 85 10 Trainees, Industrial Relations (Care-' fully Selected, Superior Group, College Graduates, Advanced Training, and 1-4 Years Work Experience) 9 Critical Thinking Score ' •. 65 ' •79 . 87' Age in Years 25 29 31 • '•Courtesy Bertis E. Capehart, Director'of Guidance, Oak Ridge Public Schools, Tennessee. • 2 The high school standardization population. . 'Mean, 61.9; Stan. Dev.,'10.5. Courtesy Professor Ulrey K. Wilson, Director of Testing and Guidance, University of Chattanooga, Tennessee; 4 Mean, 69.3; S.D., 9.4. Courtesy Dr. La Verne Buckton, Coor- , dinator of Testing, Bureau of Testing and Research, Brooklyn College, New York. 5 Mean, 70.5; S.D., 9.8. Courtesy Bureau of Psychological Services, Institute for Human Adjustment, University of Michigan, Ann Arbor. 6'Mean, 67.4. Courtesy Dr. J. Wesley Crum, Central Washington College of Education, Ellensburg.... 7 Courtesy Drs. Julian C. Stanley and W. J. Griffin, George Peabody College for Teachers, Nashville, Tennessee. 8 Courtesy Testing and Guidance Bureau, University of Texas,-Austin. 9 Courtesy Division of Personnel Procedures, Pittsburgh Plate Glass Company, Pennsylvania. carried on over a period, of time to find out whether the test is in fact useful for this purpose. ... , -; The specific interpretation of results will vary ..with the purpose for which the tests were given. If individuaLdjag-nosis.and remedial work are a purpose, then all items incor-rectly answered should be reviewed with the individual, to determine both the route by which he tends to arrive at,his wrong answers, and whether there seem to be a few. main sources of, difficulty, such as a tendency to over-generalize on the basis of insufficient evidence; inability to distinguish between a necessary inference and merely a probable o.r.even just.a possible inference; inability to recognize unstated,as7 . sumptions; inability to think objectively; reading compre-hension difficulty; etc. Remedial teaching and practice may then be geared to the diagnosis. In diagnosing and interpreting the test results, several different supplementary analyses may help give the instructor' usefiif in-sights.- One procedure,-which gives promise of yielding consid-erable insight, into the thinking of particular individuals,'is...to have the persons taking the .test, especially subtests ,2,-.'and. 5; indicate on the answer sheet whether or not they tend to, approve of or agree with the general idea expressed in the premise state-ments or questions. "Yes" or "No" could be recorded,' before answering'the particular group of-items based upon-any state-ments which .lend themselves to such evaluation, possibly just above the item number of the first item based upon-the statements. The instructor could then determine whether the individual tested tended to miss a disproportionate per 'cent of items' that (a) are opposed to the individual's expressed opinion; {b) are in agreement with his expressed-opinion, or (c) do not' ' lend themselves-, to -such evaluation. -The .number, of.-uterus missed in each of these. categories could be divided by..the re:pective total number of items in each of these categories^ ' and" each student's results evaluated by comparing them with each other and with the distributions of the corresponding'per^ centagesfor.'the, class. .:• ' '-<-,-, - : i . Some teachers may find it helpful to determine a student's: objectivity in answering the "emotionally toned" items as.:com-, pared with his ability to answer "neutral" items. In order to do' this, it would be necessary for the.teacher to identify'those items which would most clearly have an emotional loadihg-'fbf the particular group involved and those items which the-teacher is confident would have no such emotional loadingfor the local, group of students. It would then be possible to determine each, student's score on the emotionally 'loaded items and his score on the neutral items. Dividing the score on the loaded items' by the score on the neutral items yields an "index of objectivity"-which would be corrected to some extent.for the student's ability tot think critically on neutral topics.1 In such an index, a, high,score-• would indicate high objectivity and a low score low objectivity, or subjectivity. ,. " For a relatively small "number of items such indices arid 'special' scores would not have high statistical reliability, and hence atten-tion should be.paid,only to extreme deviates. For this reason norms for these special scores are not given and they are; sug-gested only as an aid in helping students. Many instructors will be able to determine by inspection any tendency for the items missed by each individual to have characteristics in common. This inspection procedure would locate, for example, any stu- -dents who.-made relatively low critical thinking scores .because; they missed a much larger portion, of the. emotionally, toned items than of the neutral items. . • . . . . . . •^The total score minus the score on the.neutral items is the score on the loaded items,. The total score plus 100 (to avoid negative numbers) and minus fwice the score on the neutral items also yields an objectivity-index.- . . . . 8 Watson-Glaser Critio Reliability For practical purposes the reliability of a test may be considered as expressing the degree of consistency of results which may be expected from repeated application of the test. The reliability of the test as a whole and of the separate sub-test scores has been determined by both the split-half and -the inter-form method for several types of groups. Table 5 presents the basic reliability data. They indicate that the total score has adequate statistical reliability for use with groups when one form is used. When maximum precision is desired for an individual's total scores, or when it is desired to study an individual's subtest scores, both forms can be given and the average of results from the two forms used.' Validity There are two related validity problems in connection with a test of this kind. One.is_the soundness or logical "correctness" of thejtev. The other is the usual concept of a test's content validity: How well does this test fulfill its function of measuring ability to think critically? Does an individual have to demonstrate one or more aspects of criti-cal thinking when answering the questions? The key represents the "judgment" of thirty-five persons, 'selected for their advanced training in logic and language meaning, plus their demonstrated leadership in such fields as chemistry, biology, physics, psychology, education, and busi-ness administration, who agreed unanimously that the key answers (after many revisions and refinement of items) are logically correct and that correct response to the questions requires some of the most important skills or abilities funda-mental to critical thinking. High correlations between success on individual items and on the total test yield'further evidence in support of the validity of the key_and_the_test_itself. Several groups of eleventh- and twelfth-grade students and superior college students took the experimental forms prepared in refining the test. The items retained from the successive experi-vnental forms differentiated sharply and significantly between '"individuals scoring in the upper and the lower_ 2.7_per cent of their group's distribution of total critical thinking scores. If a person scores well above the norm for his group (except by chance), and has not had coaching on the test, it seems probable that his relatively high score is evidence of superior ability to comprehend and reason logically about the kind of problems contained in the Critical Thinking Appraisal. Validation against independent criteria has been carried out with early experimental forms in several ways over the twelve years that these tests have been in process of refine-ment. In one study with an early edition of the test (1938), several high school science ^ teachers were asked to identify their students who appeared markedly able or markedly poor in ability to reason accurately_and to think logically. The test distinguished significantly between the two groups. Similar experiments have been conducted with college groups in subjects such as science, current affairs, logic, philosophy, and English composition. All such experiments yielded a significant difference in mean test score between those stu-l Thinking Appraisal dents who gave evidence in classroom discussion and in written assignments of ability to think logically and to marshal their ideas clearly, and those students, who were relatively poor in these abilities. Later experimental editions of the test were tried out with groups of fifteen practicing research chemists, twelve biolo-gists, eighteen engineers, and fifteen accountants. Their supervisors were asked to rate the members of each group on a rank-order scale of observed critical thinking ability as de-fined in this test. The mean test score of those ranked by supervisors in the top half of their group, in manifest critical thinking ability, was significantly greater than that of those ranked in the bottom half. When the upper and lower 25 per cent in supervisors' rankings were compared in relation to their respective mean scores on the critical thinking battery, the difference between the means was still higher and even more significant statistically. Additional evidence as to the abilities measured in the test is given in the last section of this Manual. The Authors' Concept of Critical Thinking Ability to think critically involves three things: (a) An attitude of wanting to have supporting evidence for opinions or conclusions before assuming them to be true. (b) Knowledge of the methods of logical inquiry which help determine the weight of different kinds of evi-dence and which help one to reach warranted conclu-I sions. (c) Skill in employing the above attitude and knowledge. Briefly, a critical thinker effectively examines beliefs or proposals in the light of supporting evidence, of the relevant facts in the case, instead of jumping prematurely to a con-clusion. In general, critical thinking requires that one be able to comprehend and use language for accurate and discriminating