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The relative role of positive and negative instances in concept formation Wood, John Edward 1943

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THE RELATIVE ROLE OF POSITIVE AND NEGATIVE INSTANCES IN CONCERT FORMATION by John Edward Wood A Thesis submitted i n P a r t i a l Fulfilment of The Requirements for the Degree of M A S T E R O F A E T S in the Department of / EDUCATION THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1943 ACKNOWLEDGMENT The writer wishes to express h i s thanks to Mr, Ho Straight for permission to conduct t h i s i n v e s t i -gation i n the Vancouver Schools, and to Mr, A, Rines, P r i n c i p a l of Lord Roberts School, Mr, L.H. Rohb, P r i n c i p a l of General Wolfe School, Mr. S.D. Meadows, P r i n c i p a l of Simon Iraser School, Mr, T.B, Spencer-Baynes, P r i n c i p a l of Charles Dickens School, Mr, W.R. Johnson, P r i n c i p a l of Livingstone School, Mr, C.R. Messenger, P r i n c i p a l of Dawson School, Mr, T, 'Woodcock, P r i n c i p a l of MacKenzie School, and to Mr, P.A. Armstrong P r i n c i p a l of McBride School, f o r t h e i r generous assistance i n the preliminary t e s t i n g , and to the Grade Six classroom teachers who co-operated so w i l l i n g l y throughout the experiment. TABLE 0S"; CONSENTS CHAPTER I . - THE EXPERIMENTAL 3ETBLS Off CONCEPT • •• - ; aORMATIOg 1 . The Value of Laboratory Studies 2 . The Importance of Concept Formation 5 . YJhat i s Concept Formation? 4 . C r i t e r i a of Concept Formation (a) Introspective (b) Abstraction'of a Part (c) C l a s s i f i c a t i o n . d) Induction of a Rule Ce) 1 9 S O and Since ... Review of Experimental F i e l d of Concept Formati on. (a) Introspective Studies (la) Studies Approaching O b c t i v i t y . . . (c) I 9 3 6 and Since .. 6 , The Present Experiment &) The Problem b) .-Definitions.»,..... ,Q) c r i t e r i a . » • 9 » CHAPTER I I . - SUBJECTS. APPARATUS AKD PROCEDURE »L Q OlX 0 Q uS ^  ^  « « • » « • »e**«»<»»«*<» • • o • • CHAPTER I H i - EXPBRIEEBTAL CRITERIA OF LEARHIBG 1 , Is Verbalisation a "Level" which Appears Later than Recognition?. *. (a) ' Are There Always as Many Recognitions Achieved as Verbalizations? (b) Are the Number of Correct Recognition S i g n i f i c a n t l y Greater than the Number of Acceptable Verbalizations? CHAPTER I I I (Oont»d) Page (c) Are the Cases of Verbalization Preceding Recognition R e l a t i v e l y Rare? „ 50 (d) Does Recognition on the Average Always Precede Verbalization? ...... >1 2 . Which C r i t e r i o n , Recognition or Verbalization, i s More Vulnerable to Reversals of Judgment?... 5 3 3 . l^hich C r i t e r i o n , Verbalization or Recognition, i s the More Subjective? „ 54 (a) The "Meaning"'of Verbalizations Given... 55 (b) P a r t i a l Verbalizations - Omissions "Understood" ............... 65 (e) Omissions Which May or May l o t be Expected to be "Understood" „. 65 (d) Verbalizations - Relatively Incorrect or Incoherent. .» 66 4 . Correct Verbalizations Hhose Significance i s not Under sto od 68 5 . S t a t i c Verbalizations 69 6. An Interesting Case.. 70 7. Summary and Oonclusi ons 71 CHAPTER IV.- SOME RESULTS AND CONCLUSIONS 1 . Ihieh Method, the P o s i t i v e or the P o s i t i v e -Negative, was Antecedent to the Greater Tendency Toward Description Rather than G e n e r a l i z a t i o n ? . . . . . . 7 3 2 . I s the Recognition of a Concept Gradual or Sudden?. 74 3 . Uhioh of the Two Experimental Types of Presen-tation Gave the Greater Impetus to Caution?..... 80 4 . Factors of D i f f i c u l t y i n Concepts 82 (a) "Mental i n e r t i a " or " R i g i d i t y " - and the Influence of Negative Instances. 82 CHAPTER IV (Gorxt'd) Page (b) The Acceptance by the Subject of Incomplete Hypotheses and the Influence of Negative Instances 85 (c) Complexity of Concept................... 86 (d) Abstractness of the Concept 87 (e) "Minimum Number of Words Required" 88 5 . Relationship of Presentation Method and Time... 89 6 . Summary and Conclusions. 90 CHAPTER V.~ THE RELATIVE ROLE OF POSITIVE AND NEGATIVE - / ^ ' " H i ^ ^ . — 1 . In the Present Experiment, Which Method of Presentation, the Positive or the P o s i t i v e -Negative , Produces the Greater Achievement?.... 92 (a) Comparison of the Two Methods as to the Achievement on Each Concept, and also on the Totals of a l l Eight Concepts 92 (b) Comparison of the Achievement of the Icicle Positive Group with the Achieve-ment of the Whole Positive-Negative Group 94 (c) Comparison of the Achievement of the Group having both the Highest 1.0,. l e v e l and the Positive Presentation, with the Achievement of the Group Having both the Lowest I.Q. Level and ";bhe P o s i t i v e -Negative Presentation 9p (d) Comparisons of the Amount of Advantage Received from the Introduction of Negative Instances by Pupils of Different I.Q. Levels 97 A. Yihich Groups, the D u l l or the Bright, Received the More Advantage from the Introduction of Negative Instances? And Shy? 98 B. Vilhich Method of Presentation, the Positive or the Positive-Negative i s Antecedent to the Mors Uniform Amount of Achievement? And Why? 101 CHAPTER 7 ( C on t * d ) Page 2. The Relative Roles of Positive and Negative Instances, 105 (a) Positive Instances . 103 (t>) Negative Instances. ... 106 (c) The Process of Concept formation. 109 3, Summary and Conelusions 110 CHAPTER 71.- SUMMARY AND CONCLUSIONS 1, The Present Experiment. 113 2. Re suit s and done l u s i ons....................... llj> 3* Educational Implications..... *................ 118 4 „ Sugge s t i ons for fur t h e r Re search.............. 122 (a) "With Memory" 123 'b; Sex Differences.......................... 123 (oj Readiness to Generalize.................. 125 (d) Incorrect Hypotheses and Achievement 124 (e) Order and Frequency of Positive and ' Negative Instances 124 (f) Maturity and Negative Instances 124 •IH2EX TO ILLUSTRATIONS Figure No. Page 1 . A Page from the Record Booklet Showing a Subject's Performance on Two Concepts 5j? 2 e Dax - 52 Instances (both Positive and Negative) 5j? 5. Mef - 32 Instances (both Positive and Negative )....... 36 4. Vec - 32 Instances (both P o s i t i v e and Negative) 56 ? a Mib - 52 Instances (both Positive and Negative )..... 37 6. Sum - 32 Instances (both Positive and Negative)...... 37 7 . Tov - 32 Instances (both Positive and Negative) 38 8. Pog - 52 Instances (both Positive and Negative)....... .... 38 9 . Ylez - 32 Instances (both Positive and Negative )..... 3? 1 0 . Z i f - 52 Instances (both Positive and Negative ) 39 11. Mef - Cumulative Achievement i s Plotted Against Number of Instances Shown 76 12„ Yee - Cumulative Achievement i s Plotted Against Number of Instances Shown 76 15. Mib - Cumulative Achievement i s Plotted Against Number of Instances Shown. 77 14. Sum ~ CJumulative Achievement i s Plotted Against Number of Instances. Shows, ,,, „ „ 77 1 5 . Tov - Cumulative Achievement i s Plotted Against Number of Instances Shown 78 1 6 . Pog - Cumulative Achievement i s Plotted Against -Number of Instances Shown 78 I M S TO IUiU'STBATIONS (Cont'd) Figure No. Page 1 7 , Wez - 'Cumulative Achievement i s Plotted Against Number of Instances Shown. 79 1 8 . Z i f - Cumulative Achievement i s Plotted Against Number of Instances Shown 79 IND3K HQ TABLES A l l Subjects: I.Q.'s Paired V e r t i c a l l y to Form Iwo Matched Experimental Groups Comparison of Two Matched Groups formed "by V e r t i c a l S p l i t t i n g of the Lowest 9 Pairs of I.Q.?s (I .Q. Range 95 plus and Comparison of the Two Matched Groups Formed "by V e r t i c a l S p l i t t i n g of the Middle 10 Pairs of I .Q..Ts (I.Q. Range 110 plus and minus 7 . 5 ) Comparison of the Two Matched Groups Formed by V e r t i c a l S p l i t t i n g of the Highest -6 Pairs of I .Q.' s (I.Q. Range 125 plus and minus 7 . 5 ) . . . . . . . . . The Comparison of the Number of Recog-n i t i o n s and Verbalizations Achieved Comparisons of the Mean. Number of Verbal-izat i o n s and Recognitions Achieved per Subject by Each Method of Presentation.,, The Order of Appearance of the -Criteria.. Comparison per Subject of the Mean Number of Times Each of tha Two C r i t e r i a Preceded Number of Reversals of judgment Verbalization. Meaning Disparate from Recognition Meaning. Order of D i f f i c u l t y of the Concepts Relation of Time Factor to Method of Pre sentati 011 C r i t i c a l Ratios Between the Two Methods for Eacn Concept. C r i t i c a l Ratios Beforeen the Mean Scores Achieved by Each Method Comparison of the Number of Concepts Learned by the Positive Highest 1.0 Group and the Positive-Negative Lowest I.Q. Group IKIMX TO TABLES (Cont'd) Table, Hb. Page XVI. Comparison of tlie I „Q. Groups Showing the Amount.of Advantage i n Each Given by the Introduction of Negative Instances.. <;..... 99 £711,, Comparison of the Achievement Made by the'Lowest with the Highest I .Q. Groups by each Type of Presentation.. 102 CHAPTER I , THE ESPERIMENTAL TiTELD OF CONCEPT FORMAT! CM 1. The Value of Laboratory Studies "No greater harm can be done to education than to believe that laboratory workers solve the problems of f i e l d workers". Continuing from these words, A.S. Barr (4) states that laboratory studies make important contributions toward the solution of these problems, but that the problems themselves must be solved through the concerted e f f o r t s of many persons including laboratory workers and f i e l d workers a l i k e . Barr finds that teachers and f i e l d workers i n education demand methods which w i l l a c t u a l l y produce r e s u l t s i n p r a c t i c a l situations; that the professor, on the other hand,.free as he i s from the pressure of having to produce immediate r e s u l t s , i s interested i n the search for truth f o r i t s own sake; e.g., i n problems which have persisted over long periods of time and over extensive areas. He finds also that the v a l i d i t y of the findings i n the controlled laboratory cannot be taken for granted i n the p r a c t i c a l s i t u a t i o n where there are many uncontrollable factors. F i e l d workers i n education are greater consumers than producers of research. The studies of a f i e l d worker, by the very nature of h i s p o s i t i o n , must be p r a c t i c a l though not necessarily s u p e r f i c i a l ( 4 ) . Research i n the f i e l d i s no primrose path. Lack of teachers trained for research, inadequate t o o l s , time f i l l e d with d a i l y duties, and the unwillingness.of parents to having t h e i r children '*experi-mented™ upon, a l l contribute to the d i f f i c u l t y of producing • research, Brownwell (9) points a searching finger at experi-mental studies i n teaching methods to expose several of their weaknesses. He says that pedagogical research i s fragmentary and sporadic; that learning studies have been confined too much to elementary l e v e l s ; that teaching rather than learning has been studied; that fear of being c a l l e d u n s c i e n t i f i c has paralysed the attack on many v i t a l problems; that there exists too bl i n d a f a i t h i n s t a t i s t i c s and other techniques; and that problems are seen too narrowly. Brownwell also shows, however, that pedagogy has benefited from experimental studies. He states that i n Reading, Arithmetic and Social Studies, techniques and • materials have been improved through experiments; that diagnostic techniques have pointed tife way to remedial pro^* cedures; that ways of measuring intangibles are being devised and that many new methods are available f o r studying the learning and teaching processes. Laboratories must assi s t i n the i n i t i a l stages of educational problems. The writings of such men as Freeman, Buswell, Judd and Thorndike show that the laboratory method provides one of the chief bases of theorizing. The fact that psychological laboratory studies have proved of value to classroom teaching i s j u s t i f i c a t i o n for the present i n v e s t i -gation. This study may suggest problems which can be attacked i n the classroom, or i t may resu l t i n generaliz-ations of dir e c t value to classroom procedure. I t c l a r i f i e s , to a certain extent, the importance of negative instances i n the formation of new concepts, and suggests certain d e f i n i t e l i m i t a t i o n s to verbalization as a means of communication. 