communication of thought, recognize the ex-istence (or non-existence) of logical, relationships between propositions, interpret data and draw warranted conclusions or generalizations, appraise the adequacy and weight of alleged evidence, weigh it and judge between different degrees of probability of certain conclusions, recognize unstated as-sumptions, and evaluate arguments. Critical thinking also involves skill in searching out the "what," "when," "where," and "who," which helps in defin-ing an unanswered question or problem"; it involves skill in sizing up a given situation or problem, examining possible explanations and alternative courses of action which might be taken to meet the problem, and then arriving at sound conclusions. These often entail choosing the most effective courses of action for achieving the desired objectives. Critical Thinking and Creative Thinking Critical thinking, it should be noted, is in no way opposed to spontaneous, free-flowing, uninhibited creative thinking or exercise of one's constructive imagination in such activities Manual as inventing, designing, contriving, hypothesizing, theoriz-ing, composing, and planning. But the creative thinker who zestfully piles up ideas and alternatives eventually needs to look them over with a judiciously critical eye, pick out the more promising, and either improve or discard the rest. Sensitively discerning observation and insightful'interpreta-tion of minimal cues can be a valuable applied art, especially when based upon relatively expert knowledge in a given field. But one who interprets minimal cues, as often needs be the case in clinical diagnosis, should recognize that his "shrewd guesses" may well be quite wrong at times and are only hypotheses subject to verification. There is no inherent opposition between imagination and reason. As the late philosopher and logician, Morris R. Cohen, put it, "The process of building up a new view or picture of the hitherto unseen may be not only controlled but helped by a regard for the rules of logical consistency and probability" (6). Studies of creative behavior (15)', in fact, suggest that some of the basic abilities involved therein (such as sensitivity to problems, fluency of ideas, flexibility of mental operations, originality, analytical ability, synthe-sizing ability, reorganizing or redefining ability, ability to penetrate beyond the obvious and the immediate, and evalu-ating ability) are similar to some of the basic abilities in-volved in critical thinking. Critical Thinking and Intelligence The Critical Thinking Appraisal differs considerably from f abstract tests designed to measure basic intellectual abilities, such as those measured by the Thurstone Primary Mental Abilities 1 battery, the Holzinger-Crowder Uni-Factor Tests,2 or other intelligence test batteries. The Critical Think-ing Appraisal is not an intelligence test as such. Corre-lation coefficients with various intelligence tests are re-1 Published by Science Research Associates. 2 Published by World Book Company. ported in the last section of this Manual; they tend to cluster around .45. Many persons who have very, superior, mental ability as measured by an intelligence^test may^  make a relatiwh^Jowscoreon the Critical TMnk^^p^p^saL But if a person makes a relatively high score on the Critical Thinkingjlppraisal, he also is likely to score relatively high j on an intelligence test-. ~"~ — — — Construction and Technical Characteristics of the Test The precursors of these tests were developed by Watson (37) in connection with his study, The Measurement o) Fair-mindedness. In 1937 Glaser modified and revised them extensively for use in-his An Experiment in the Development of Critical Thinking (12). Since 1937 the tests have gone through seven successive experimental analyses and refine-ments. Many improvements of the items as well as of the subtests have resulted from these repeated tryouts on various groups, item analyses, intercorrelation studies and analysis studies having a bearing upon the concept and measurement of critical thinking. The end result is an entirely new battery which includes those- tests and items which were found to be most useful and significant. Various experimental studies have been carried on with high school and college students, with specialized graduate students, with applicants for personnel, administrative, and professional positions in civil service, and with executives and scientific personnel (chemists, biologists, and engineers) in industry. Disagreements with the key answers were in-vestigated, leading to even further refinement of items or the dropping of old items and their replacement by new. and better ones. Tables 6-8 present some of the more useful data secured for the 1949 experimental edition. Most of the 224 items in this edition, together with a few new ones, were divided between the 118-item standardization edition of Forms AM and BM. Although the instructions for two of the subtests T A B L E 5. RELIABILITY COEFFICIENTS POPULATION FORM OR FORMS RELIABILITY COEFFICIENT OF MEAN STANDARD STANDARD ERROR OF MEASUREMENT ON ONE FORM TOTAL SCORE ON ONE FORM AVERAGE SCORE ON BOTH FORMS SCORE DEVIATION 400 Adult Applicants for Civil Service Administrative Positions Special Form (146 items selected from 1949 expl. ed.) .93 .95 96.7 - 14.0 4 Systematic Sample of 100 Brooklyn College "Presophomores" A M 1 .84 .91- 81.1 — 57 Jrs., Oak Ridge (Tenn.) H.S. A M 1 .84 :91 60.9 — — 48 Jrs., Oak Ridge (Tenn.) H.S. Sophomore Class of 30, Oak Ridge (Tenn.) H.S. AM 1 (first) BM 1 (second) A M 1 . 8 1 2 .79 .90 .88 60.9 62.6 58.3 12.0 12.3 5 1118-item standardization edition from which 19 of the least reliable items were deleted in making the final published edition. * These are inter-form reliabilities which normally are lower than the split-half reliabilities. 10 Watson-Glaser Critical Thinking Appraisal were improved considerably, the changes would not tend to-reduce the reliability of similar data if obtained from the .1951 editions. Hence, the data for the 1949 edition may be considered as closely approximating the data that would be obtained from the administration of both Forms AM and BM and using the average of each individual's score on the two. Form AM was used in the standardization programs. After the final item analyses were completed, 19 of the least reliable items were eliminated from each form in such a way that the two final 99-item forms were matched both in average difficulty (51.6 vs. 51.2) and in the distribution of their, difficulty coefficients. Using a population of 338 eleventh- and twelfth-grade students from seven schools, the two final 99-item forms were equated to the. 118-item Form AM and the standardization population's scores converted to the equivalent scores on the final forms, thus obtaining the appropriate normative data for the published edition. . The data presented in the following tables will be helpful to those interested in knowing more about the test and'its norms or. in making special, uses of the test. Unless others wise indicated, the data in these tables are based on Form AM of the final edition (99 items). TABLE 6, INTERCORRELATIONS AMONG SUBTEST SCORES (Based on 758 Brooklyn College "Presophomores" Tested February, 1950, with 1949 Edition) SUBTESTS TEST 2 RECOG. or ASSUMP. TEST 3 DEDUC-TION TEST -4 INTER-PRETA-TION TEST 5 EVAL. • OF . ARG. OBJEC-TIVITY TOTAL 1 1. Inference .271 . .385 .291 !l72 .176 .519 2: Recog. of A. — - • .449 .424 .183 ' .158 : .563 3. Deduction — — .546 .244 .431 .836 4. Interp. — — — .319 .419 .782 5. Eval. of Arg. — — — — . • .282 :439 ' Object. — — — — — .690 1 Includes objectivity score which was later, discarded because of its lack of reliability. TABLE 7. CORRECTED SPLIT-HALF RELIABILITY COEFFICIENTS FOR W-G CTA SUBTESTS (Based on 758 Brooklyn College "Presophomores" Tested February, 1950, with 1949 Experimental Edition) TEST 1 INF. TEST 2 Ass. TEST 3 DED. TEST 4 INT. TEST 5 ARG. TOTAL rn .51 .61 .70' .78 .36 .83 Stan. Dev. • 3.46 3.46 6.93 5.66 2.65 12.21 Mean 18.15 20.98 52.01 37.45 25.22 153.75 No. Items 30 33 70 53 38 224 TABLE 8. CORRELATIONS OF SUBTESTS AND TOTAL SCORE WITH SELECTED.VARIABLES (Based on 758 Brooklyn College "Presophomores" Tested February, 1950, with 1949 Edition) ., TEST A.C.E. Psycho-logical Exam. COOPE READ-ING RATIVE ENG-LISH COOP. GEN. CULTURE SCI. TOTAL Inference Recog. of A. Deduction Interp. Evaluation of Argu. Objectivity Total ACPE . Coop. Rdg. Coop. English C G. C. Science .433 .269 .363 , .297 .132 .179 .411 .454 .270 .340 .273. .101 .133 .380 . .639 • .449 .293 .411 .311 . .186 .149 .438 ' .674 .790 .289 .120 .198 .215 .007 .090 .231 .471 .429 .287 . .427 .224 .327 .291 .095 .140 .370 .602 .712 .614 .676 Mean. Stan. Dev. 117.41 17.72 64.19 7.93 62.02 7.42 31.61 10.46 209.72 52.12 TABLE 9. RELATIONSHIP BETWEEN TERMAN-MCNEMAR IQ AND W-G CTA FORM AM SCORE (Sample of;192 Eleventh-Grade Students from One County) T-M IQ W-G CTA Mean Stan. Dev. Correlation 104.60 13.08 50.84 9.90 .697 T A B L E 10. INTERCORRELATION BETWEEN CRITICAL THINKING TOTAL SCORE (1938 EDITION) AND OTHER PERTINENT VARI-. ABLES AFTER SPECIAL TRAINING IN CRITICAL THINKING (127 High School Students. See reference 12, pages 142-147.) 