2. The Importance of Concept Formation To observe and to reason about observation i s of major importance. Warren (73) argues that r a t i o n a l behaviour i s possible only after concepts have been formed. To Warren (75: 426) a concept i s "an experience b u i l t up i n the indi v i d u a l as the r e s u l t of many past experiences i n which the r e l a t i v e l y universal i n those experiences becomes emphasised and the p a r t i c u l a r eliminated" Warren ( 7 3 : 284 ,285) further states that "a concept i s a thought which includes only the characteristic elements of meaning or value'*; He defines a judgment as a thought which combines two concepts. The language equivalent of a concept he c a l l s a term, and of a judgment, a p r o p o s i t i o n Concepts and judgments are r a t i o n a l thought, and r a t i o n a l behaviour i s often called reason (73)» Reasoning i s a series of thought experiments. Few aspects of human behaviour are more important than the a b i l i t y to reason„ Thus, the factors influencing concept formation become of major interest to educators and psychologists a l i k e . The present study investigates certain aspects of the role played by p o s i t i v e and negative instances i n "concept formation* 3. What i s Concept Formation? '*We see our problems too narrowly", said Brownwell, i n c r i t i c i s i n g experimental education,, C r i t i c s of other experimenter's d e f i n i t i o n s of concept formation may well pause to consider Brownwell's words. "There are as many definitions of concept as there are schools of psychology", states Smoke (66) i n commenting on the great confusion i n the psychological l i t e r a t u r e regarding the meaning of the term "concept formation". Sinoe the term "concept formation" i s nothing more than an arbit r a r y verbal symbol, i t has a technical meaning as narrow or as varied as the situations to which i t i s applied by those philosophers and psychologists who are recognized as authorities i n thei r respective f i e l d s . Accordingly, a review of the use of the word "concept1* i s necessary i n order to c l a r i f y i t s meaning. "The process of concept formation may be treated from two points of view—the philosophical and the psycho-l o g i c a l " , says Pratt (57) i n h i s summary of the experimental work done between 1922 and 1926« Wolff (85) stated i n 1939 that much contemporary philosophy views the concept as a pointer directed toward objects which are sensational; that the concept i s said to be true i f i t leads to a percept; that a l l philosophies are based on indefinables; and that divergences are due to incongruity i n the sets of indefinables assumed i n the discourse and those recognized by the reader. Many are the philosophies on which the various schools of psychology are based. Accordingly, i n the case of the meaning of concept formation, i t i s not surprising to f i n d a host of interpretations entering through the numerous portals of indefinables. Added confusion i s to be expected concomitant with the selection of experimental c r i t e r i a by i n d i v i d u a l psychologists who c r y s t a l i z e their theories into the concrete form of psychological experiment,, The Oxford English Dictionary defines a concept as: (1) a thought--an idea; (2) the product of the f a c u l t y of conception, an idea of a class of objects, a general notion. For a psychologist, defining a concept as a thought makes the application of the word so broad that the term becomes nearly useless. I f a concept i s the "product of"the faculty of conception1* as stated above i n (2), then Yedenov, and Berkenblit, can be supported i n their view that concepts must be sensory. On the other hand, i f a concept i s "an idea of a class of objects", as i n (2) above, the opposing views of Welch and Long may be held. The further d e f i n i t i o n above, that a concept i s "a general notion", i s so broad 6 that i t becomes useless as a d e f i n i t i o n for a psychologist, Further evidence of overlapping of d e f i n i t i o n , and d e f i n i t i o n i n terms of i t s e l f , i s given i n the Oxford - Dictionary i n i t s meaning of "generalize"; v i z . , (1) to form into a general concept, to reduce to general laws; (2) to designate by a general name; (3) to i n f e r inductively from particu l a r s ; (4) to form general notions by abstraction from part i c u l a r instances. According to ( 1 ), concept formation becomes a process of generalizing. Smoke, Yerkes, H u l l , Kuo, Welch and Long either i m p l i c i t l y or e x p l i c i t l y accept this point of view. Defining generalizing as "to reduoe to general laws"' supports the thought that the induction of rules or p r i n c i p l e s i s generalization.. This l a t t e r statement i s rejected by Smoke i n these words: "Concepts are indispen-sable constituents of -rules, formulae, and p r i n c i p l e s , but there i s no j u s t i f i c a t i o n f o r i d e n t i f y i n g them". Definition (2) allows workers l i k e Welch ( 7 7 ) , Long (45), and Berger (6) to speak of generalizing i n terms of abstraction of "classes", "genus" and " h i e r a r c h i c a l develop-ment of concepts". D e f i n i t i o n ( 3 ) , which speaks .of general-ization as induction, i s i n harmony with both Thurstone's and Warren's usage. Definition (4) speaks of generalization i n terms of abstraction, and could be quoted to support Hull's and Kuo's c r i t e r i a , the abstraction of common elements. According to the Oxford Dictionary, therefore, induction, generalization, formulation of rules or p r i n c i p l e s , d i s c r i m i -nation between genus or classes, and abstraction are properly considered as aspects of concept formation Warren's Dictionary of Psychology gives the following d e f i n i t i o n for concept: "A mental state or process which - means or refers to more than one object or experience, or to one object i n r e l a t i o n to others. (When i t represents different individuals or items, i t i s called a class concept or general concept; when i t represents a common aspect or attribute of the class, i t i s an abstract idea). The formulation of a concept into words i s called a term. (Conception refers to the process, concept to the product)." Warren's Dictionary defines generalizing as follows: (1) (introspective)—The process of perceiving or conceiving a general cha r a c t e r i s t i c or fact or meaning i n single or i n complex situations or things; (2) ( b e h a v i o u r i s t i c ) — Responding to the common aspects (from any point of view) of the sp e c i f i c elements i n a complex s i t u a t i o n . Warren's Dictionary defines induction as follows: (1) ( l o g i c ) — T h e process of reasoning from the p a r t i c u l a r to the general; (2) The end r e s u l t of such reasoning. Reasoning i s explained as "The process of solving a problem by means of a concept or general p r i n c i p l e " . Tyler (71) states that "an induction may be defined as a generalization based upon observed f a c t s " (p. 1 ) . Tyler speaks of the " a b i l i t y of subjects to form a general-i z a t i o n from serially-presented different examples of a common rule'* as one example of r a t i o n a l learning (p. 3 ) . 8 He defined r a t i o n a l learning as "The a b i l i t y to make general-izations or to do inductive reasoning" (p. 4). He says that "Yerkes multiple-choice method can be used to investigate -generalizing a b i l i t y " . Thus Tyler points out the s i m i l a r i t y between induction, generalization, rational learning, and multiple-choice techniques. In 1 9 2 3 , Kuo pointed out the close relationship between hi s study of inductive inference, Hull's experiment on concept formation, and Hamilton's (1911) and Yerkes' (1921) studies using-multiple-choice techniques. Kuo classes the multiple-choice problems as inductive inference. In 1 9 3 2 , i n reporting t h e i r study, Ewert and Lambert considered concept formation and generalization to be synonymous terms. In 1 9 3 2 , Smoke also (67) i d e n t i f i e d concept formation with generalization,, "Inductive problems consist of specimens, and the result i s to obtain a d e f i n i t i o n , or at least a working knowledge of the 'class' represented .-by the given specimen", says Woodworth,(84:800). "In the laboratory a problem i n induction or concept formation c a l l s f o r the development of an effective response to a class of objects and a different response to objects not belonging to t h i s class". With these words Woodworth i d e n t i f i e s induction and concept formation. From the opinions quoted, i t would seem that a complete review of the studies i n concept formation would include a history of the experiments involving r a t i o n a l learning, inductive inference, generalizing abstractions, multiple-choice techniques, generalizing and concept "formation, 4, C r i t e r i a of Concept Formation (a) Introspective: In 1916 , Fisher (23) adopted as a c r i t e r i o n of concept formation the a b i l i t y to discover class character-i s t i c s from a series of ten drawings having certain common characteristics of shape, and to formulate a d e f i n i t i o n , (b) Abstraeti on of a Part: H u l l (40) i n 1 9 2 0 , and Kuo (44) i n 1 9 2 3 , considered that the a b i l i t y to abstract common elements (radicals i n Chinese characters) from .a complex pattern was a c r i t e r i o n of concept formation. In 1 9 3 4 , Drever (17) used the recog-n i t i o n of the presence of a right-angle i n certain polygons as his c r i t e r i o n of the presence of of concept. In 1932,Smoke (68) c r i t i c i s e d and avoided the use of common "elements" i n the sense of parts such as Chinese r a d i c a l s , and made the common characteristic consist i n r e l a t i o n between the parts. Since Smoke's work has a close relationship to the present study, Smoke's d e f i n i t i o n and c r i t e r i o n of a concept w i l l be considered at greater length l a t e r . (c) C l a s s i f i c a t i o n : Woodworth (p. 804) l i s t s c l a s s i f i c a t i o n problems 10 as studies i n concept formation. Ach (1) i n 1 9 2 1 , Huper (29) i n 1 9 2 8 , and Hanfmann and Kasanin (35) i n 1937 , considered a concept to have been formed when a subject was -able to discover the pr i n c i p l e s by which a c o l l e c t i o n of blocks could be sorted into four classes,, Woodworth (p. 806) c l a s s i f i e s the induction of a rule of action as an aspect of concept formation. In t h i s type of experiment the concept to be formed i s not of a class of objects, but the correct formula f o r meeting a class of sit u a t i o n s , -the experiment i s l i k e a game played between the experimenter and the subject, with subject's task to discover and to verbalize the rules of the game. This type of mental a c t i v i t y i s induction., (d) Induction of a Rules Thurstone (29) accepts that induction i s a type of generalization, for he speaks of inductive generalization* He speaks of the verbalization of some rule or p r i n c i p l e from a series of observations as being an induction. Peterson (55) i n 1920 used as his c r i t e r i o n of concept formation the induction of discernable arithmetical p r i n c i p l e i n his arithmetic game. In 19^A s Heidbreder's (39) subjects were asked to determine the rules of a game which she played with them. She considered the concept to be formed when the subjects had discovered the ru l e s . In 1 9 3 9 , Tyler used a complicated l i g h t i n g apparatus which rendered highly objective a sit u a t i o n requiring the subject to induce rules by which l i g h t s were to be controlled. Although several of these workers did not c a l l their experiments studies i n concept formation, they may be considered to be i n that " f i e l d , according to Woodworth's c l a s s i f i c a t i o n . (e) 1936 and Since: In spite of Smoke's protestations i n 1932 against the loose and i n d e f i n i t e usage of the term concept, and his discussion and d e f i n i t i o n of the term concept, l a t e r exper-imenters have continued to use the term broadly and to adopt many and varied c r i t e r i a of i t s presence. i n 1937 , Meyer and Piaget (29) studied "children's conceptions of speed and time". They accepted an "idea" (as did Oxford Dictionary) of speed and time as a "concept" and they adopted verbalized d e f i n i t i o n s (as did Gibson, Heidbreder, Smoke,-..'Welch and others) as their c r i t e r i o n * In 1937? Berger (p.) accepted "abstract ideas 1* as concepts and used as c r i t e r i a verbalizations i n terms of: (a) defin-i t i o n s of objects (Oxford's "general notion o f " ) ; (b) verbal* ized c l a s s i f i c a t i o n s such as genus (Oxford's idea of a class of objects); (c) verbalizations of p r i n c i p l e s such as cause (Oxford's d e f i n i t i o n of generalize, as "to reduce to general laws"); and (d) recognition of color ( l i k e both Berkenblit's and Yedenov's usage of concepts as sensory experience). In 1937» Hanfmann and Kasanin (35) assumed that a relationship between meaningless objects and meaningless words i s a concept, and accepted ver b a l i z a t i o n as a c r i t e r i o n of the 12 presence of "superordinate" concepts between unrelated words, Graham (29) speaks of concept formation as generalizing, and generalizing as a form of learning, Vedenov (72) speaks of Isolated concepts and general concepts. "Isolated concepts", he says, "are sensory, and i f they are excluded from the structure of perception, they beoome primary abstractions". Thus Vedenov used the term, abstraction, when many psychol-ogists l i k e Yerkes, Kuo, Smoke.and Tyler, and when, according to Wolff, many contemporary philosophers, would employ the terms concept or generalization. Nineteen thirty-nine added i t s tribute to the broad usage of the term concept. Berkenblit (7) speaks of the "single concept" i n the same type of situation where Mott (51) uses the words "abstract idea", and where the Oxford Dictionary defines generalization as a "general notion by abstraction from p a r t i c u l a r instances". In 1940, Welch (78) speaks of abstract thought and concepts i n the same breath. He also 'discusses "hierarchical development of concepts" as though c l a s s i f i c a t i o n generaliza-tions were concepts. Long and Welch (80) apply the term concept to both objects and classes. (f) Summary: . Thus i t i s seen that even yet, experimental psychol-ogists use the term concept i n a variety of ways. The c r i t e r i a used for the detection of concepts are numerous. Verbalization remains the usual c r i t e r i o n of concept formation. 13 As w i l l be shown l a t e r , the use of verbalization renders even an otherwise objective experiment highly subjective, 5 . RQ^ JQW of Studies of Concept Formation The following discussion i s divided into three arbitrary sections; namely, (a) Introspective; (b) Studies Approaching Objectivity, and (c) 1936 and Since, (a) Introspective Studies: Introspective techniques were applied i n the pioneer studies of concept formation. Early exploration of t h i s . type yielded comparatively barren r e s \ i l t s . Fisher (23) i n 1916 confronted her trained psychological observers with a series of 10 drawings belonging to a class c a l l e d , for example, " z a l o f S u b j e c t s were to discover the character-i s t i c s of this class and formulate a d e f i n i t i o n . F u l l i n t r o -spective reports were required. Fisher concluded that a concept i s a readiness to respond appropriately to any member of a class of objects; and that the response may be an overt movement or a verbal or v i s u a l image, so long as i t conforms to the essential c h a r a c t e r i s t i c s of the class. Other introspective studies by English ( 1 9 ) , Stevanovic (69) and Chant (12) were published i n 1 9 2 2 , 1 9 2 7 , and 1 9 3 3 , respectively. These studies agreed i n finding two main l i n e s of attack i n forming concepts of novel objects: (1) assimi-l a t i o n by the new object to some fa m i l i a r object, and (2) analysis of the new object into parts which are f a m i l i a r . 14 The f i r s t method may give quicker mastery of the single specimen, but since the e x t r i n s i c resemblance no longer holds good, i t i s l i k e l y to break down when the variations come into view. The a n a l y t i c a l process i s more dependable in reaching a new concept. (b) Studies Approaching Objectivity: Important objective studies of concept formation have been made by H u l l (41), Ach ( 1 ) , Kuo (44), Smoke (66768) and Drever ( 1 7 ) . In 1920, H u l l used a paired association technique i n which Chinese characters were paired with nonsense names. The subjects were required to abstract common radicals from the Chinese characters i n order to name them. This abstraction of common elements was called concept formation by H u l l . In his experiments on concept formation, Kuo adapted Hull's technique of testing f o r the i d e n t i f i c a t i o n of common elements. In 1932 and 1 9 3 3 , Smoke (66) published h i s studies of concept formation. These are of great importance to the present paper. Smoke c r i t i c i z e s previous objective experi-ments i n concept formation (such as those made by Kuo and H u l l ) , which define the concept i n terms of the common element to be found i n a series of geometrical figures, Chinese characters, and the l i k e , on the grounds that such studies deal with a purely a n a l y t i c a l process; and that they impose upon the subject the task of discovering some hidden or camouflaged element. Smoke's viewpoint i s that 15 »the sine qua non of concept formation i s a response to relationships common to two or more stimulus patterns 1 1'. Acting upon t h i s theory, he constructed a series of geomet-r i c a l designs which represented patterns rather than common elements, and used nonsense syllables to designate them. For example, a "Dax" was "a c i r c l e and two dots, one dot being outside the c i r c l e and the other being on the inside of i t " . This series, together with other series of designs, made up his exposure material, which was presented to the subjects by an e l e c t r i c a l l y driven exposure apparatus. Thus Smoke avoided common "elements'* i n the sense of parts such as Chinese r a d i c a l s , and made the common character-i s t i c consist i n certain rela t i o n s between the parts. When the subject, after examining a number of specimens, one at a time, believed himself able to define the class, he was asked for three things, namely: (1) to give his d e f i n i t i o n (Verbalization); (2) to distinguish i n a test series those figures which did and those which did not belong to the class (Recognition); (3) to draw some specimens (Reproduction), and in agreement with H u l l , Smoke found his subjects sometimes able to pass the other tests while s t i l l unable to give an adequate verbalization. The f a u l t y d e f i n i t i o n s were usually too i n c l u s i v e . In one form of the experiment Smoke i n t r o -duced "negative" instances. He concluded that the negative instances were: (1) of very l i t t l e assistance; (2) of use to some subjects; and (?) d i s t r a c t i n g to others. 16 A frequent process of reaching the concept involved the formulation, testing and rejection of hypotheses, t i l l one was found that stood up f o r a series of specimens. Definite r e c a l l of previous members of the series played a part, as was shown by the "thinking out loud" required i n this experiment. By a i d of'memory, similar specimens were grouped as a step toward d e f i n i t i o n of the whole class. Smoke gives a technical meaning to the term "elements" and "relationship". He c r i t i c i z e s the use of the term "common elements" i n the studies of concept formation because, following Hull and Kuo, the experimental l i t e r a t u r e has used "common elements" to refer not to a condition but to a section of a pattern; e.g., Kuo's ra d i c a l s . Accordingly, Smoke i n s i s t s that the term "common elements" be used technically' to designate only some section of a pattern. In studies of concept formation, Smoke uses the term " r e l a t i o n -ship" only i n a technical sense, ignoring the "elements" which are required i n order'that there be a relationship. Tyler (71) i n c l a r i f y i n g Smoke's terminology points out that a relationship without elements to be related would be impossible. Tyler states that "generalization or concept formation involves both elements and relations between these elements". Although on one hand Tyler speaks of concept formation as involving both elements and relationships, and on the other hand, Smoke defines concept formation as involving only r e l a t i o n s , both Tyler and Smoke are actually i n agreement i n t h e i r i m p l i c i t d e f i n i t i o n of concept formation. Smoke's 17 technical use of the term " r e l a t i o n " includes but i s less clear than Tyler's two terms "re l a t i o n s " and "elements". "By 'concept formation', 'generalization' and 'concept learning''' ,says Smoke ( 6 7 ) , "we refer to the process whereby an organism develops a symbolic response . (usually but not necessarily l i n g u i s t i c ) which i s made to the members of a class of stimuli patterns but not to other s t i m u l i . " The present study considers Smoke's de f i n i t i o n as an adequate and a f r u i t f u l vehicle for an experimental approach to an investigation of concept forma-t i o n * In common with Smoke's work, the present study defines t r i a n g l e s , rectangles, c i r c l e s , l i n e s and dots as elements, while abstract ideas, such as i n s i d e , outside, i n a direct line, with, touching and' near are defined as rel a t i o n s . Guesses as to what the concept i s , i n a given learning s i t u a t i o n , are defined as hypotheses. In the c l a s s i f i c a t i o n problem introduced by Ach (1) i n 1921 and used by several experimenters including Huper (29) i n 1 9 2 8 , and Hanfmann and Kasinin i n 1937> 'a c o l l e c t i o n of blocks i s to be sorted into 4 classes. The basis of c l a s s i f i c a t i o n must be discovered by the subject* In one form the blocks are 5 different colors and of 6 different shapes, color and shape being i r r e l e v a n t . They are t a l l or short, large or small, and by c r o s s - c l a s s i f i c a t i o n , f a l l into 4 classes. Grouping or "convergence" appears to be an important part of the process of reaching the concepts. In another type of experiment, the concept to be formed i s not that of a class of objects, but that of the correct formula for meeting a class of situations. The experiment has somewhat the form of a game played between the experimenter and the subject. The task of the l a t t e r i s to discover the rules of the game. He discovers them by playing and meeting with success or f a i l u r e . The rules may be e n t i r e l y arbitrary as i n YerkesV "multiple-choice' 6 problems The rules may depend'upon some discernible p r i n c i p l e , as i n the Peterson's arithmetical game. Tyler ( 7 1 , p. 9) states " that Kinnamon (43) i n 1 9 0 2 , and Hamilton (32) i n 1 9 1 1 , were among the f i r s t to report studies employing the multiple-choice technique. (p. 9 ) . In 1 9 2 3 , Brown and w h i t t e l l (8) used a multiple-choice technique with adults. In 1 9 3 2 , Roberts modified the technique to investigate the a b i l i t y of pre-school children to see and apply a p r i n c i p l e of r e l a t i o n -ship. In 1 9 3 3 , Arons (3) studied the "generalizing abstrac-t i o n " a b i l i t y of under-graduates, using the multiple-choice technique. Extensive experiments performed by Heidbreder i n 1924 required the subject to discover the rules of a game played between the subject and the experimenter. The materials consisted of geometrioal figures and check marks. The subject endeavored to discover the rules by which composite geometri-cal figures were to be marked. After making a t r i a l by marking the figure i n the way that he thought i t might be correct to mark i t , the subject was informed that he was '•Right'* or "Wrong1*. At the end of each t r i a l and before being informed of i t s Tightness or wrongness, the subject reported "everything that went on i n his mind" during the t r i a l . Other double figures of t h i s class are treated s i m i l a r l y , t i l l the subject discovered the rule as proved by correct statement ("Verbalization) , and response (marking the fig u r e s ) . When the f i r s t game was mastered, the second game followed,, Heidbreder's outstanding result was the demonstration of "spectator" behaviour. The more usual "participant" behaviour consists i n trying out hypotheses. In "spectator" behaviour, the subject has no hypothesis; a l l his guesses have been proven erroneous and he can only make some random response and remain on the watch for some new hypothesis to emerge. Says Woodworth (p. 8 0 7 ), "Spectator behaviour affords a clue toward answering the question of how hypotheses ari s e . The receptive attitude may at times be just what i s necessary to get us out of a rut and allow some hitherto neglected aspect of the situation a chance to exert i t s eff e c t . The receptive phase of the inductive process i s less observable, either objectively or i n t r o -spectively, than the more active phase of trying out the hypothesis, but i t may be no less essential". Peterson, i n 1 ? 2 0 , defined r a t i o n a l learning as purposive thinking i n which ideas were used i n the effective solution of problems and devised a letter-number memory-reasoning t e s t , which made a pioneer contribution to studies of generalization, but which was not en t i r e l y satisfactory due to the p o s s i b i l i t y of problem solutions by other than ra t i o n a l behaviour. Haught (36) subjected Peterson's findings and other related data to s t a t i s t i c a l analysis. Whereas i n certain tests modified from Peterson's problems the best measures of learning were time and uncl a s s i f i e d errors, i n Peterson's tests themselves, perseverative errors constituted the sign i f i c a n t measures. In his discussion Haught pointed out that i n studies where the experimenter determines to some extent the rate at which the subject works, time as a c r i t e r i o n becomes of l i t t l e value. This conclusion has a bearing on the present study. (c) 1936 and Since: Soslow (62) i n 1936 reported a study requiring subjects to induce a p r i n c i p l e , but Tyler (71) suggests several ways i n which h i s s t a t i s t i c a l analysis could have been improved. The use of Tyler's methods would have produced s t a t i s t i c a l results of greater inclusiveness and conclusiveness than those employed by Roslow 0 Tyler (71) i n 1 9 3 9 , investigated the a b i l i t y of junior high school pupils to solve r a t i o n a l learning problems of the type requiring the subject to generalize or to formulate a rule from a succession of problems involving a common 21 principle . The apparatus used- to study rule induction consisted e s s e n t i a l l y of a panel of switches for the subject to manipulate and a group pattern of l i g h t bulbs for him to -observe. A pattern of l i g h t i n g was set up by the experimenter and from these the. subject was to formulate the rule'Which, would indicate how the key which turns out a l l the l i g h t s : could be selected without error. Tyler found: ( 1 ) that the majority of cases were not consistent i n using exclusively either an exploratory or am analytic approach to the problems but that most cases employed both methods; (2) that many-sub jects appear to wait to v e r i f y a tentative i m p l i c i t hypothesis before verbalizing i t ; (3) that many subjects gave evidence of a b i l i t y to select the proper key but were unable to give, the, corresponding verbalization; and (4) that v e r i -f i c a t i o n may be done by using either positive or negative instances. In I 9 3 6 Heidbre&er ( 5 8 ) conducted a series of experi-ments related to t h i s 'study. In these, she gave evidence of the role of language i n the acquisition and use of concepts. The procedure was a modification of that used by ...Hull i n what was apparently a memory experiment. Each subject learned to associate given nonsense syllables with given-situations under conditions which permitted him to discover that the many different situations to which a given s y l l a b l e was applied possessed a common cha r a c t e r i s t i c . The subjects, 220 college students^ were studied i n d i v i d u a l l y , but were c l a s s i f i e d into groups on the basis of variations i n the experimental procedure and the materials presented. The process of concept formation was measured i n terms of repetitions, prompts, and opportunities to apply the concept to new situations. At the close of the experiment each subject was required to write d e f i n i t i o n s (Verbalizations) or descriptions of the concepts he had formed, and also to take an objective examination of the single choice type. In view of the findings of the present study, the conclusions of Heidbreder are of interest . She suggests that there are several different ways i n which language i s used as a to o l during concept formation and that these methods vary with the sit u a t i o n ; that a concept may be used with consistent correctness even though the subject cannot formulate (verbalize) i t ; that the a b i l i t y to formulate (verbalize) a concept i s more closely related to the nature of the referent than to the readiness with which i t i s acquired or to the accuracy with which i t i s applied; that the readiness with which a concept i s formed i s determined not by the ease or d i f f i c u l t y with which i t s name (nonsense syllable) can be memorized but by-the r e l a t i o n between i t s referent and the perceptual situation i n which i t i s presented. In 1937 Hanfmann and Kasanin (35) published a paper describing a test of concept formation adapted from Sakharov and Vigotsky who employed i t for the study of conceptual thinking i n psychotic patients. The test had i t s o r i g i n i n a method employed by Ach for studying the development of concepts. I t consisted i n general in confronting the subject with a number of meaningless objects and a number of meaning-- less words between which the subject i s made to discover relationships through prolonged manipulations and demonstra-tions. The study i s of interest to t h i s paper c h i e f l y as an example of one of the many techniques employed to study concept formation. In 1937 , Berger (6) examined the role of age, sex and environmental differences i n the a b i l i t y of school children to form abstract judgments. Children were asked to state i n writing the difference between f i f t e e n pairs of objects or ideas, such as milk and water, a mistake and a l i e . Berger found that older children, more often than younger ones, di f f e r e n t i a t e i n terms of genus, cause, and generalized ideas, while younger ones refer to external features such as colour and form, and that c i t y children more often make their d i s t i n c t i o n s i n terms of values and consequences, while r u r a l children more often resort to examples and description. This study contributes to the present paper not only some conclusions about concept formation, but also an example of the prevalent practice of using the subject's verbalizations as an experimental c r i t e r i o n . A l a t e r chapter indicates the high subjectivity inherent i n t h i s procedure* Sibano's experiment (64) i n 1938 was an introspective investigation of concept formation as productive thinking. 