2 3 4 READING MENTAL ABILITY CRITICAL THINKING 1. School Marks .47 .31 .12 2. Nelson-Denny Reading — .71 .36 3. Otis Gamma — — .48 T A B L E 11. CORRELATION BETWEEN TOTAL CRITICAL THINKING SCORE (1938 EDITION) AND AVERAGE OF TEACHERS' RATINGS OF PUPILS ON EIGHT KINDS OF BEHAVIOR ASSOCIATED WITH ABILITY TO THINK CRITICALLY (See 12, pages 110-112.) TWELFTH-GRADE ENGLISH CLASSES ' ! CORRELATION BETWEEN TEACHERS' RATINGS AND CRITICAL THINKING SCORE E 1 (N = 25) . .52 E 2 (N = 29) .48 • E 3 (N = 32) .33 -E 4 (N =41) .40 Manual 11 T A B L E 12. AVERAGE CRITICAL THINKING SCORES OF MEN AND WOMEN ON 1949 EDITION (917 Brooklyn College "Presophomores" Tested February, 1950) MEN WOMEN • TOTAL MEAN MEDIAN MEAN MEDIAN MEAN MEDIAN STAN. DEV. Test 1. Inference 19.0 19.3 18.3 18.3 18.6 18.7 3.6 Test 2. Recognition of Assumptions 20.8 20.9' 20.7 20.9 20.8 20.9 3.2 Test 3. Deduction 48.4 48.5 47.7 48.5 48.0 48.5 8.3 Test 4. Interpretation 34.9 35.0 34.0 34.1 34.4 34.7 6.0 Test 5. Evaluation of Arguments 24.3 24.6 24.7 25.1 24.5 24.8 3.6 Objectivity Score 103.5 104.7 102.8 104.1 103.1 104.4 7.6 Total Score 250.7 252.8 248.2 249.7 249.5 251.3 22.2 Number of Students 464 s 453 917 T A B L E 13. AVERAGE AMERICAN COUNCIL PSYCHOLOGICAL EXAMINATION TOTAL SCORES OF MEN AND WOMEN (759 Brooklyn College "Presophomores" Tested February, 1950) MEN WOMEN TOTAL MEAN MEDIAN MEAN MEDIAN MEAN MEDIAN A C P E -Number of Students 119.9 120.4 .350 114.6 113.3 409 117.0 116.7 759 T A B L E 15. SOME CHARACTERISTICS OF THE HIGH SCHOOL STANDARDIZATION POPULATION -(5476 Eleventh- and Twelfth-Grade Students) MEDIAN MEAN STAN. DEV. Terman-McNemar IQ 103.3 103.7 14.9 Age in Years and Months — 17-3 — W - G CTA Total 53.3 54.3 10.9 T A B L E 16. SOME CHARACTERISTICS OF THE BROOKLYN COLLEGE "PRESOPHOMORE" NORMATIVE POPULATIONS (The W - G C T A College Standardization Population was a typical group.) COOPERATIVE GENERAL CULTURE TEST, FORM X X (1168 "Presophomores" tested June, 1951) SUBTEST MEAN SCORE History and Social Studies 46.3 Literature 36.0 Science 30.8-Fine Arts 33.1 Mathematics 29.1 Total * 175.2 COOPERATIVE ENGLISH TEST 4033 "Presophomores" tested'January, '48-June,'49) SUBTEST MEAN SCALED SCORE Mechanics of Expression 59.4 Effectiveness of Expression 63.5 Reading Vocabulary, 64.8 Speed of Comprehension . 67.1 Level of Comprehension 66.9 Reading Total. 67.0 English Total 64.0 T A B L E 14. HIGH SCHOOL POPULATION'S MEAN TERMAN-MCNEMAR IQ, AGE, AND CRITICAL THINKING SCORE (118-ITEM FORM AM), BY GRADE AND SEX "ELEVENTH GRADE TWELFTH GRADE ELEVENTH AND TWELFTH GRADES BOYS GIRLS BOTH BOYS GIRLS BOTH BOYS GIRLS BOTH T-M IQ Age (Yrs.-Mos.) W - G CTA Score No. Students , 103.35 16-8 76.49 1513 104.85 16-10 79.32 1343 104.05 16-9 77.82 2856 102.69 17-7 74.89 1718 104.68 17-9 77.88 1395 103.59 17-8 76.23 3113 103.00 . 17-2 75.64 •. 3231 104.76 17-4 78.59 2738 103.81 17-3 76.99 5969 12 Watson-Glaser Critical Thinking Appraisal REFERENCES 1. BEARDSLEY, M . C. Thinking Straight. Prentice-Hall, Inc.; 19S0. 2. BLACK, MAX. Critical Thinking. Prentice-Hall, Inc.; 1946. 3. BURTON, A. , and JOEL, W . "Adult Norms for the Watson-Glaser'Tests of Critical Thinking." Journal of Psychol-ogy; 1945, 19, 43-48. 4.. BURTT, E . A . Right T/linking. Harper & Brothers; 1946. 5 .* CLARK, E . L . The Art of Straight Thinking. D . Appleton-Century Company, Inc.; 1939. 6. COHEN, M . R. Reason and Nature. Harcourt, Brace & . Co., Inc.; 1931. . , 7. COHEN, M . R., and NAGEL, E . An Introduction to Logic and Scientific Method. Harcourt, Brace & Co., Inc.; 1934. 8. DAWEY, J . How We Think. D . C. Heath & Co. ; 1933. 9. DIMNET, E . The Art of Thinking. Simon & Schuster, Inc.; 1928. ' 10. DUNCKER, K . On Problem Solving. Psychological Mono-• y graph No. 270, American Psychological Association; 1945. FAWCETT, H . P. The Nature of Proof. Thirteenth Year-/ book, National Council of Teachers of Mathematics; 1938. \/. GLASER, E . M . An Experiment in the Development of Critical Thinking. Contributions to Education, No. 843. Bureau of Publications, Teachers College, Columbia Uni -versity; 1941.' 13. GUILFORD, J . P. "Creativity." American Psychologist; •1950, 5, 444-54. 14. GUILFORD, J . P., et al. " A Factor-Analytic Study of Rea-soning Abilities." Reports from the Psychological Lab-oratory, University of Southern California; June 1950 and Apri l 1951. 15. GUILFORD, J . P., et al. " A Factor-Analytic Study of Crea-, tive Thinking." Reports from the Psychological Labora-tory, University of Southern California; Apri l 1951. 16. HOLMES, R. W . The Rhyme of Reason. D . Appleton-Century Company, Inc.; 1939. 17. * HUMPHREY, G. Directed Thinking. Dodd, Mead & Co., Inc.; 1948. 18. HUSSERL, EDMUND. Ideas. The Macmillan Company; 1931. 19. * JEPSON, R. W . How to Think Clearly. Longmans, Green & Co., Inc.; 1936. 20. JOHNSON, D . M . " A .Modern Account of Problem Solving." Psychological Bulletin; 1944, 41, 201-229. 21. * KEYES, K. S. HOW to Develop Your Thinking Ability. McGraw-Hi l l Book Company, Inc.; 1950. 22. LEFFORD, ARTHUR. "The Influence of Emotional Subject Matter on Logical Reasoning." Joiirnal of General Psy-chology; 1946, 34, 127-151. 23.* MANDER, A . E . 'Logic for Millions. Philosophical Library; • 1947. 24* MCCLURE, M . T. How to Think in Business. McGraw-H i l l Book Company, Inc.; 1923. 25. National Council for the Social Studies. Teaching Critical Thinking in the Social Studies. Thirteenth Yearbook. The Council; 1942. 26. National Society for the Study of Education. The Meas-urement of Understanding. Forty-fifth Yearbook, Part I. University of Chicago Press; 1946. ; 1 27. NOLL, V . H . The Habit of Scientific Thinking: A Hand-book for Teachers. Bureau of Publications, Teachers College, Columbia University; 1935. 28. NORTHROP, F. S. C. The Logic of the Sciences and Human-ities. The Macmillan Company; 1947. -29. * OVERSTREET, H . A . The Mature Mind. W . W . Norton & Co., Inc.; 1949. 3 0 * REILLY, W. J . Twelve Rides for Straight Thinking. Harper & Brothers; 1947. 31. "REINER, WILLIAM B. "Value of Cause and Effect Analysis in Developing Ability to Recognize Cause and Effect Re-lationships." Journal of Experimental Education; 1947, X V , 324-330. 32. SINCLAIR, JAMES H , and TOLMAN, RUTH S.' " A n Attempt to Study the Effect of Scientific Training upon Prejudice and Illogicality of Thought." Journal of Educational Psy-chology; 1937, X X V I I I , 362-370. ' 33. STARCH, DANIEL. " A n Analysis of the Careers of 150 Executives." Psychological Bulletin; 1942, 39, 7. 34. STEBBING, L . S. Thinking to Some Purpose. Penguin ' Books; 1939. 35. SYMONDS, P. M . Education and the Psychology of Think-ing. McGraw-Hi l l Book Company, Inc.; 1936. 36. * THOULESS, R. H . HOW to • Think Straight. Simon & Schuster, Inc.; 1939. 37. WATSON, G. .B . The Measurement of Fair-mindedness. Contributions to Education, No. 176. Bureau of Publica-tions, Teachers College", Columbia University; 1925.. 38. WECHSLER, D . "Cognitive, Creative, and Non-Intellective Intelligence." American Psychologist;' 1950, 3, 78-83. 39. WERTHEIMER, M . Productive Thinking. Harper & Broth-ers; 1945. 40. WHITE, E . E . " A Study of the Possibility of Improving Habits of Thought in School Children by a Training in Logic." British Journal of Educational Psychology; 1936, 6, 267-273. ' 41. WILLIAMS, D . E . The Effects of Training in College Debat-ing on Critical Thinking Ability. Unpublished Master's Thesis, Purdue University; 1951. W A T S O N - G L A S E R C R I T I C A L T H I N K I N G A P P R A I S A L Form AM by G O O D W I N W A T S O N Professor of Education, Teachers College, Columbia University and E D W A R D M A Y N A R D G L A S E R Consulting Psychologist, Rohrer, Hibler, and Replogle, Los Angeles D I R E C T I O N S : This booklet contains several different types of tests designed to find out how well you are able to reason analytically and logically. Do not turn this page until instructed to do so. Do not make any marks on this test booklet. " All answers are to be marked on the separate Answer Sheet provided. If you wish to change an answer, be sure to erase your old answer completely. , • , • Published by World Book Company, Yonkers-on-Hudson, New York, and Chicago, Illinois. Copyright 1951-2 by World Book Company Copyright in Great Britain. All rights reserved. Printed in U.S.A. WGCTA:AM-2 • O T E S T l . Inference W a t s o n - G l a s e r : Alt D I R E C T I O N S . An inference is a conclusion which a person draws from certain "observed or' supposed facts. Thus, from the electric light visible behind the window shades and from the sound of piano music in a house, a person might infer that someone is at home. But this inference may or may not be correct. Possibly the people in the house went out leaving the lights on, and the piano music could be corning from a radio or phonograph they left playing. In this test each exercise begins with a statement of facts which you are to regard as true. After each statement of facts, you will find several possible inferences — that is, inferences which some persons might make from the stated facts. Examine each inference separately, and make a decision as to its degree of truth or falsity. On the Answer Sheet you will find for each inference spaces marked with the letters T , PT, I D , PF, and F. For .each inference make a mark on the Answer Sheet under the appropriate letter as follows: T — if you think the inference is definitely true; that it properly follows from the statement of facts given. PT — if, in the light of the facts given, you think the inference is probably true; that there is better than an even chance that it is true. ID — if you decide that there are insufficient data; that you cannot tell from the facts given whether the inference is likely to be true or false. PF — if, in the light of the facts given, you think the inference is probably false; that there is better than an even chance that it is false. F — if you think the inference is definitely false; that it cannot possibly be drawn from the facts given or that in some manner it con-tradicts the facts. Sometimes, in deciding whether an inference is prob-ably true or probably false, you will have to use certain commonly accepted knowledge or information which practically every person knows. This'will be illustrated in the example which follows. Here is the example; the correct answers are indicated in the block at the right. E X A M P L E . A thousand eighth-grade students recently attended a voluntary week-end conference in a Midwestern city. At this conference questions of race rela-tions and means of achieving lasting world peace were discussed, since these were the problems the students felt to be most vital today. * 1. As a group, the students who attended this conference had a keener interest in humanitarian or broad social prob-lems than most eighth-grade students have 2. The majority of these students were be-tween the ages of ,17 and 18. , 3. The students came from all sections of the country 4. The students came to discuss trade-union problems 5. Some eighth-grade students felt that discussion of race relations and means of achieving world peace might be worth-while . -. In