24 Two stimulus words were given from which the subjects made "superordinate™ concepts common to these two words. Subjects were asked for introspective reports of their experiences - during the process of concept formation. Results seem to be of l i t t l e value as they depend upon the experimenter's selection and interpretation, Sibano concluded that the inevitable factors i n concept formation are adequacy of stimulus words, ground and figure of thinking, images of things and words, emotion and w i l l * (Whatever these things mean!). This review was included to show that introspective techniques have been used even l a t e l y , and to contrast the type of conclusion given i n introspective studies with those of objective ones, Vedenov's (72) experimental investigation of the structure of concepts takes the opposite view, concluding (1) that i s o l a t e d concepts must be sensory, but that when excluded from the structure of perception they go over into a primary abstraction; and (2) that the structure of general concepts and the process of their evolution i s determined by the object, so that a l l thought has i t s basis i n 'sensation, "The problem of evolution from sensory to abstract i s one of the main problems i n psychology", says Yedenov, Graham's study ( 2 9 ) , i n 1 9 3 8 , considered generalizing to be a form of learning and examines some special conditions imposed by certain types of learning. He developed a general pattern f o r the construction of exercises i n developing s k i l l s 25 i n generalizing, and i l l u s t r a t e s t h i s pattern with detailed examples and references to other tasks employed. In support of the observations, inferences, and conclusions given, the experimental evidence i s u t i l i z e d largely i n an i l l u s t r a t i v e manner. In his study of generalizing, Graham points out the lack of a b i l i t y to obtain part scores for analysing the s k i l l components. His subjects reported d i f f i c u l t y i n reporting the i r p lanful manipulations, sets, techniques or processes for the illuminating of their a c t i v i t i e s . Graham suggests that the c r u c i a l aspects of learning are esse n t i a l l y subjec-tive mental discriminations and i n his treatment of data he points out t h e i r lack of o b j e c t i v i t y . In 1938 Crudden (15) investigated form abstraction by children. In his experiment the material was the counterpart of the negative instance i n the present investigation. Crudden used simple learned geometrical figures which were imbedded i n r e l a t i v e l y unknown geometrical-figures of varying degrees of complexity. He used 65 children from 65 to 78 months old. He found that the degree of d i f f i c u l t y i n abstracting the known material increases roughly-in proportion to the degree i n which i t i s imbedded i n a more complex figure; that "that-whioh-is-to-be-avoided" i n abstraction has almost as much influence i n successful abstraction as "that-which-is-to-be-ohosen"; and that knowledge of the "figure-to-be-abstracted" frequently results i n successful response where previously no abstraction could be made. 26 In 1939 Berkenblit (7) reported on a study of the genesis of concepts. He investigated the formation of single as well as general concepts i n children from 16 to 28 months old, Berkenblit concluded that single concepts connected with a certain object depend upon the child's sensory experience with, as well as on his emotional attitude toward, the object while playing with i t . By generalizing single concepts of the acting object general concepts about action were formed. Sensory perception, and the child's motor manipulations with the object,says Berkenblit, play a decisive part in the formation of general concepts. During the years 1938 to 194-0, i n c l u s i v e , Welch has published a greater number of studies on concept formation than any other experimenter. For one a r t i c l e during 1936 he collaborated with Davies; i n 1940,jointly with Long, he published two experiments; and during the years 1938 to 1940 he published s i x a r t i c l e s of h i s owns Welch's subjects have been young children, p r a c t i c a l l y a l l of them less than 7 years 6 months of age. Two of Welch's conclusions are related to this investigation, Welch found that the associa-tio n a l or memory development necessary for the f i r s t mani-festation of genus-species phenomena at the l i n g u i s t i c l e v e l comes l a t e r than the requisite development as discrimination and generalization from the same behaviour; and that the genetic development of the structure of abstract thought may be described as passing through rather d e f i n i t e stages^ Except for these conclusions, his studies and findings have l i t t l e e x p l i c i t connection with the present experiment. I t "i s advisable, however, that any worker i n the f i e l d of concept formation be fa m i l i a r with Welch's contributions, 6. The Present Experiment (a) The Problem; > The present study i s designed to investigate the part played by both p o s i t i v e and negative instances i n the generalizing process whereby twelve-year-old boys form concepts. (b) Definitions: For purposes of t h i s experiment, Smoke's d e f i n i t i o n i s accepted. He said, ltBy concept formation, generalization, and concept learning, we refer to the process whereby an organism develops a symbolic response (usually, but not necessarily l i n g u i s t i c ) which i s made"" to the members of a class of stimuli pattern but not to other s t i m u l i " . More s p e c i f i c a l l y , concept formation i s the abstraction of the highest common factor found i n a series of examples of the concept. This highest common factor i s composed of both relations and the elements required for those re l a t i o n s . Guesses as to what the concept i s are defined as; hypotheses. Formulation of hypotheses similar to those which the experi-menter had i n mind when he constructed' the instances i s ca l l e d generalization and concept formation. Geometrical figures i n which the relationship and the necessary and s u f f i c i e n t common elements are found, are defined as positive instances. Figures exhibiting any - deficiency i n the relationship or i n the elements necessary and s u f f i c i e n t thereto are called negative instances 0 Triangles, rectangles, c i r e l e s , l i n e s , and dots are defined as elements^ while abstract ideas, such as ins i d e , outside, i n a"direct l i n e with, touching, and near are referred to as rela t i o n s . (c) C r i t e r i a : In t h i s experiment, the three c r i t e r i a employed to determine the nature of the subject's hypotheses are called Verbalization, Recognition, and Reproduction. Verbal definitions of the concept are called Verbalizations, Performance on a test i n which the subject indicates the figures he considers to be, and those not to be, the concept i s termed Recognition, Examples drawn by the subject of his idea of the concept are defined as Reproductions. Recognition i s the non-verbalized symbolic response accepted as a c r i t e r i o n of achievement toward concept formu-l a t i o n . Recognition i s accepted as a more objective experi-mental c r i t e r i o n than Verbalization. In u t i l i z i n g Recog-n i t i o n rather than Verbalization as the c r i t e r i o n to deter-mine when a given amount of concept formulation had occurred, t h i s study d i f f e r s from many of the experiments i n the same f i e l d . The j u s t i f i c a t i o n for t h i s selection of c r i t e r i a i s given i n Chapter I I I . 30 CHAPTER I I . SUBJECTS, APPARATUS AND PROCEDURE 1 . Subjects S i x t y - f i v e twelve-year-old Grade YI boys from the Vancouver school system were divided into 3 groups: 15 boys for pretesting and standardizing the experimental situation; arid 50 boys divided into two comparable experimental groups--one receiving the positive presentation and the other the positive-negative presentation of material. Individual testing was employed throughout. Comparable experimental groups were selected by matching boys f o r chronological age, i n t e l l i g e n c e quotient, school grade, sex, native tongue and socio-economic status. Subjects were chosen so that four groups of paired I.Q,.' s could be made. F i r s t , the whole group was s p l i t into two matched sets of I.Q,.' s. The twenty-five p a i r s of I.G> Ts were arranged i n descending magnitude. Then the p a i r s were s p l i t v e r t i c a l l y producing two comparable I.Q,. groups, each ranging from I.Q. «s of 88 to 1 3 3 . Second, the subjects were segregated horizontally into three paired groups, the d u l l normals with I.Q.'s of 95 plus and minus 7 * 5 , the brighter normals with I.Q.'s of 110 plus and minus 7 . 5 , and the superiors with I.Q.1s of 125 plus and minus 7»5« The number of subjects i n each group was chosen to conform roughly to the normal d i s t r i b u t i o n having A.M. equal to 1 0 0 , and S.D. equal to 1 6 . The I.Q,. comparability of these groups i s shown below: TABLE I , - ALL SUBJECTS: I.Q,.1 s PAIRED VERTICALLY TO - v , . FORM TWO MATCHED, EXPERIMENTAL' GROUPS. Po s i t i v e Positive-negative Presentation Presentation No. of cases 25 •-. : : 2 5 - •' A r i t h . Mean (A.M.) 1 0 8 . 3 1 0 8 . 6 Standard Dev. (S.D. 1 0 . 7 1 0 . 6 TABLE II.-COMPARISON OF THE TWO MATCHED GROUPS FORMED BY VERTICAL SPLITTING OF THE LOWEST 9 PAIRS OF I.Q.'s (I . Q.. 'RANGE 95 PLUS AND MINUS 7 .5) No. of cases A r i t h . Mean (A.M.) Standard Dev. (S.D.) P o s i t i v e Presentation Positive-negative Presentation 9 -9 6 . 8 3 . 9 9 91.2 3 . 9 TABLE I I I . - COMPARISON OF THE TWO MATCHED GROUPS FORMED BY VERTICAL SPLITTING OF THE MIDDLE 10 PAIRS OF I.Q. « S. P o s i t i v e Presentation Positive-negative Presentation No. of cases 10 10 A r i t h . Mean (A.M.) 1 0 9 . 9 1-10.7 Standard Dev. (S.D.) 4 .3 3.0 TABLE IV.- COMPARISON OF THE TWO MATCHED GROUPS FORMED BY VERTICAL SPLITTING OF THE HIGHEST 6 PAIRS OF I.Q.' S. ' P o s i t i v e Positive-negative Presentation Presentation No, of cases 6 6 A r i t h , Mean (A.M.) 1 2 3 . 0 1 2 3 . 0 Standard Dev. (S.D,) 2 , 8 4 .6 On March 31, 1941, a l l subjects f e l l within the chronological age range of 12 years plus- and minus 6 months. A l l subjects spoke English as t h e i r mother tongue. Socio-economic status was roughly controlled by matching pupils from the same schools Experimental testing was carried out between May 27 and June 2 9 , 1941, 2 . Apparatus The apparatus consisted of individual record booklets and 9 sets of concept cards, each set composed of 8 positive instances, 4 negative instances, and 16 test instances. Two hundred eighty-eight white cards 3™ x 5" shown i n Figures 2 to 10 were employed. On each card an instance (either p o s i t i v e or negative) of one of the nine experimental concepts was drawn i n India ink. The 32 cards for eaoh . concept were divided into 3 packs, two teaching packs of 8 cards each and one testing pack of 16 instances. A l l cards were numbered s e r i a l l y on the back; the teaching sets from 1 to 8 , and the testing pack from 1 to 16. The teaching pack of 8 p o s i t i v e instances was used with one experimental group, hereafter called the positive group. The other pack,consisting of 8 instances alternately positive and negative, was employed with the other experi-mental group, hereafter known as the positive-negative group. The same test pack composed of twelve negative instances and 4 p o s i t i v e instances,arranged o r i g i n a l l y i n chance order, was used for both groups. In the two teaching packs of each concept, the odd-numbered cards (positive instances) were i d e n t i c a l . The - even-numbered cards i n the pos i t i v e teaching set were posit i v e instances, while the even-numbered cards i n the positive-negative teaching pack were negative instances. The negative examples (even numbered) i n the p o s i t i v e -negative teaching series were designed to d i f f e r from the correspondingly numbered cards i n the p o s i t i v e series only s u f f i c i e n t to allow them to become negative instances and to contribute c l a r i f y i n g c h a r a c t e r i s t i c s . These negative cards were intended to eliminate the acceptance of a concept composed of common elements or relationships l e s s than the concept (the highest common factor found i n the positive instances)« ; -In the test series, the 12 negative instances were designed to be diagnostic, so that i f the subject f a i l e d to learn the concept, a glance- at h i s response revealed whether i t was elements, relations,or both, that he had not recognized,. The instances were composed and selected with the following p r i n c i p l e s of construction i n mind. Integrated patterns i n which the relationships between the elements gave a sense of unity to the whole pattern were desired, and the more interesting the design, the better. Simple figures with a minimum of elements and rel a t i o n s were employed with a view to diagnosis through systematic v a r i a t i o n i n both the 34 teaching and the testing packs. Each card made a unique contribution of at least one c l a r i f y i n g aspect. The concepts were named after the nine nonsense syllables having the least associative value. This technique was borrowed d i r e c t l y from Smoke's experiments. The concepts used i n t h i s study were as follows:-"Dax"'- triangle with dot inside; (see F i g . 2) "Mef" - a c i r c l e h a l f black and half white; (see F i g , J>) "Vec" - a l i n e with a dot at one end and i n direct l i n e with the l i n e ; (see Fig. 4) "Mib" - a c i r c l e touching a square; (see Fig . 5) "Zum" - a c i r c l e and 2 dots, the one dot being inside the c i r c l e , and the other outside; (see Fig, 6) "Tov" - a square having one cross near each of the four sides; (see Fig. 7) "Pog" - two l i n e s unequal i n length; (see "Fig, 8) "Wez" - a c i r c l e and a tr i a n g l e with the c i r c l e touching the t r i a n g l e on i t s shortest side; (see Fig. 9) " Z i f " - a rectangle and a c i r c l e with the c i r c l e inside the rectangle and touching i t s two longest sides, but not touching either end. (see Fig. 10) In the six-page record booklet, space was provided for the subject's name, age, birthday, grade, I.Q., school, and parents' n a t i o n a l i t y . Frames i n the booklet were provided for the subject's responses on the three l e v e l s — V e r b a l i z a t i o n , Recognition, and Reproduction. A t y p i c a l page i s shown i n Figure 1, In the Verbalization section, under "Attempt Number", was recorded the s e r i a l number of the subject's attempt to V A' V 7^ 1 V A V M o ra-ft • CO w © •H •H 44 o — o ij P o) m o to ftPM P4 P 1 I «8 • CM m o §3 H£ S H O O I [J in 4 i 4 rt JUS — •j> \ X \ s 111 if •1 o : k \ X > -d O O FH o © © ft H © *--P o © in 2 -P <i-l © ft © © © o w a ©wo ft fl o g o £ fl o 1: I © o o a o © 36 1 1 4 o o O 9 "o 3 ,d -p • o — {> •H ro -p © cd 0 «) d <J> cd Pi P ro d a •H cd CM © K\ *> •H 1 -P •H o ro M o t> ft PS •d o — ,0 CD — t> ro +3 © cd o bD a © cd d p> ro -cj d d •H CO o cd ft W) cd o © cd ro © •H © ro +3 ro © ft +3 © !> •H »H P ,d cd o 60 cd © © d -P i © > »H -P •H ro d o •H +3 •H d o o © © •H -p i *ro O 0 o A< P4 d 1 i cd pes H O (J ® o 9 » e 0 O • CM © •H i P fc, ro N o S ft i • « B Is 37 f o o o o o o o o o o O o o •o o I o •o « o 43 -P p o 1—1 o • o o 3 • • o o «; m o 8 © 3 Q o o 8 • O © • (") o o Lf\[ El 38 • n. 0 •• • LJ a o 0 o • • • Q xi -p • o —-> •H ro +3 © cd o tsD d © cd a -P ro fd d d •H cd • CM © M K\ •H ac• 1 P ft ro •H ft © c5 ro w •H o o d (M ft •H © (M ft 43 • ro 1 o M • cd O P oo © cd ro H 43 p • o <-» x> © — !> •H CD +3 © cd o W cd d p ro d d •H 3 CM © K\ $> •H ! P T4 t> ra o o E-* ft I B » © p © p cd W) cd o> © d P I © i> p •H ro o I I © !> •H P •H ra o d « o o © « I •d H O o 39 j 1 -q g o I 1 1 [g n o 1—1 53 1 en a ! «5> CD o[ o 4 4 O 43 43 O — X CD — |> «H CO +3 CD cd 0 bO S3 CD cd ?3 ro <tJ S3 S3 •H cd 00 CD K\ f> •H 1 P „ >H CQ H O !SJ p) O H « D H 43 -p • O 43 © «—• J" -H ra P © cd o S3 © 3 S3 -p 0} rp S3 S3 •H cd CM © •H 1 P N »rH ra o Pt ON H o cd 04 ro © S3 © •H ra 43 • 0 M -P cd o ra © cd © P ft-P © to S3 !> S3 O •H »r4 -H P 43 P cd O -H W cd S3 © © w Pi -P O 1 o © © © > t> « •H >H P P I •H -H ra ro P 0 o PH P4 *cf S3 1 I cd <1 pq o s e o o verbalize the concept. In the eolumn,headed "Card Number'*, was recorded the number of the l a s t card shown before that attempt. Under "Verbalization", the pupil's word-for-word d e f i n i t i o n of the concept was recorded. Verbalization was scored as successful only when a subject made a generaliza-tion c l e a r l y applicable to the conoept. Recognition was recorded i n the following manner: the s e r i a l numbers of the test cards i n which only some of the necessary elements appeared are given i n Column 1. S i m i l a r l y , the s e r i a l numbers of the test cards which lacked some of the necessary relations but which included a l l the elements, are found i n Column 2. In other words, the numbers shown i n the f i r s t two columns are the s e r i a l numbers of cards which did NOT represent the concept. The t h i r d column contains the numbers of the cards representing the positive instances i n the test pack. Under "Number Wrong" was recorded the number of errors made by the subject i n the 16 t r i a l s . Recognition was scored as successful only when the recognition test cards had been i d e n t i f i e d with 100 per cent accuracy. To test Reproduction, two sets of 5 squares were provided i n which, for each Reproduction attempt, the subject drew f i v e freehand pictures of his idea of the concept. In some cases the examiner found i t necessary to provide for further attempts to reproduce the concept. Reproduction was marked as successful only when a l l f i v e drawings s a t i s f i e d the conditions necessary for the concept. g e Procedure, Each subject underwent one experimental period only. After rapport was established,, and the subject was seated to the l e f t of the experimenter at a table, a preliminary concept, "Dax,s, was employed to introduce and explain experimental procedure,, - The preliminary teaching pack was placed face downward and i n order from numbers 1 to 8, with 1 on top within the subject's reach. He was instructed to turn the cards over one at a time and place them face upward on the table where they remained i n sight through-out both the learning and testing period for that concept. He was told that the puzzle was to figure out"what a Dax" was, and that the fewer cards he had to turn over to discover i t the better his score would be, Following the exposure of any card and as soon as he thought that he might know what the concept was, a subject was allowed to t r y the tes t s . On exposure of card numbers 4 and 8, regardless of previous test perfor-42 mances, successful or otherwise, samples^ of the developing^ concept were taken by means of a l l three c r i t e r i a — Verbalization, Recognition, Reproduction. Procedure for presenting the instances was i d e n t i c a l for both pos i t i v e and positive-negative groups, except that the subjects were given to understand i n the one case that a l l cards represented the concept and i n the other that alternately the cards were and were not examples of i t . In sampling the concepts, three c r i t e r i a representing the subject's ideas were recorded; i . e . , Verbalization, Recognition and Reproduction. In the spaces provided In the booklet, word-for-word statements (Verbalizations), and responses of "Dax" or "not Dax" to the test cards (Recog-nition) were noted, and then the subject drew f i v e examples of his idea of the concept. He was encouraged to draw examples of his own rather than to copy any positive cards i n front of him. No rule that he must, not copy was made. Such an instru c t i o n would raise the philosophical d i f f i c u l t y of defining "copy" - i t being impossible for him to reproduce an i d e n t i c a l r e p l i c a , anyhow, no matter how hard he t r i e d . 0he word "sample'" i s used to mean evidence' available to the experimenter revealing the nature of the subject's concept. Since there may be other aspects of the concept not revealed by our testing s i t u a t i o n , our c r i t e r i a give a "sample" which may be p a r t i a l . I f through Verbalization, Recognition and Repro-duction a complete picture of the subject's concept has been revealed to the experimenter, then the "sampling" was complete. ##The word "developing" i s used to indicate the p o s s i b i l i t y of progressive growth of the concept from incomplete stages to more complete. At times the complete concept i s formed very quickly, but at other times incomplete concepts are formed which are progressively altered to accommodate them to addi-tio n a l instances seen. 43 Smoke made an experimental error i n hi s study with negative instances, and as a result did not f i n d the chief contribution made by negative examples. In his instructions to subjeots receiving the allegedly positive presentation, Smoke used the words, "That i s part of the concept, but not a l l of i t " . 1 In saying "but not a l l of i t " , Smoke i n t r o -duced a factor which invalidated those resul t s which pertain to the effect of introducing negative instances. This statement w i l l be substantiated i n a l a t e r chapter. At present i t ' i s s u f f i c i e n t to say that procedure must be car e f u l l y controlled to the end that "NO GLUE EXTERNAL TO THE TEACHING- PACK MUST BE ALLOWED TO GIVE EVIDENCE TO THE SUBJECT AS TO THE ACCEPTABILITY (COMPLETE OR INCOMPLETE, CORRECT OR INCORRECT) OF HIS TEST RESPONSES. In other words, neither verbally nor by any change in pro-cedure must the experimenter allow the subject to know whether his response to the test situation was successful or otherwise. ' Once t h i s point had been recognized i t was easy to ref r a i n from giving the subject a verbal clue. To r e f r a i n from giving t h i s information to the subject by an insidious change of procedure following correct responses, however, requires constant v i g i l a n c e . Following a test s i t u a t i o n , s t r i c t adherence to i d e n t i c a l procedure must be the r u l e , whether the response be successful or unsuccessful and whether the presentation be p o s i t i v e or positive-negative, lUnderlining not i n the o r i g i n a l . The individual record booklet remained i n the hands of the experimenter except while i t was given to the subject for the purpose of recording his Reproduction responses. Since the subject could know what the experimenter had written i n the record booklet, Verbalization and Reproduction had to remain unevaluated, u n t i l after the experimental period was over and the subject had l e f t the room. The c i r c l e s placed around the numbers i n the Recognition frames were explained as being notes the experimenter wanted to make, but which notes had nothing to do with the subjects' responses. During the pos i t i v e presentation, i n the oases where subjects made errors, f a i l u r e to observe these rules would have suggested to some subjects that the response was not correct. In t h i s way, the "Not-a-Dax" idea would have been introduced into a situation which was supposed to be purely p o s i t i v e . In other words, to neglect to observe t h i s precaution Is to commit through the scoring method the same experimental error that Smoke committed verbally i n his instruction already noted. To allow re p e t i t i o n of the experiment and-minute inspection of the present procedure, a word-for-word detailed account of the procedure has been included i n the appendix. 45 CHAPTER I I I . EXPERIMENTAL CRITERIA Off LEARNING In experimental work on concept formation, i t has been commonly, assumed, that the a b i l i t y to formulate a concept into words comes la t e r than the a b i l i t y to recognize the presence of that concept i n an observed example. Among many experimenters who have found that subjects could pass recognition tests when they could not verbalize correctly are Berkenblit ( 7 ) , Long (45) and Smoke ( 6 7 ) . The acceptance of the idea that Recognition precedes Verbalization has been a contributing factor to the use of Verbalization rather than Recognition as an experimental c r i t e r i o n of concept formation. The present study u t i l i z e s recognition tests rather than verbal responses as the more useful experimental c r i t e r i o n . The chief arguments submitted i n support of th i s action' are presented under the following headings:-(1) Is Verbalization a " l e v e l " which appears l a t e r than Recognition? ........ <r (2) "Which c r i t e r i o n . Recognition or Verbalization, i s more vulnerable to reversals of judgment? (5) Which c r i t e r i o n , Verbalization or Recognition, i s the more subjective? 1. Is Verbalization a "Level" which Appears Later than Recognition? Assuming that the a b i l i t y to formulate concepts into words comes l a t e r than the a b i l i t y to recognize the presence of that concept i n an observed example, and assuming further that the c r i t e r i a , Verbalization and Recognition, as employed i n the present study, indicate the presence of . those two a b i l i t i e s respectively; therefore -(a) there must always be on the average at least as many Recognitions achieved as Verbalizations; (b) the number of correct Recognitions should be s i g n i f i c a n t l y greater than the number of acceptable Verbalizations; (c) cases of Verbalization preceding Recognition w i l l be r e l a t i v e l y rare; (d) Recognition w i l l on the average always precede Verbalization. Should any or a l l of these four conclusions f a i l to be found i n the res u l t s of the present experiment, i t i s questionable whether the assumptions are sound. The l a s t two assumptions are strongly supported by d e f i n i t i o n . The weaker assumption i s that. Verbalization i s a " l e v e l " which appears l a t e r than Recognition, Accordingly, should the conclusions be unsubstantiated i n this experiment, doubt would be cast on t h i s l a t t e r assumption. (a) Are there always as many Recognitions achieved as Verbalizations? Table V shows the s t a t i s t i c s of the present study pertinent to t h i s question. 47 TABLE V.