the above example, inference 1 is probably true (PT) because (as is. common knowledge) most eighth-grade students are not likely to evidence such serious concern with broad social problems. Inference 2 is probably false (PF) because (common knowledge) there are relatively few eighth-grade students in the United States between 17 and 18 years of age. There is no evidence for inference 3. Thus there are insufficient data (LD) for making a judgment in the matter. Inference 4 is definitely false (F) because it is given in the statement of facts that race relations and means for achieving world peace were the problems discussed. Inference 5 necessarily follows from the given facts; it therefore is true (T). In the exercises which follow, more than one of the in-• ferences from a given statement of facts may be true (T), or false (F), or probably true (PT), or probably false (PF), or have insufficient data (ID) to warrant any conclusion. That is, you are to consider each inference by itself. Make a heavy black mark in the space under the letter that you think best describes each inference. If you change an answer, erase thoroughly. Make no extra marks on the answer sheet. [ 2 ] Go on to the next page. W a t s o n - G l a s e r : AM An English teacher arranged for the students in one of her classes to see the movie Great Expectations, while the students in other classes studied the book itself, without seeing the picture. Tests to measure apprecia-tion, and understanding of the story were administered, immediately upon completion of each type of instruc-tion. On all tests the class which was taught with the aid of the movie did better. The class, which saw the movie became so interested that before the semester was over most of those students read the book, entirely on their own initiative. 1. The tests to measure appreciation and understanding of the story were administered both to the students who saw the picture and to those who only studied the book. 2. The children who were taught with the aid of the motion picture were required to read, the book before the end of the'semester.,. . .• 3. Pupils who see movies instead of reading books lose interest in reading v 4. Most of the children in the class which saw the pic-ture would have preferred to study the book Great Expectations in the usual way without the aid of the movie ._... 5. The teacher who conducted the experiment will hereafter try to use motion pictures when they are available, as an aid in teaching literary appreciation. 6. Pupils can learn more about any. given subject from motion pictures than they can from books The first newspaper in America, edited by Ben Harris, appeared in Boston September 25, 1690, and was banned the same day by Governor Simon Bradstreet. The editor's long fight to continue his little paper and print what he wished marks an important episode in the continuing struggle to maintain a free press. 7. The editor of the first American newspaper died within a few days after his paper was banned 8. Governor Bradstreet felt he had the legal authority to ban Ben Harris's paper 9. The editor of this paper wrote articles against taxes,, of the kind which later brought about the "Boston . Tea Party." ' 10. Ben Harris was a man of persistence in holding to some of his interests and convictions.. I 3 Some time ago a crowd gathered in Middle town, Mississippi, to hear the new president of. the local Chamber of Commerce speak. He said, "I am not ask-ing, but. demanding, that labor unions accept their full share of responsibility for civic betterment and com-munity interests. I am not asking, but demanding, that they join the Chamber of Commerce." The listening representatives of the Central Labor Unions, applauded enthusiastically, Three, months, later all the labor unions in Middletown were represented in the Chamber of Commerce, where they served enthusiastically on com-mittees, spoke their minds, and participated actively in ' the civic betterment projects. , \ : 11. Both the labor union representatives and the other members of the Chamber of Commerce came to recognize \one another's problems and viewpoints better through their Chamber of Commerce contacts. 12. Labor unions' participation in the Middletown Chamber of Commerce has largely eliminated worker-management disputes in that town 13. The active participation of the labor unions caused friction at the meetings of the Chamber of (Commerce. 14. The union representatives soon regretted having accepted the invitation to participate in the Chamber of Commerce 15. Many of the Chamber of Commerce members came1 to feel that their president had been unwise in asking the union representatives to join the Chamber 16. The ^representatives of the Central Labor Unions joined the Chamber of Commerce against the desires of the great majority of their membership Studies have shown, that there is relatively much more tuberculosis among Negroes in the United States than among whites. There is no difference, however, in rate qf tuberculosis between Negroes and whites who have the same level of income. The average income of whites in the United States is considerably higher than the average income of Negroes. • 17. Tuberculosis can be cured.. . 18. Raising the economic level of Negroes would reduce tuberculosis. 19. Tuberculosis is less prevalent among Negroes with relatively high incomes than among Negroes with relatively low incomes 20. Whether a white person is rich or poor makes no difference in the likelihood of his getting tuberculosis. ] Go on to the next page. W a t s o n - G l a s e r : A u T E S T 2. Recognition of A ssumptions D I R E C T I O N S . An assumption is something supposed or taken for granted. When someone states, " I'll graduate in June," he takes for granted or assumes that he will be alive in June, that he will remain in school until that time, that he will pass his courses, and similar things. Below are a number of statements. Each statement is followed by several proposed assumptions. You are to decide for each assumption whether it necessarily is taken for granted in the statement. If you think the given assumption is taken for granted in the statement, make a heavy mark between the dotted lines under " A S S U M P T I O N M A D E " in the proper place on the Answer Sheet. If you think the assumption is not necessarily taken for granted in the statement, make a heavy line under " A S S U M P T I O N N O T M A D E " on the Answer Sheet. Below is an example: the block at the right shows how these items should be marked on the Answer Sheet. If you do not see why the answers marked are right, ask the examiner to explain. In some cases more than one of the given assumptions is necessarily made; in other cases none of the given assumptions is made. E X A M P L E . STATEMENT: "We need to save time in getting there, so we'd better go by plane." PROPOSED ASSUMPTIONS: 1. Going by plane will take less time than going by some other means of transportation. (It is assumed in the statement that greater speed of a plane over other means of transportation will enable the group to get to their destination in less time.) 2. It is possible to make plane connections to our destination. (This is necessarily assumed in the statement, since, in order to save time by plane, it must be possible to go by plane.).. . . 3. Travel by plane is more convenient than travel by train. (This assumption is not made in the statement — the statement has to do with saving time, and says nothing about convenience or about any other specific mode of travel.) • , TEST 2 A S S U M P T I O N M A D E H O T M A D E I I 3 N S T A T E M E N T : "Let us immediately build superior armed force and thus keep peace and prosperity." P R O P O S E D A S S U M P T I O N S : 21. If we have superior armed force, that will insure the maintenance of peace and prosperity 22. Unless we increase our armaments immediately we shall have war.' 23. We now have peace and prosperity S T A T E M E N T : " A wise man will save at least twelve dollars each week out of his earnings." P R O P O S E D A S S U M P T I O N S : 24. No fools have sense enough to save twelve dollars a week 25. A person needs to be wise in order to save twelve dollars a week S T A T E M E N T : "Even if all the wealth in the country suddenly were to be distributed equally, some people soon would again become rich and others poor." P R O P O S E D A S S U M P T I O N S : 26. - The real causes of wealth and poverty would not be much affected by such Socialism 27. Our present economic system is better than such Socialism. •• ~~ ' [ 4 S T A T E M E N T : "Mary isn't going to invite John to her ' party." P R O P O S E D A S S U M P T I O N S : 28. Mary hasn't yet had her party 29. Mary now doesn't like John 30. The party will be at Mary's house S T A T E M E N T : ."Live in the city of Zenith — lowest taxes." P R O P O S E D A S S U M P T I O N S : 31. Efficient management of a city implies lower taxes. 32. An important consideration in deciding where to live is avoidance of high taxes 33. The people of Zenith are content with their present city government S T A T E M E N T : "Our school is fortunate in having all American pupils, so we have no race problems." P R O P O S E D A S S U M P T I O N S : 34. American pupils do not present any race problems. 35. If we practiced democracy, there would be no race problem 36. A school is unfortunate if its pupils are of varied nationalities.. ] Go on to the next page. T E S T 3. Deduction Watson-Glaser: A n e D I R E C T I O N S . Each exercise below consists of two state-ments (premises) followed by several proposed conclu-sions. For the purposes of this test, consider the two statements in each exercise as true without exception. Read the first conclusion beneath the statements, and if you think it necessarily follows from the statements given, answer by making a heavy black mark between the pair of dotted lines under " C O N C L U S I O N F O L L O W S " in the corresponding blank on the Answer Sheet. If you think it is not a necessary conclusion from the given statements, then put a heavy black mark under " C O N C L U S I O N DOES N O T F O L L O W , " even though you may believe it to be true from your general knowledge. Likewise read and judge each of the other conclusions. Try not to let your prejudices influence your judgment — just stick to the given statements and judge each con-clusion as to whether it necessarily follows from them. Mark all your answers on the Answer Sheet. Here is an example; the block at the right shows how your answers should be marked on the Answer Sheet. TEST 3 C O N C L U S I O N F O L L O W S D O E S N O T F O L L O W H! I 31! I E X A M P L E . Some holidays are rainy. All rainy days are boring. Therefore — 1. No clear days are boring.