- THE COMPARISON OF THE NUMBER OF RECOGNITIONS AND "VERBALIZATIONS ACHIEVED Positix re Presentation (25 subjects, 8 concepts each) Positive-Negative Presentation (25 subjects, 8 concepts each) Verbaliz-ations Achieved Recog-nit i o n s ." Achieved Verbaliz-ations Achi eved Recognitions Achieved Total Aohieved 8 5 78 143 158 . Table V shows that by the positive-negative present-ation, 158 Recognitions and 143 Verbalizations were achieved. This group, therefore, had successful performances i n 15 more Recognitions than Verbalizations. By the p o s i t i v e presentation, 78 Recognitions and 85 Verbalizations were successful. In t h i s group, therefore, there were seven less Recognitions than Verbalizations. The re s u l t s of the positive-negative group add supporting evidence to conclusion (a); i . e . , that perhaps there must always be on the average at least as many Recog-nitions achieved as Verbalizations. However, i n the positive presentation, more Verbalizations than Recognitions were successful. This suggests that i t i s not necessary that there always be on the average as many Recognitions achieved as Verbalizations. Perhaps the explanation for t h i s seeming contraduction i s that sometimes one " l e v e l " appears f i r s t and sometimes the 48 other. Perhaps the order of the appearance of Verbalization and Recognition i s traceable not to r e l a t i v e i n t r i n s i c d i f f i c u l t i e s i n the c r i t e r i a themselves so much as to the method by which the concept i s presented, the nature of the concept i t s e l f , or the f a c i l i t y with which subjects can employ the c r i t e r i a themselves. Perhaps one type of c r i t e r i o n lends i t s e l f more re a d i l y as a vehicle of expression i n one type of conceptual s i t u a t i o n , while the other may be the more appropriate i n another. That subjects' can Recognize when they cannot Verbalize has been corroborated by several experimenters. The resul t s of the positive-negative group of the present experiment (Table V) agree with t h i s finding. Where then i s the weakness i n the conclusion that Verbalization i s a higher " l e v e l " ; i . e . , a more d i f f i c u l t achievement? An answer might be that while i t i s true that Recognition does at times appear when Verbalization cannot be successfully accomplished, experimenters,in formulating t h i s conclusion, have f a i l e d to take into account the number of cases where Verbalization can be achieved but Recognition cannot. (b) Are the number of correct Recognitions s i g n i f i -cantly greater than the number of acceptable Verbalizations? Table VI exhibits resul t s dealing with t h i s question. 49 TABLE VI;- COMPARISONS OF THE MEAN NUMBER OF VERBALIZATIONS AND RECOGNITIONS •., • ACHIEVED PER SUBJECT, BY EACH METHOD . OF PRESENTATION" Positive Presentation (25 subjects-, 8 concepts each) Positive-Negative Presentation (25 subjects, 8 concepts each) Verbal-iza t i o n s achieved Recog« hit!ons achieved Verbal-i z a t i o n s achieved Recog-nitions achieved A.M. per Subject 3.40 3.12 = 5o72 6.52 .94 1.31 .1.15' 1.09 — .28 •4 1.61 1.58 D - - .17 (57 chances) (in 100 ) .25 (60 chances) (in 100 ) Table VI indicates that there i s not a significant difference between the number of Recognitions achieved and the number of Verbalization successes. In the positive-negative presentation, the c r i t i c a l r a t i o i s .25 ; i . e . , there are only 60 chances out of 100 that on the average there w i l l always be more Recognitions than Verbalizations correct. The c r i t i c a l r atio of the pos i t i v e presentation i s .17, showing no s i g n i f i -cant d i f f e r e n c e — i n f a c t , showing that there are 57 chances i n 100 that Verbalization w i l l precede Recognition. These results 50 deny conclusion (t>); i . e . , that the number of correct Recognitions should be s i g n i f i c a n t l y greater than the number of acceptable Verbalizations. (c) Are cases of Verbalization preceding Recognition r e l a t i v e l y rare? Table VII shows the number of times i n t h i s experiment that the two c r i t e r i a preceded one another. TABLE VTi:. THE ORDER OF APPEARANCE OF THE CRITERIA Po s i t i v e Presentation Positive-negative (25 subjects Presentation 8 concepts each) (25 subjects 8 concepts each) Verbal-i z a t i o n preceded Recognition Recog-n i t i o n preceded Verbalization Verbal-iz a t i o n preceded Recognition Recog-n i t i o n preceded Verbalization Total \ 24 26 26 I f conclusion (c) were to be v a l i d , there would be a r e l a t i v e l y greater number of Recognition preceding Verbal-ization than vice versa. Table VII indicates that by the positive-negative method just as many Verbalizations preceded Recognitions (26) as vice versa. Furthermore, i n the positive s i t u a t i o n , the two c r i t e r i a appeared with Verbaliz-ation preceding Recognition three times as often as i n the opposite order. Clearly, therefore, the resul t s of t h i s experiment do not support the conclusion that Verbalization 51 rarely precedes Recognition. Furthermore, these results are i n direct contradiction to the o r i g i n a l assumption that Verbalization and Recognition are "levels'* i n the sense that one always precedes the other i n their order of appearance and d i f f i c u l t y , and that Recognition i s the lower " l e v e l " . (d) Does Recognition on the average always precede Verbalization? Table VIII shows the r e s u l t s of the present study computed on a per subject basis. TABLE V I I I . - COMPARISON PER SUBJECT OF THE MEAN NUMBER OF TIMES EACH OS* THE TWO CRITERIA PRECEDED THE OTHER. Posi t i v e Presentation • • • • ' (25 subjects, 8 concepts each) Positive-negative Presentation (25 subjects, 8 concepts each) Verbal-izat i o n s preceded Recognition Recog-n i t i o n preceded Verbalization Verbal-izations preceded Recognition Recog-nitions preceded Verbaliz-ation ' A.M. per subject >96(Mi) 9?2(M 2) ' 1 B04(M 1) lo04(M 2) 1.00 .545 % 1-M 2 .64 0 1.14 D <TD .56 (71 chances) (in 100 ) 0 Since i n the positive-negative sit u a t i o n both A.M.'s are 1,04, the conclusion to be drawn i s that under the present experimental conditions, Verbalization and Recognition w i l l , on the average, precede one another an equal number of times. Neither one seems to appear on the average more than the other. By the positive presentation the D of ,56 *fD indicates that i n 71 cases out of 100, Verbalization w i l l on the average always appear before Recognition, These r e s u l t s , therefore, contradict conclusion (d) and indicate that there i s NOT a si g n i f i c a n t difference between the order of appear-ance of Verbalization and Recognition, The evidence from t h i s experiment bearing on the question of "levels'* has been presented. I t has been shown that i f Verbalization i s a"higher l e v e l " than Recognition, then four conclusions would follow. I t has been indicated that the resul t s of t h i s study supported none of those four conclusions. In neither the p o s i t i v e nor the p o s i t i v e -negative sit u a t i o n can either Verbalization or Recognition be depended upon to precede the other. The order of t h e i r appearance, therefore, allows either c r i t e r i o n to-be used equally advisedly. I t may be concluded, therefore, that for this study i t would be unwise to assume that the a b i l i t y to verbalize a concept indicated a "higher l e v e l " of under-standing of the concept, than did the a b i l i t y to recognize i t s presence i n an observed example. There are several decided objections to Verbaliz-53 ation as an experimental c r i t e r i o n . These disadvantages are not inherent i n Recognition as a c r i t e r i o n of learning. Further discussion of the r e l a t i v e merits of, and objections to, the two c r i t e r i a follow i n the next section of t h i s chapter. 2. Whioh C r i t e r i o n , Recognition or Verbalization, i s More Vulnerable to Reversals of Judgment? " Reversal of judgment for a given c r i t e r i o n (Verbalization, Recognition, Reproduction), i s defined as retrogression to an incorrect response for a given concept after a correct response has been given. A l l other factors being equal, the fewer the reversals of judgment to which a c r i t e r i o n i s subject, the better. Table IX shows the number of times i n which reversal of judgment occurred. TABLE IX.- NUMBER OF REVERSALS OF JUDGMENT. Ooncept Verbalization Recognition !Reproduction Po s i t i v e Pos.-Neg. P o s i t i v e Pos. -Neg. Positive Pos. -Neg Mef 2 1 tat 1 2 -Vec . Si* •• • ' .Mr* - -Mib - - - 2 2 Zum - 1 M l Tov - 1 - 1 -Pog 1 - - 4 4 Wez - fax 3 -Zif - - - - 1 -Total: 2 2 1 2 • 13 6 54 Reversal of judgment i n Verbalization was present twice i n the p o s i t i v e and twice i n the positive-negative situation. In Recognition, 2 positive-negative and 1 positive reversal of judgment occurred. In Reproduction, 13 positive and 6 positive-negative reversals took place. The v u l n e r a b i l i t y to reversals of judgment i n Reproduction and Verbalization i s small, while that of Recognition i s comparatively great. With respect to reversals of judgment, therefore, either c r i t e r i o n , Recognition or Verbalization, serve equally w e l l . * 3. Which C r i t e r i o n , Verbalization or Recognition, i s the more Subjective? Language In experimental work on generalization, Verbalization has been used frequently as the chief c r i t e r i o n . The question arises, which of Verbalization or Recognition, as defined i n the present experiment, i s the better c r i t e r i o n to use i n this study. «-? The author encountered considerable d i f f i c u l t y in marking, right or wrong, many of the Verbalizations given by the subjects. I t i s hard to know what a subject "means" by what he says. The experimenter evaluated the subject's responses found i n the Record Book on two occasions; the f i r s t time was within a few days of giving the test,while the second time was about two months l a t e r . The experimenter's second evaluation of the Verbalizations did not always agree 55 with his f i r s t one. The d i f f i c u l t y was that the experimenter did not interpret the Verbalizations i n the same way both times. I f i t was d i f f i c u l t for one experimenter to give consistent interpretations, how much greater would be the d i f f i c u l t y for different persons to agree on the interpre-tation of a given set of verbalizations! The greater the amount of subjective interpretation required, the more objectionable i s Verbalization as an experimental c r i t e r i o n . The present study y i e l d s evidence of at least four aspects of Verbalization which render i t highly subjective. These four l i n e s of evidence are submitted below. (a) The "Meaning" of Verbalizations Given In the following discussion, the "meaning" of the Verbalization was determined by the experimenter i n terms of the Recognition cards which the subject chose as conforming to h is idea of the concept. A consideration of the subject's selection of the Recognition cards and Reproduction responses i s the only experimental j u s t i f i c a t i o n of such a statement as, "the subject said 'round' when he meant 'oval'". Table X shows the different ways i n which the subjects attempted to verbalize the same thought. The column headed "Meaning" shows the thought that the subject's selection of the Recognition cards would lead the experimenter to conclude the subject was thinking. The words "positive" and 56 "positive-negative 1* indicate the type of learning situation which produced the Verbalizations shown i n the table. The figure i n the column headed "Frequency1* shows the number of times a given Verbalization was used to express the thought indicated i n the "Meaning'* column. 57 TABLE X.- VERBALIZATION MEANING- DISPARATE FROM RECOGNITION MEANING "Meaning" Frequency Concept Verbalization "In direct line'* P o s i t i v e 7 Vec "after". 17 n "at end" 2 »» "and" 1 t» "under" 1 » " i n front of" 1 n "beside" 1 tt "over the top" Total: 30 Pos,-Neg. 1 rt "above i t ' * 15 • ti "at one end" ' > 1 tl " l i k e an exclamation mark" 1 It "beside" 1 tt "behind or i n front of" 7 tt "behind" and "after" 1 ft "and'* Total: 27 "Oblong" P o s i t i v e 7 ; Z i f "square" 1 "long square" 1 " "long shaped box" Total: 9 Pos«-Neg„ 1 "long square" 1 tt " t r i a n g l e " 1 !» "box" 2 tt "square" 1 11 "oblong square" 1 "Wez "a long s t i c k l i k e a Total: 7 square wi.th short ends'! " C i r c l e " Positive 5 Mib "oval" 12 n "round c i r c l e " 5 »t "ball™ 1 it "globe" Total: 23 Pos. -Neg. 1 u "round c i r c l e " 3 rt "oval" Total: 4 58 TABLE X (Cont'd). -VERBALIZATION MEANING- DISPARATE •••••..•/• - EROM RECOGNITION MEANING. "Meaning" Frequency Cone ept Verbalization "Touching" Positive 2 Mib Wez "joined together" 1 Wez "beside" 1 *Wez "put together i n any fashion. 1 Mib. "connected" 1 n "hitched on to" 1 n "together" ' I - * - * : t» "fixed on the side" Total: 8 Pos.-Neg, 1 Wez , Doesn't say "touch-V ing" but Rec. and Ref. show this . meaning. 1 Z i f Doesn't say "not touching end" but both Rec. and Re£. showed th i s idea. 1 Mib "stuck together" 2 Mib "joined" 1. Wez "on" Total;: • 6 . "Shortest end" Posit i v e 1 Wez "blunt end" Total: 1 Pos.-Neg0 1 Wez t " t h i s end here", pointing. 5 t» "the end part of the triangle". 1 tt "the f l a t end of the triangle". ' 1 • tt "the top of the Total: a triangle". "Square" Positive i Mib "box" i « "block" Total: 2 "Straight l i n e " Positive A great many " l i n e " ;• Pos.-Neg. A great many " l i n e " £>hort sides of Oblone" ( l v i ns hnvi ™tall-y on i t s long sides) -. Pos.