- (The conclusion does not follow, as you cannot tell from these statements whether or not clear days are boring and some may be.) 2. Some holidays are boring. (The conclusion necessarily follows from the statements, since, according to them, the rainy holidays must be boring.) 3. Some holidays are not bbring. (The conclusion does not follow from the statements even though you may know that some holidays are very pleasant.). All musicians are temperamental. Some musicians are not proud. Therefore — 37. All temperamental- people are musicians 38. No proud people are temperamental. 39. Some proud people are musicians ! . . . No jockey is a heavyweight boxer. ,A11 heavyweight boxers are large men. Therefore — 40. No jockey is a small man 41. No heavyweight boxer is a small man 42. Jockeys are small men Some cannibals are sincere idealists. All cannibals are fanatics. Therefore — 43. Some sincere idealists are fanatics : . . 44. Some fanatics are sincere idealists 45. No fanatics are sincere idealists , 46. All fanatics are cannibals All mice that are injected with substance " A " develop disease " X . " Mouse #24 was not injected with sub-stance " . A . " Therefore — 47. Mouse #24 did develop disease " X . " 48. Not all mice with numbers between 20 and 30 were injected with substance " A . " 49. Mouse #24 did not develop disease " X . " . . - ; [ No Republican is a Democrat. All Democrats favor prosperity. Therefore — 50. Republicans favor prosperity. 51. No Republican opposes prosperity 52. No Democrat opposes prosperity 53. No Republican favors prosperity. All Jews feel friendly toward the State of Israel. David feels friendly toward the State of Israel. There-fore — 54. David is not friendly toward the Arabs. 55. David is Jewish 56. Some aon-Jews also feel friendly toward the State of Israel. . . . . . . . If an adult has the ability to give love to others, he must have received love as a child. Some adults did not receive love when they were children. ThereforeN— 57. Some adults do not have the ability to give love to others : : 58. If an adult received love as a child, he has the ability to give love to others. If a. person is superstitious, he believes fortunetellers. Some people do not believe fortunetellers. Therefore — 59. No superstitious person doubts fortunetellers 60. If a person is not superstitious, he will not believe fortunetellers . 61. If a person believes fortunetellers, he is super-stitious S ] Go on to the next page. T E S T 4. Interpretation VVatson-Glasci : AM D I R E C T I O N S . Each exercise below consists of a short paragraph followed by several proposed conclusions. For the purpose of this test assume that everything in the short paragraph is true. The problem is to judge whether or not each of the proposed conclusions logi-cally follows beyond a reasonable doubt' from the infor-mation given in the paragraph. If you think that the proposed conclusion follows beyond a reasonable doubt (even though it may not follow absolutely and necessarily), then make a heavy black mark between the appropriate dotted lines under the " C O N C L U S I O N FOLLOWS ".column on the Answer Sheet. If you think that the conclusion does not follow be-yond a reasonable doubt from the facts given, then make a mark under " C O N C L U S I O N DOES. N O T F O L L O W . " In some cases more than one of the proposed conclu-sions may follow; in other cases none of the conclusions may follow. A report of the U. S. Census states that during 1940 there were approximately 1,656,000 marriages and 264,000 .divorces granted in the United States. 62. Getting a divorce is a quick and easy matter in the United States. 63. If the above ratio still holds true, then about six times as many people get married each year as get divorced 64. The divorce rate in the United States is much too high : Victims of radiation sickness (for example, after an atomic explosion) are likely to die of anemia because the blqodrbuilding properties of the bone marrow are dam-aged. In everyday medical practice, X-ray dosages have to be worked out with utmost care to keep the patient from falling prey to radiation sickness. Experi-menting on rabbits, Dr. Leon Jacobson found that when the spleen and appendix were protected with lead, the animals survived what would otherwise have been a fatal overdose of X rays. The undamaged spleen and ap-pendix make enough blood to. enable the damaged tissue to recover. 65. If from the blood-forming organs a substance could be isolated which would speed an individual's re-covery from radiation sickness, that substance prob-ably would also enable X-ray patients to take heavier doses ' 66. Dr. Jacobson's experiments on rabbits should be tried on a sufficiently large scale with people to see whether the same results would hold true ' Usually I fall asleep promptly, but about twice a month I drink coffee in the evening; and whenever I do, I He awake and toss for hours after I go to bed. 67. My problem is mostly mental; I am over-aware of the coffee when I drink it at night, anticipating that it will keep me awake, and therefore it does 68. I don't fall asleep promptly after drinking coffee at night because the caffeine in coffee stimulates my . nervous system for several hours after drinking it.. ; At the end of the semester the pupils in Mr. Black's class averaged 10 points higher than the pupils in Miss Walter's class on the same geometry test. Mr. Black and Miss Walter used a somewhat different method of teaching geometry. 69. Mr. Black probably is a better teacher than Miss Walter.. 70. The pupils in Mr. Black's class were brighter as a group than the pupils in Miss Walter's class, and therefore they learned more easily.. 71. The method used by Mr. Black in teaching geometry was superior to the method used by Miss Walter.. . When Great Britain began to offer free public medical service, the government was surprised because far more people than they had expected came for eyeglasses and dental work. 72. People who previously had neglected their eyes and teeth now chose to have such treatment 73. People who didn't really need-these services sought them because they were free.,, 74. People in Great Britain previously had been careless about the state of their eyes and teeth 75. The British public was pleased with the government health program. [ 6 ] Go on to the next page. W a t s o n - G l a s e r : A M TEST 4. Interpretation {Continued) The Los Angeles Times made a survey of the number of men and women drivers, involved in automobile acci-dents in the Los Angeles area during a given period of time. They found that men drivers were involved in 1210 accidents while women drivers were involved in only 920 accidents. 76., If the survey figures constitute a representative sam-ple, men drivers are involved in accidents more frequently than women drivers in the Los Angeles area. 77. More men than women drive cars in the Los Angeles area . 78. Women are safer drivers than men in the Los'Angeles area Intelligence tests show that Negro children in Northern cities surpass JSTegro children in Southern cities but do not score as high as white children in Northern cities. 79. White children as a group score higher because they are born with higher, native intelligence than Negro children : The Negro families who moved to the North are on the average more intelligent than those who re-mained in the South 80 81. Northern Negroes receive better schooling than Southern Negroes, which in turn influences per-, formance on the tests The history of the last two thousand years shows that wars have become steadily more frequent and more destructive, the • twentieth century being the bloodiest on record. 82. Mankind has not advanced as much in the art of keeping peace as it has in the science of waging war. 83. Wars are caused by basic traits of selfishness, greed, and pugnacity, which are rooted in human nature. . 84. Increased industrialization, competitiveness, and improved weapons bring on increasingly frequent wars. 85. There will be increasingly frequent future wars, and they will become steadily more destructive than past wars. Go on to the next test. T E S T 5. Evaluation of Arguments DI R E C T I O N S. In making decisions about important questions it is desirable to be able to distinguish between arguments that are strong and those which are weak in so far as the question at issue is concerned. Strong arguments must be both important and di-rectly related to the question. Weak arguments may not.be directly related to the question, even though they may .be of great general importance; or they may be of minor importance; or they may be related to trivial aspects of the question. Below is a series of questions. Each question is fol-lowed by three or four arguments. For the purpose of this test you are to regard each argument as true. The problem then is to decide whether it is a STRONG argument or a WEAK argument. You are to answer by making a heavy mark on the Answer Sheet under "STRONG" if you think the argu-ment is strong, or by' making a heavy mark under "WEAK" on the Answer Sheet if you think the argu-ment is weak. When evaluating an argument, judge it on its own merit; try not to let counter-arguments or your own attitude toward the question influence your judgment. Judge each argument separately. In some questions all the arguments may be STRONG, in others all may be WEAK. [ Here is an example. The block at the right shows how these arguments should be marked on the Answer Sheet. Study them carefully until you know just what is ex-pected of you. Note that the argument is evaluated as to how well it supports the side of the question indicated. E X A M P L E . Should all young men go to college? 1. Yes; college provides an opportunity for them to learn school songs and • cheers. (This would be a silly reason for spending years of one's life i i i college.) 2. No; most young men profit more from work experience than from college classes. (According to the directions, we must accept this argument as true; hence it is a strong and important one against all young men going to college.) . . . . . . . . . 3. No; excessive studying permanently warps an individual's personality. (This argument, although of great general im-portance when accepted as true, is not directly related to the question, because attendance at college does not neces-sarily require excessive studying.) TEST 5 A R G U M E N T S T R O N G W E A K 7.1. Go on to the next page. Watson-Glaser: AM Remember that for the purpose of this test each argument is to 'be regarded as true. Can rich and poor people who happen to oppose each other at law obtain approximately equal justice from the courts? 86. No; a rich person can hire better lawyers and technical experts, pay for the time of more witnesses, . and continue the fight in higher courts 87. No; rich people win the majority of their lawsuits against poor people. Should married women be eligible for employment as public school teachers if they are otherwise qualified? 88. No; there are more single women in our country than there are school-teaching jobs 89. Yes; women tend to become better teachers after marriage 90. No; a mother's first responsibility is to her own children ". Should infants be fed by regular schedule rather than whenever they seem to be hungry? 91. No; babies know best when they are hungry and ready to eat 92. Yes; children must sooner or later learn that they can't always have their own way 93. Yes; a regular schedule is easier for the parents.... Should the government take over all the main indus-tries in the country, employ all who want to work, and offer the products at cost prices? 94. No; so much concentration of economic and bureau-cratic power in government would undermine our . personal and political freedom. 95. No; elimination of competition and the profit motive would result in much less initiative for production of useful new goods and services 96. Yes; the government already operates post offices, highways, parks, military forces, public health services, and other public services Should groups in this country who are opposed to some of our government's policies be allowed unrestricted freedom of press and speech? 97. Yes; a democratic state thrives on free and unre-stricted discussion, including criticism 98. No; if given full freedom, opposition groups would disunite the American people, weaken our position, and ultimately lead to loss of our democracy 99. No; the countries opposed to our form of government do not permit the free expression of our point of view in their territory ; Go back and check your work. [8 I W A T S O N - G L A S E R C R I T I C A L T H I N K I N G A P P R A I S A L FormBu by G O O D W I N W A T S O N Professor of Education, Teachers College, Columbia University and E D W A R D M A Y N A R D G L A S E R Edward Glaser &* Associates, Consulting Psychologists, Pasadena D I R E C T I O N S : This booklet contains several different types of tests designed to find out how well you are able to reason analytically and logically. Do not turn this page until instructed to do so. Do not make any marks on this test booklet. All answers are to be marked on the separate Answer Sheet -provided. If you wish to change an answer, be sure to erase your old answer completely. Published by World Book Company, Yonkers-on-Hudson, New York, aad Chicago, Illinois. Copyright 1951-2 by World Book Company Copyright in Great Britain. All rights reserved. Printed in U.S.A. W G C f A : B M - 2 Jj Watson-Glaser: BM. T E S T l . Inference D I R E C T I O N S . An inference is a conclusion which a person draws from certain observed or supposed facts. Thus, from the electric light visible behind the window shades and from the sound of piano music in a house, a person might infer that someone is at home. But this inference may or may not be correct. Possibly the people in the house went out leaving the lights on, and the piano music could be coming from a radio or phonograph they left playing. In this test each exercise begins with a statement of facts which you are to regard as true. After each statement of facts you will find several possible inferences — that is, inferences which some persons might make from the stated facts. Examine each inference separately, and make a decision as to its degree of truth or falsity. On the Answer Sheet you will find for each inference spaces marked with the letters T , PT, ID, PF, and F. For each inference make a mark on the Answer Sheet under the appropriate letter as follows: if you think the inference is definitely true; that it properly follows from the statement of facts given. if, in the light of the facts given, you think the inference is probably true; that there is better than an even chance that it is true. PT ID PF - if you decide that there are insufficient data; that you cannot tell from the facts given whether the inference is likely to be true or false; if the facts provide no basis forjudging one way or the other. - if, in the light of the facts given, you think the inference is probably false; that there is better than an even chance that it is false. - if you think the inference is definitely false; that it is wrong, either because it misinter-prets the facts given, or because it con-tradicts the facts or necessary inferences from those facts. Sometimes, in deciding whether an inference is prob-ably true or probably false, you will have to use certain commonly accepted knowledge or. information which practically every person knows. This will be illustrated in the example which follows. Here is the example; the correct answers are indicated in the block at the right. E X A M P L E . A thousand eighth-grade students recently attended a voluntary week-end conference in a Midwestern city. At this conference questions of race rela-tions and means of achieving lasting world peace were chosen by the students for dis-cussion, since these were the problems the students felt to be most vital today. 1. As a group, the students who attended this conference had a keener interest in humanitarian or broad social prob-lems than most eighth-grade students have 2. The majority of these students were be-tween the ages of 17 and 18 3. The students came from all sections of the country 4. The students discussed only labor rela-tions problems 5. Some eighth-grade students felt that discussion of race relations and means of achieving world peace might be worth-while In the above example, inference 1 is probably true (PT) because (as is common knowledge) most eighth-grade students are not likely to evidence such serious concern with broad social problems. Inference 2 is probably false (PF) because (common knowledge) there are relatively few eighth-grade students in the United States between 17 and 18 years of age. There is no evidence for inference 3. Thus there are insufficient data (ID) for making a judgment in the matter. Inference 4 is definitely false (F) because it is given in the statement of facts that race relations and means for achieving world peace were the problems discussed. Inference 5 necessarily follows from the given facts; it therefore is true (T). In the exercises which follow, more than one of the in-ferences from a given statement of facts may be true (T), or false (F), or probably true (PT), or probably false (PF), or have insufficient data (ID) to warrant any conclusion. That is, you are to consider each inference by itself. Make a heavy black mark in the space under the letter that you think best describes each inference. If you change an answer, erase thoroughly. Make no extra marks on the answer sheet. ] Go on to the next page. W a t s o n - G l a s e r : B u A study in the Elmtown High School showed that the students from high-income homes received better grades on the average than did pupils from low-income homes. Differences in school grades given by teachers were con-siderably greater than differences on standard tests of intelligence and achievement. Students from high-in-come homes took part in many more of the extracur-ricular school activities which cost money than did the students from low-income homes. Student officers were usually chosen from the high-income group. 1. Elmtown parents of high income and low income sent their children to the same high school 2. Some students from low-income homes felt they couldn't afford to participate in extracurricular school activities which cost money 3. The students from low-income homes actually studied harder than did the students from wealthy homes 4. There were no differences between students from high-income homes and students from iow-income homes on standard tests of intelligence and achieve-ment 5. The majority of the students from low-income homes, recognizing the general superiority of the students from high-income homes, wanted them to lead the student groups The town of Westfield, beginning twenty years ago, has been buying up farms abandoned by owners who failed to pay taxes, and by this time has set out some 3600 acres of community forest. The oak trees have grown' rapidly. The town forests yielded $9000 net profit on lumber last year and $8500 the year before. Local authorities believe that the net profit on the lum-ber will eventually be $40,000 a year. 6. It costs the town more to cut and sell the lumber than it realizes from the sales 7. The operating expenses were less than $9000 last year 8. The owners who abandoned their farms and failed to pay their taxes were either incompetent farmers or lazy ones 9. The town of Westfield is continuing to buy up tax-delinquent farms to be set aside as community forests 10. The Westfield community forests will yield an annual net profit of $40,000 within two or three years When a Negro doctor bought a home in a suburban residential district where only whites of various nation-alities had lived before, a mob stoned the house and broke many windows. The mayor, at the request of his Committee on Race Relations, sent extra police to keep order in this district. 