-Neg. Z i f "bottom and top" Table X t aaci the further evidence furnished below, suggest that no experimenter can know from the subject's words what thought the c h i l d has i n mind. In other words, i t i s impossible to t e l l from the words a c h i l d uses, what he actually "means". The following examples support this conclusion. "Tec" i s defined as "a dot i n a direct l i n e with a straight l i n e " . At times when the Recognition performance indicated the existence of the idea " i n a direct l i n e " , subjects verbalised as follows; "above i t " , "under", " l i k e an exclcanation mark" , "beside" , " i n front of" , " a f t e r " , "and", "under51, "over the top". Some subjects verbalized a "Yec" as "a straight l i n e and a dot" and then properly i d e n t i f i e d . a l l of the Recognition cards and produced drawings, a l l of which were "Yec". !Ehese subjects verbalised that "Yec" was "a l i n e and a dot" , but i n the Recognition did not accept those cards on which a l i n e and a dot appeared, i f the dot was not i n a direct l i n e with the l i n e . At another time, although a subject verbalized that a "Yec" was "a riot under a l i n e " , he i d e n t i f i e d as a "Yec" cards showing the dot h o r i -zontally to the l e f t of a horizontal l i n e , diagonally to the right and above a diagonal l i n e , and v e r t i c a l l y above a v e r t i c a l l i n e . She subject who verbalized a "Yec" as "a l i n e with a dot over the top", i d e n t i f i e d as "Yec" those cards show-ing the dot d i r e c t l y under the v e r t i c a l l i n e . In the face of this 60 evidence the experimenter has reached the conclusion that i t i s very d i f f i c u l t to interpret what a subject may "mean" . by a Verbalization. The evidence shown i l l u s t r a t e s that Verbalization requires a great deal of subjective i n t e r -pretation by the experimenter when i t i s used as a c r i t e r i o n . Subjects expressed their idea of the "shortest side" of a triangle i n a number of interesting ways. One subject attempted his Verbalization of "Wez" (a c i r c l e touching the shortest side of a triangle) with the statement, "A c i r c l e touching a triangle on t h i s end here", pointing to the short side of: several triangles which were i n sight. Another subject expressed the idea of "shortest end" by saying, "the f l a t end of a t r i a n g l e " . Actually, i t could be argued that both of the. longer sides of a triangle are " f l a t t e r ends" of the triangle than i s the short side. Another subject expressed the idea of the shortest end by the words "the top of the t r i a n g l e " , regardless of whether the triangle was lying on i t s side or standing on the'* so-called "top of the tr i a n g l e " . Another subject expressed the same idea with the words "blunt end". These methods of expressing the idea of "shortest end" are i n t e l l i g i b l e i n the presence of other clues to t h e i r meaning i n addition to Verbalization. Taken alone, without other clues, these Verbalizations would convey l i t t l e d efinite meaning to an auditor. The experimenter was interested to observe that "line* meant "straight l i n e " to several subjects. In many cases when the geometrical meaning of the word " l i n e " was wanted, the boys indicated i t by saying " l i n e , which i s either straight or crooked". In those cases where the subjects l e f t the word " l i n e " unqualified, i t p r a c t i c a l l y invariably meant a "straight l i n e " . Several interesting labels for the idea of "touching" were given. Two subjects, expressed the idea by the words "joined together"; other subjects by "beside"; "put together i n any fashion"; "connected"; "together"; "fixed on the side"; "stuck together"; "joined"; and "on". "Wez" (a c i r c l e touching a triangle on shortest side) was defined as a c i r c l e beside a tri a n g l e . At the same time t h i s subject i d e n t i f i e d as "not Wez" any figures i n which a triangle and a c i r c l e lay i n a horizontal position but not touching. He also correctly i d e n t i f i e d as "Wez" c i r c l e s and triangles i n a horizontal position tangent to one another. The Verbalization of Wez which said a "triangle and a c i r c l e fastened together i n any fashion'" could mean almost any relationship between a triangle and a c i r c l e . The subject, however, i d e n t i f i e d as "Wez" only those figures which were Wez and discarded as "not Wez" a l l those figures i n which a triangle and a c i r c l e "were put together i n any fashion" i f they were not touching on the short side of the triangle. Verbal labels applied by the subjects to triangles were varied and numerous. Simultaneously with Recognition performance vfcich to the experimenter would have indicated the word "rectangle", the subjects applied such verbal phrases as: "square", n l o n g square", "long shaped box", " t r i a n g l e " " b o x " , "oblong square", "a long s t i c k l i k e a square with short ends". One subject indicated the short v e r t i c a l sides of a rectangle l y i n g horizontal as "bottom" and "top". I t would be very d i f f i c u l t for any experimenter who r e l i e d on Verbalization alone and had no further clues of meaning to know what a subject was thinking who labelled h i s idea of "rectangle" with the verbal l a b e l , " t r i a n g l e " or "square". I f Verbalisation as defined i n the present experimen i s to be used as a c r i t e r i o n of learning, every misapplied word described i n t h i s section, plus the many mora which these i l l u s t r a t e , must be evaluated. The Verbalisations must be marked as accept able or not acceptable„ Are they to be judged according to the standard set by the experimenter's vocabulary, or by the child's? I t seems hardly reasonable to judge the de f i n i t i o n s e l i c i t e d from a twelve-year-old Grade 6 boy by the vocabulary standards of a university graduate. On the other hand, then, i s i t more satisfactory to evaluate the verbal response on the subject own vocabulary l e v e l ? I f so, what i s that level? This description sisggests that the great amount of interpretation required i n evaluating Verbalizations, renders "Verbalization highly subjective as a c r i t e r i o n . In contrast, Recognition responses required no i n t e r -pretation, being either correct or incorrect. Thus, Recognition* i s the more objective of the two c r i t e r i a . (b) P a r t i a l Verbalizations—Omissions "Understood" One factor increasing the sub j e c t i v i t y of the evaluation of a Verbalisation i s the subject's frequent omission of part of the Verbalization as being "under-stood". The folloTJing examples i l l u s t r a t e t h i s s i t u a t i o n . One subject who attained complete Recognition, verbalized the concept "Wez" ( c i r c l e touching shortest side of triangle) as " c i r c l e touching the shortest l i n e " . This Verbalisation was given both during the t r i a l on which the subject achieved Recognition and also on subsequent t r i a l s . These .subsequent t r i a l s produced correct Recognition and Reproduction. The subject omitted the idea of triangle from his Verbalization, probably because i t was so obvious that he considered that the term "shortest l i n e " would mean to the experimenter tke "shortest l i n e (side) of the triangle". In other words, the subject omitted to verbalize tho idea, triangle—perhaps leaving i t tc be understood i n the same way that i n common English the subjects of imperative sentences are l e f t by the Verbalizer'"to be understood". A further i l l u s t r a t i o n was found i n a Verbalization of " S i f " . The Verbalization under consideration was acceptable on the second t r i a l but.subsequently, i n a t h i r d t r i a l , the Verbalization (according to the l e t t e r ) was incomplete. Recognition and Reproduction were achieved on the second t r i a l and consistently maintained i n the t h i r d . I t seemed to the experimenter that the subject intended parts of his previous Verbalization "to be understood". Another i l l u s -t r a t ion i s to be found i n one subject's treatment of the concept "Mef" (a c i r c l e half black and half white). In t h i s subject's Verbalization no mention i s made of " c i r c l e " , but in his Recognition he did not accept the blackened half-c i r c l e as being "Mef" even though t h i s would have been the figure which would have corresponded to the actual words of his Verbalization. Although his Verbalization contained no mention of " c i r c l e " , i n Recognition tile subject i d e n t i f i e d as "Mef" only those figures i n which a complete circumference, half blackened, was shown. Furthermore, i n drawing his Reproductions, a l l examples of "Mef" were complete circum-ferences, half blackened; i . e . , "Mef" was correctly recog-nized and reproduced.- Perhaps the subject omitted the idea of complete circumference from his Verbalization because he considered i t obvious that i t was to "be understood". Since "to-be-understood" omissions seem to occur, how should an incomplete Verbalization be interpreted? The presence of t h i s problem suggests that (as a c r i t e r i o n of learning) there i s a -subjective quality i n Verbalization. On the other hand, Recognition as a c r i t e r i o n of learning meets no such objection. (c) Omissions TShich May or May Not be Expected to be "Understood" Another factor contributing to the subjectivity of Verbalization as an experimental c r i t e r i o n i s that omissions which may or may not be expected to be "understood" appear i n Verbalization simultaneously with achievement i n Recog-n i t i o n and Reproduction..- The concept " Z i f " contributes many examples of t h i s factor. " Z i f " i s defined as a "'circle inside a rectangle, the c i r c l e touching both long sides of the rectangle, but not touching either end". Five subjects, i n verbalizing t h i s concept did not mention "touching both sides". However, they i d e n t i f i e d as ''Zif" only cards containing this characteristic and rejected any cards which were an actual graphic representation of their Verbalization but i n which the c i r c l e did not touch both sides. Their Reproduction as well as Recognition gave the idea of "touching both sides", even though the Verbalizations continued to omit this c h a r a c t e r i s t i c . In one case the subject i n making a spontaneous comment about " Z i f " stated that i t did not matter whether the c i r c l e touched both sides or not, as long as i t was i n the square. Subsequent to making his comment he 66 rejected any Recognition cards i n which the c i r c l e did not touch both sides, Further examples were found where both .Recognition and Reproduction conveyed the idea of "not touching end*6, while Verbalization did not mention t h i s l i m i t a t i o n . In one case, although the Verbalization of "Tov" did not mention "near'*, the Recognitions and the Reproductions showed the existence of the idea of nearness. In determining the acceptability of such responses, great dependence upon the experimenter's judgment i s thus necessitated when using Verbalization as a c r i t e r i o n of concept formation. In contrast, the subject's responses to the Recognition test require no interpretation by the experimenter. Verbalization i s shown, therefore, to require a greater amount of interpretation by the experimenter than does Recognition, (d) V e r b a l i z a t i o n s — R e l a t i v e l y Incorrect or Incoherent In view of vocabulary differences between experimenter and subject, where i s the dividing l i n e between acceptable and unacceptable Verbalizations? When does incoherent wording become coherent? A fourth factor contributing to the subjectivity of Verbalization as a c r i t e r i o n of concept formation i s the appearance of numerous incorrect and incoherent Verbalizations simultaneously with correct Recognition and Reproduction,, I t might be argued that such performance indicates that a concept 67 has not yet been formed completely but only i n the Recognition and Reproduction levels and for t h i s reason the achievement of Verbalization would be a good c r i t e r i o n of concept "formed". This argument carries l i t t l e weight, however, i n the l i g h t of the many "Verbalization-precedes-Recognltions reported i n th i s experiment. One subject verbalized "Mef" as a " c i r c l e with a black and white spot'", but i d e n t i f i e d only those figures as "Mef "whioh were half black and half white. In the concept "Toy", many Verbalizations gave the idea of only one "X", while the corresponding Recognitions e.nd Reproductions have the idea of four "X's". One Verbalization of "Vec" used the words "horizontal l i n e " i n the Verbalizations but recognized and reproduced his "Vec" l i n e s i n any po s i t i o n , horizontal, v e r t i c a l or oblique. Many meaningless Verbalizations were given f o r the harder concepts, even though Recognition and Reproduction were correctly indicated. For example; for "Wez" (a c i r c l e touching triangle" on shortest side) the incoherent Verbalization "a c i r c l e that touches the bottom" was offered with correct performances of Recognition and Reproduction. For the concept " Z i f " , the Verbalization "touching twice, both sides of square" was given to corres-pond to Recognition and Reproduction performances i n which a " c i r c l e touched both sides of a rectangle once". The Verbalizations given by the subjects were often incoherent when divorced from any other clues to meaning. The following i s an example of t h i s incoherence, "a square with a c i r c l e touching the two oblong sides of the square". Verbalized responses have to be marked as d e f i n i t e l y right or d e f i n i t e l y wrong. There i s no such def i n i t e l i n e of demarcation i n the Verbalizations themselves. Yftiere the di v i d i n g l i n e s h a l l be, becomes a matter of judg-ment by the experimenter. This shows that Verbalization, when used as a c r i t e r i o n of learning, i s inherently subjective. 4 . Correct Verbalization Whose Significance i s .: not Understood" ~ Another factor contributing to the questionable nature of Verbalization as an experimental c r i t e r i o n .of concept formation was the a b i l i t y of subjects to express the correct Verbalization before they were aware of the s i g n i f i -cance of -the words they were using. The correct Verbaliza-t i o n was often given while Recognition could not be achieved. The concept "Mef" was often.verbalized cor r e c t l y with the words "a mef i s a c i r c l e half black and half white". Immediately after t h i s Verbalization, several subjects accepted as "Mef" cards i n the Recognition test which the experimenter would describe as " o i r c l e s partly black". These instances accepted as "Mef" were c i r c l e s some more than half black and some l e s s than h a l f blaok. In other words, i n many cases the subjects said "half" when they 'meant* "part". Another subject i n verbalizing " Z i f " used the words "touching both edges", but the Recognition test accepted s i x cards which, did not touch "both edges. One subject gave the acceptable d e f i n i t i o n that "Mib" was a "square with a c i r c l e touching i t " . In geometrical termin-ology t h i s d e f i n i t i o n allows the c i r c l e to "touch" the square either i n t e r n a l l y or externally. On the Recognition test, the instances showing external tangency between c i r c l e , and square were accepted as "Mib", The figures exhibiting internal tangency were rejected as "not a Mib". These are examples where the subject gave the acceptable experimental Verbalization. I t seems, however, that he did not reali z e the significance of his words, and, consequently, he could not pass the Recognition Test. In these cases, the exig-encies of poor habits of speech (saying "half" for "part" and omitting d e t a i l by saying "touching" instead of "touching on outside") reaped f o r the subject the f r u i t s of the combin-ation of generalizing a b i l i t y and precise expression of ideas. I f Verbalization i s used as the c r i t e r i o n of concept forma-ti o n , situations l i k e t h i s a r i s e . This aspect of Verbaliza-ti o n detracts from i t s usefulness as a c r i t e r i o n of learning. 