11. The immediate neighbors of the Negro doctor liked him and did not join the mob 12. The Negro doctor was a better citizen than the white people who lived around him 13. The mob was composed of citizens who upheld demo-cratic principles 14. The Negro family sold the house after a few months and moved elsewhere 15. The white families in the district all quickly sold their homes and moved away Mr. Brown, who lives near the town of Salem, was brought before the Salem municipal court for the fourth time in the past month on a charge of keeping his dance hall open after midnight. He again pleaded guilty and was fined the maximum, $100, as in each earlier instance. 16. Mr. Brown thought that it would pay him finan-cially to keep his place open after 12 o'clock, even though he had to risk paying frequent fines 17. Mr. Brown's dance hall was held to be within the legal jurisdiction of the town of Salem 18. The regular patrons of Mr. Brown's dance hall are habitual lawbreakers 19. The maximum fine of $100 was fully effective in keeping all dance halls in the vicinity of Salem closed after midnight 20. The midnight closing law was enacted because one of the patrons of the dance hall complained to the police about the noise Go on to the next page. [ 3 1 W a t s o n - G l a s e r : B i t T E S T 2. Recognition of Assumptions D I R E C T I O N S . An assumption is something supposed or taken for granted. When someone states, "I ' l l graduate in June," he takes for granted or assumes that he will be alive in June, that he will remain in school until that time, that he will pass his courses, and similar things. Below are a number of statements. Each statement is followed by several proposed assumptions. You are to decide for each assumption whether it necessarily is taken for granted in the statement. If you think the given assumption is taken for granted in the statement, make a heavy mark between the dotted S T A T E M E N T : "The coach isn't going to let Ed play in any more games this season." PR O P O S E D AS S U M P T I O N S : 21. The coach can prevent Ed from playing 22. Ed must have done something terribly wrong 23. The games for this season are not yet over 24. There will be a chance for Ed to play next season.. . . S T A T E M E N T : "The less government interferes with business, the better for everyone." PR O P O S E D AS S U M P T I O N S : 25. Government is inefficient 26. Most businessmen are superior in character to most government officials 27. Any good cause is injured if it gets mixed up in politics 28. If free from government controls, business would do what is good for us [ 4 lines under " A S S U M P T I O N M A D E " in the proper place on the Answer Sheet. If you think the assumption is not necessarily taken for granted in the statement, make a heavy line under " A S S U M P T I O N N O T M A D E " on the Answer Sheet. Below is an example: the block at the right shows how these items should be marked on the Answer Sheet. If you do not see why the answers marked are right, ask the examiner to explain. In some cases more than one of the given assumptions is necessarily made; in other cases none of the given assumptions is made. TEST 2 A S S U M P T I O N M A D E N O T M A D E N I 'I 3 H | S T A T E M E N T : "I want to be sure I don't get typhoid fever while I'm in South America, so I shall go to my physician and get typhoid injections before I sail." PR O P O S E D AS S U M P T I O N S : 29. If I don't take the injections, I shall become ill with the fever 30. Only a physician can give typhoid injections 31.1 am going to South America very soon S T A T E M E N T : "Only a fool would try to keep the pleas-ant taste of wine by having his mouth always full of it." PR O P O S E D AS S U M P T I O N S : 32. Some fools don't like wine 33. A wise man never has his mouth full of wine 34. Some fools get drunk on wine S T A T E M E N T : "If war is inevitable, we'd better launch a preventive war now while we have the advantage." PR O P O S E D AS S U M P T I O N S : 35. If we fight now, we are more likely to win than we would be if forced to fight later 36. War is inevitable Go on to the next page. ] E X A M P L E . STATEMENTS: "We need to save time in getting there, so we'd better go by plane." PROPOSED ASSUMPTIONS: 1. Going by plane will take less time than going by some other means of transportation. (It is assumed in the statement that greater speed of a plane over other means of transportation will enable the group to get to their destination in less time.) 2. It is possible to make plane connections to our destination. (This is necessarily assumed in the statement, since, in order to save time by plane, it must be possible to go by plane.).... 3. Travel by plane is more convenient than travel by train. (This assumption is not made in the statement — the statement has to do with saving time, and says nothing about convenience or about any other specific mode of travel.) W a t s o n - G l a s e r : B u T E S T 3. Deduction D I R E C T I O N S . Each exercise below consists of two state-ments (premises) followed by several proposed conclu-sions. For the purposes of this test, consider the two statements in each exercise as true without exception. Read the first conclusion beneath the statements, and if you think it necessarily follows from the statements given, answer by making a heavy black mark between the pair of dotted lines under " C O N C L U S I O N F O L L O W S " in the corresponding blank on the Answer Sheet. If you think it is not a necessary conclusion from the given statements, then put a heavy black mark under " C O N C L U S I O N DOES N O T F O L L O W , " even though you may believe it to be true from your general knowledge. Likewise read and judge each of the other conclusions. Try not to let your prejudices influence your judgment — just stick to the given statements and judge each con-clusion as to whether it necessarily follows from them. Mark all your answers on the Answer Sheet. Here is an example; the block at the right shows how your answers should be marked on the Answer Sheet. -TEST 3 C O N C L U S I O N F O L L O W S D O E S N O T F O L L O W n i I E X A M P L E . Some holidays are rainy. All rainy days are boring. Therefore — 1. No clear days are boring. (The conclusion does not follow, as you cannot tell from these statements whether or not clear days are boring and some may be.) 2. Some holidays are boring. (The conclusion necessarily follows from the statements, since, according to them, the rainy holidays must be boring.) 3. Some holidays are not boring. (The conclusion does not follow from the statements even though you may know that some holidays are very pleasant.) All good typists must be able to spell correctly. Anne can spell correctly. Therefore — 37. Anne has one of the qualifications of a good typist. 38. Anne's typing ability cannot be inferred from the information given 39. Anne is a good typist If Negroes are segregated, there is racial discrimina-tion. If democratic principles are not violated, Negroes are not segregated. Therefore — 40. Racial discrimination is limited to Negroes . . . 41. If there is racial discrimination, Negroes are segre-gated 42. If democratic principles are violated, there is racial discrimination All radicals are foreign-born. No patriotic citizen is a radical. Therefore — 43. No radical is either of native birth or a patriotic citizen. 44. No foreign-born person is a patriotic citizen 45. No patriotic citizen is foreign-born 46. Some foreign-born people are patriotic citizens Some Russians would like to control the world. All Russians seek a better life for themselves. Therefore — 47. Some people who would like to control the world seek a better life for themselves 48. All people who seek a better life for themselves would like to control the world 49. Many Russians find life under their dictatorship miserable, and therefore seek a change.. :  " . is All students hate to get up early in the morning. Some students keep late hours. Therefore — 50. All students who hate to get up early in the morning were up late the night before 51. No student who keeps late hours likes to get up early in the morning 52. Some students who hate to get up early in the morn-ing keep late hours 53. Keeping late hours causes students to hate to get up early in the morning Some young children take hikes. Some hikers sleep outdoors overnight. Therefore — 54. Some young children sleep outdoors overnight 55. Some people who sleep outdoors overnight are not young children 56. The hikers who sleep outdoors overnight are adults. No responsible leader can avoid making difficult decisions. Some responsible leaders dislike making difficult decisions. Therefore — 57. All difficult decisions are distasteful to some respon-sible leaders 58. Some responsible leaders must do things they dislike. If a person thinks straight, he will define the problem to be solved. Some people do not define the problem to be solved. Therefore — 59. If a person does not think straight, he will not define the problem to be solved. 60. If a person defines the problem to be solved, he thinks straight. 61. Some people do not know how to define the problem. 1 Go on to the next page. Watson-Glaser: Bu T E S T 4. Interpretation D I R E C T I O N S . Each exercise below consists of a short paragraph followed by several proposed conclusions. For the purpose of this test assume that everything in the short paragraph is true. The problem is to judge whether or not each of the proposed conclusions logi-cally follows beyond a reasonable doubt from the infor-mation given in the paragraph. If you think that the proposed conclusion follows beyond a reasonable doubt (even though it may not follow A salesman for Brown's Liniment claimed that his product would promptly soothe sore muscles in the body because it would penetrate very quickly to the affected parts. In order to demonstrate the penetrating quali-ties of Brown's Liniment, the salesman poured ten drops on a thick piece of sole leather, and the liniment quickly went through this substance. 62. The liniment which the salesman poured on the sole leather was effective in penetrating the kind of sole leather used in the demonstration 63. The salesman deliberately misrepresented his product. 64. The salesman's demonstration was good evidence for his claim that the liniment would promptly soothe sore muscles in the body 65. There is no relationship between the liniment's ability to penetrate this particular piece of sole leather and its ability to penetrate into the human body In a certain city where school attendance laws are rigidly enforced, it was found that only 15 per cent of the male school population had a perfect attendance record during any single school semester. Among those who sold newspapers, however, 25 per cent had a perfect attendance record during the same period. 66. If truants were given jobs selling newspapers, their school attendance would improve 67. Newsboys in another city would have a similarly superior attendance record 68. Those who carry partial responsibility for their own support tend to take their schooling more seriously.. absolutely and necessarily), then make a heavy black mark between the appropriate dotted lines under the " C O N C L U S I O N F O L L O W S " column on the Answer Sheet. If you think that the conclusion does not follow be-yond a reasonable doubt from the facts given, then make a mark under " C O N C L U S I O N DOES N O T F O L L O W . " In some cases more than one of the proposed conclu-sions may follow; in other cases none of the conclusions may follow. Among the people listed in Who's Who in America those with college degrees are about 15 times more numerous than those with only a grade-school education. 69. If the given figures hold constant, college graduates as a group have a 15 to 1 better chance of being listed in Who's W4io than have people with only a grade-school education 70. The editors of Who's Who give undue weight to the types of achievement made by college-trained people. 71. People listed in Who's Who tend to come from wealthy families who can afford to give their children many advantages, including a college education. . . . Jane's posture used to be poor; she dressed in bad taste, had very few friends, was ill at ease in company, and in general was quite unhappy and maladjusted. Then someone recommended that she visit Dr. Baldwin, a reputed expert on helping people to improve their personality. Jane took this recommendation, and after three months of treatment by Dr. Baldwin she carried herself well, dressed attractively, was more at ease and more popular, and in general felt much happier. 72. Jane's improvement may be only temporary 73. Jane's marked improvement must have been brought about by important factors other than Dr. Baldwin's treatment 74. Jane's improvement was caused solely by the treat-ment given her by Dr. Baldwin Several studies have shown that Southern Negroes make lower scores on intelligence tests than Northern Negroes, but that the average measured intelligence of Southern Negro children who move North at an early age increases' each year until their average measured in-telligence approaches that of the Northern Negroes. 75. The children of Southern Negroes who move North tend to equal the children of Northern Negroes in the kinds of ability measured by the intelligence tests used 76. The increase is due to the relative superiority of the schools Negroes attend in the North [ 6 ] Goon to the next page. W a t s o n - G l a s e r : B M TEST 4. Interpretation {Continued) A national weekly magazine published some articles criticizing the action of the Catholic Church in matters of health and censorship, and was promptly banned from the high school libraries by the school board of an Eastern city. 77. The majority of the people on that school board were afraid of the power of the Catholic Church.. . . 78. A majority of the people in that city must have been Catholics 79. The magazine should not have published those arti-cles Statistics for a certain city in the United States, which has a well-organized Boy Scout program, indicate that during the past ten years no Scouts have been convicted of juvenile delinquency. 80. The Scout program prevents delinquency 81. Scouting is a good way to meet the most important needs of boys today A sleeping wife was awakened by the sensation of a sharp blow across her mouth. Later that night her husband returned from a fishing trip, his front teeth knocked out by a sharp blow from the oar of his boat-Apparently the husband's accident and the wife's dream came at about the same time. , ,-\ 82. Under the circumstances described there was no way for any ordinary form of direct communication between the husband and wife at the time of the husband's accident 83. If the facts reported in this case are true, they can be accounted for only by the operation of mental telepathy 84. The dream was a chance coincidence which was not really influenced by the accident ' 85. There are many occurrences in life which we do not understand Go on to the next test. T E S T S . Evaluation of A rguments D I R E C T I O N S. In making decisions about important questions it is desirable to be able to distinguish between arguments that are strong and those which are weak in so far as the question at issue is concerned. Strong arguments must be both important and di-rectly related to the question. Weak arguments may not be directly related to the question, even though they may be of great general importance; or they may be. of minor importance; or they may be related to trivial aspects of the question. Below is a series of questions. Each question is fol-lowed by three or four arguments. For the purpose of this test you are to regard each argument as true. The problem then is to decide whether it is a STRONG argument or a WEAK argument. You are to answer by. making a heavy mark on the Answer Sheet under "STRONG" if you think the argu-ment is strong, or by making a heavy mark under "WEAK" on the Answer Sheet if you think the argu-ment is weak. When evaluating an argument, judge it on its own merit; try not to let counter-arguments or your own attitude toward the question influence your judgment. Judge each argument separately. In some questions all the arguments may be STRONG, in others all may be WEAK. Here is an example. The block at the right shows how these arguments should be marked on the Answer Sheet. Study them carefully until you know just what is ex-pected of you. Note that the argument is evaluated as to how well it.supports the side of the question indicated. E X A M P L E . Should all young men go to college? 1. Yes; college provides an opportunity for them to learn school songs and cheers. (This would be a silly reason for spending years of one's life in college.) 2. No; a large per cent of young men do not have enough ability or interest to derive any benefit from college training. (If this is true, as the directions require us to assume, it is a weighty argument against all young men going to college.) 3. No; excessive studying permanently warps an individual's personality. (This argument, although of great general im-portance when accepted as true, is not directly related to the question, because attendance at college does not neces-sarily require excessive studying.) TEST 5 A R G U M E N T S T R O N G W E A K [ 7 1 Go on to the next page* W a t s o n - G l a s e T : B M Remember that for the purpose of this test each argument is to be regarded as true.' Should the government provide "baby bonuses" to help support each dependent child in a family so that the family standard of living is not lowered by having children? 86. Yes; every family then could afford proper child care, which would greatly improve the general health of the nation . . . . 87. No; such bonuses would require much higher taxes, thus actually lowering the general standard of living.. . 88. No; people who do not wish to have children then would be taxed to help provide "baby bonuses" for other people Should the government continue to pay farmers the cost of soil-conservation practices on their own land? 89. Yes; food is a necessity to the entire nation, and farmers are much more likely to undertake the necessary practices which will assure abundant future crops if they get paid for the extra work in-volved 90. No; soil conservation is simply good farming prac-tice which will increase the owner's likelihood of making a good living from his land; there is no need to pay him for helping himself increase his personal profit Is it possible for man to develop a death ray that will kill all living beings on whom it is focused? 91. No; no one has ever seen such a death ray outside the comics , 92. Yes; powerful concentrations of X-rays and other i types of radiant energy do kill animals and human \ beings i 93. No; some very competent scientists doubt that such a death ray is possible 94. No; for if man ever does develop such a ray, he also will work on counter measures to offset it Would a labor party be a good thing for the people of the United States? 95. Yes; differences between Republicans and Demo-crats today are not so great as differences between liberals and conservatives within those parties 96. No; labor unions have sometimes called strikes which hurt the public at large 97. No; a labor party would make it unattractive for private investors to risk their capital in business ventures, and as a result jobs would be much scarcer, and millions of people would suffer Should pupils be excused from public schools to receive religious instruction during school hours in their own churches? 98. No; having public school children go off to their separate churches' during school hours would create greatly increased friction and feelings of hostility among different groups of children and their parents. 99. Yes; if children do not receive religious instruction during school hours, it may be difficult to get them to church at any other time Go back and check your work. I 8 ] 

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