5» S t a t i c Verbalizations Another factor contributing to the u n r e l i a b i l i t y of Verbalization as an experimental c r i t e r i o n of concept formation i s that the Verbalization sometimes remains s t a t i c while performance on the Recognition cards progresses to achievement. To i l l u s t r a t e t h i s , i n one case while successive Verbalizations of the concept'"Zif" remained 70 i d e n t i c a l , Recognition progressed, expanding on the second t r i a l to the idea of "touching both sides" and on the t h i r d t r i a l to "not touching an end". Whereas on the t h i r d t r i a l the Recognition Test and the Reproduction Test were passed successfully, Verbalization remained i d e n t i c a l to e a r l i e r attempts. Thus Verbalization remained s t a t i c , not indicating any growth or change i n the development of the concept. Assuming that the instances seen by the subject after the f i r s t t r i a l modified the concept to some extent, the conclusion follows that Recognition was the more sensitive indicator. This argument suggests that at times Recognition i s a less s t a t i c criterion, of learning than i s Verbalization. 6. An Interesting Case The i n a b i l i t y of subjects to recognize a change i n t h e i r ideas was indicated i n an interesting case where a subject learning the concept "Mef" volunteered information several successive times that he had,"not changed his mind at a l l . In t h i s case, a l l levels--Verbalization, Recognition and Reproduction—had been changed from the i n i t i a l incorrect responses to f i n a l correct responses for a l l c r i t e r i a . The subject, however, after achieving the concept on a l l l e v e l s , s t i l l happily volunteered the information that i n his l a s t t r i a l s he thought exactly the same thing he had thought i n his f i r s t ones. . 7 1 7. Summary and Conclusions 1. Verbalization i s not a " l e v e l " that can be depended upon to appear l a t e r than Recognition. In f a c t , i n t h i s present experiment, Verbalisation preceded Recognition more often than vice versa. 2. Verbalization and Recognition are approximately equally subject to reversal of judgment. In neither case dc reversals occur frequently. 5. Recognition i s a more objective c r i t e r i o n of concept formation than i s Verbalization. QIhe l a t t e r requires a great deal of interpretation by the experimenter as to what the subject "means", while the former does not. 4. Verbalization and Recognition often give c o n f l i c t i n g evidence regarding the nature of the subject rs concept. Subjects mieapply words, become incoherent, and make omissions which may, or may not, be Intended to "be under-stood", while at the same time giving correct responses on the Recognition t e s t s . On the other hand, many correct Verbalisations are made while Recognition responses are s t i l l i n c o r r e c t l y made. j>. Recognition, rather than Verbalization, i s a more sensi-t i v e indicator of the degree to which a concept has been formailatod. I t can be used to measure the progress of concept formation at any stage, and does not require the concept to be completed before i t yields numerical data convenient to s t a t i s t i c a l treatment. 72 For the acourate communication of ideas such as are used i n the testing situation of t h i s experiment, twelve-year-old Vancouver hoys require other media of expression than Verbalization alone, This study employs Recognition rather than Verbaliz-ation as i t s c r i t e r i o n of concept formation. Their advantages and disadvantages appear to be approximately even as regards (a) "l e v e l s " and (b) reversals of judgment. Recognition appears superior to Verbaliza-t i o n as an experimental c r i t e r i o n of concept formation because i t i s (a) more sensitive than Verbalization, and (b) f a r more objective than Verbalization. 73 CHAPTER 17. SOME RESULTS AWD CONCLUSIOHS 1. Ihich Method, the Positive or the P o s i t i v e -Negative was Ant8qeaentu~^o*^Ee Greater Tendency toward • Lg s c r i p t ! on" Rather than^eneraf ization? • Although i n the following two paragraphs no hard and fast d e f i n i t i o n s are given, "generalization" i s considered to he the recognition of the highest common factor found i n the positive examples of a given concept, while "description" i s a statement of many of the cha r a c t e r i s t i c s , common or otherwise t found i n the positive instances seen by the subject. An example of a description might be, "A Dax i s a long- triangle and a short triangle with a dot near the bottom or a f a t triangle with the dot i n the middle or a dot i n one end or a big triangle or a l i t t l e t r i a n g l e " . Verbal-izations did not have to .be t h i s long to be called a "description". In "description" frequent use i s made of the conjunctions "and" and "or". In other words, description i s defined as a running enumeration of the characteristics of the positive cards seen. 3?or each type of presentation, twenty-five subjects t r i e d eight concepts each, and were allowed to verbalize each concept as many times as they wished. Any, a l l , or none of the Verbalizations could have been, descriptions. The positive presentation i n t h i s experiment was antecedent to twenty-eight descriptions, the positive-negative to twenty-seven descriptions. The difference between the A.M.fs of the number of descriptions per subject 74 .was,04, while the standard error of the difference was .067. This indicates that i n 73 chances oat of 100, the positive presentation, on the average, w i l l advance more, description than w i l l the•positive-negative (24 p. 215). The difference, however, i s not s i g n i f i c a n t . The results of t h i s experiment do not indicate that either method of presentation i s antecedent to any s i g n i f i c a n t tendency toward either generalization or description. 2. Is the Recognition of a Concept Gradual or Sudden? Matheson (47 p. 260) describes the existence of insight i n these words "understanding of a situation exists i n degrees and the complete understanding which Kohler characterizes as insight represents one experiment of the d i s t r i b u t i o n when a l l cases are considered". Alport (2) reports three types of solution: (a) solution with the minimum insight; (b) solution with gradual insight which may be p a r t i a l or complete; (c) solution fwith sudden insight which may mature during exposure or between exposures. Both Tyler (71) and Pat ton (.54) i n experimentation with, problem situations whose solution depended upon the subject's discovery of a p r i n c i p l e , concluded that the emergency of insight might be gradual as w e l l as abrupt. Drever (17) s i m i l a r l y reported the discoveiy of a principle as gradual. On the graphs shown i n Figures 11 to 18, sudden insight would be indicated by a sharp upward acceleration i n 75 the curve. A comparatively straight curve, whether i t s gradient he steep or shallow, indicates gradual recognition development. A straight steep curve,like the positive presentation of "Zum", indicates gradual development of an easy concept. The sharp upward accelerations found i n Figure 11 , at Card 5 (both presentations), i n Figure 12 at Card 3 (positive-negative method), i n Figures 16, 17 and 18 at Card 5 (positive-negative presentation), cannot be interpreted as being due to sudden insight. Another factor, the compulsory discard of caution-1-, i s operative. In the present study, the following figures exhibit comparatively straight curves: fa) Figure 12 , positive presentation, cards 1-4 (b) Figure 13, positive presentation, cards 1-8 (c) Figure 15, positive-negative presentation, cards 1-8 (d) Figure 14, positive presentation, cards 1-4 (e) Figure, 15 , positive-negative presentation, cards 1-8 ( f ) Figure 16j positive-negative presentation, . / cards 1-8 (g) Figure 18 , positive presentation, cards 1-8 This suggests that during at least a part of t h e i r formula-t i o n , these concepts developed gradually. This study, therefore, shows some evidence pointing to gradual development of concepts but gives no conclusive evidence on the question of the existence or absence of sudden ins i g h t . •^This factor i s considered more f u l l y i n the next section of t h i s chapter. Y r i p.. "iioonviMi to I-i CSJ CO pi N •H 78 o Pi •H CD += O Pi © © CQ Pi O O o •H d o o © © © i H © 60 Y I <?-l"» \ o -t •a? C « 3 H O 0) •H C H 13 • O -4 _ * H c* C <H d •P OtH O d O «H © f4 -P g ©^-rj © 43 ^ d !> a &o • © P hoti •H d H O O d © 44 © 43 O <S43 •P © i>-P 01 » © d •H Q3 oa © •H 43 o G5 © > •H ! «P •H ro o © ra (X) o -P 9 2 S © 43 E-i CVH ra ,o t O >d © I -P ' H CO p ra d © I j= tt P. O V CH CVS ^4 S u »> o .s -H 0 *3 ** © •H ^ Pi tr- o iH >H -P • © -H pi pi 8)«H 60 O -P •H O © Pq © pf PI . -H o © © J> p © 0 -ri .. a M +=> O .ri © © © (J) o v •'vQ H © 1 ^ >S-P ^ d -H Pi Pi K) O «ri I CO H © ft" ' 79 *» o P. o •tt •*>• U V O J- .»> H if h Pi © © © •H •s © © !> •ri -P •ri © O P4 © J>5 © © m -H XI -p i> -p © H 2 Xl N © p: © *H Pi o o o Pi a ti © i -P &3 O © o Pi *ti © o -P r3 © +3 Pi © •H -H a o o © H © U pi W) •H ft-3. Which, of the Two Experimental Types of Presentation Gave the Greater Impetus" to Caution? The frequent appearance of a positive acceleration^ i n the curves at .Gard 3 show that many p a r t i a l concepts existed which were not s u f f i c i e n t l y well recognized to encourage the subject to volunteer them. On seeing Card 4, the subject was stripped.of h i s caution, since he was required to give expression to h i s nebular impression, and frequently he was able to make the correct generalization. I f the curve between Card 5 and 4 continued at the same pitch as the curve up to Card 3, t h i s would indicate that even when t o l d to do so, the subjects could not dip below into their general hazy'impressions. In other words, constant variation from card to card indicates there i s no change in the amount of caution being exercised. The amount of the positive acceleration of the slop© at Card 3 i s a c r i t e r i o n of-the extent to which the subject wanted to "make sure". The greater the amount of positive acceleration at Card 3, the greater was the subject's desire to test t h i s hypothesis; i . e . , the greater was h i s desire to wait and see whether following examples corroborated or refuted his generalization. Ihere the positive-negative shoiv greater difference i n pitch than the p o s i t i v e , indication i s given of greater desire to test the hypotheses when presentation i s , -Mathematically speaking, acceleration i s defined as a change i n v e l o c i t y . The v e l o c i t y i s indicated by the slope of the curve. Accordingly, i n speaking of the graph,"at" rather than "after" should introduce the phrase "at Card 3". 81 by the positive-negative method than when i t i s by the positive method. In the concept "Mef" of the present experiment, the positive presentation and not the positive-negative gave the greater positive acceleration to the curve at Card 3 (see Figure 1 1 ) . In every other concept except "Mib", however, the positive-negative presentation shows the greater corresponding acceleration (see Figures 12,13,14,15,16 and 1 8 ) . The concept "Wez" cannot enter t h i s discussion because no subject given the positive presentation achieved i t . The r a t i o i s , therefore, 5 to 2 i n t h i s experiment, that the positive-negative presentation,rather than the positive method, w i l l produce the greater positive acceleration on the graph at Card 3. These results could be explained by the hypothesis that of the two types of presentation used i n t h i s experiment the positive-negative method gave the greater impetus to caution. Apparently, the inspection of negative examples made the subjects hesitate to hazard a guess before they had seen enough examples to "make sure". Tyler's study (71) pointed out that the testing of hypotheses was a part of the generalizing process. The preceding paragraphs discuss the re l a t i v e role of positive and negative instances In increasing the desire to test hypotheses, and implies that in t h i s capacity the role of the negative i s the greater. In Chapter Y, further evidence that supports t h i s conclusion! i s presented. 4. Factors of D i f f i c u l t y In Concepts 82 (a) "Mental I n e r t i a " or " R i g i d i t y " and the Influence of Negative Instances Many factors have "been suggested as contributing to the d i f f i c u l t y of concepts. Egger's (20) findings that "Mental i n e r t i a ( f i x a t i o n , d i r e c t i o n , or perseveration) i s the factor which most markedly interferes with successful reasoning behaviour", i s i n accord with the findings of many other experimenters. Welch (79,8o) states that a relationship i s harder to learn than an element. Tyler (71) indicates a lack of correlation between the d i f f i c u l t y of the concept and the combined number of elements and relationships. He suggests the follov^ing factors of d i f f i c u l t y : -(a) The number of words required to express a rule; (b) The number of hypotheses that can be formulated; (c) The number of patterns that must be shown before a l l hypotheses are tested; ' . . . f (d) The abstractness of the elements and r e l a t i o n -ships involved. Crudden (lj?) found: (a) that the d i f f i c u l t y of the concept inoreased i n direct proportion' to the complexity of the figure i n which i t i s imbedded; (b) that knowledge of the "figure-to-be-abstracted" increases the ease of abstraction. Many psychologists i n discussing generalizing and reasoning have pointed to r i g i d i t y as a factor of d i f f i c u l t y . Crudden (15) found "that-whioh-is-to-be-avoided" i n 83 abstraction has almost as much influence i n successful abstraction as "that-which-is-to-be-chosen". Maier (46) suggests that many errors i n thinking are due to the r i g i d i t y of the reasoner's set. Duncker (18) thinks somewhat similar-l y to Maier. Rees and Israel. ( 5 9 ) state that a r i g i d mental set often prevents the subject from seeing d e t a i l s which ought t© make him reject a previous hypothesis. Chant (12) i n suggesting that associations and meanings determine many incorrect responses, was suggesting that r i g i d i t y i n the "centering points" was a contributing factor to error. Siipolo ( 6 5 ) , Ewert and Lambert (21) and Sullivan• ( 7 0 ) a l l emphasized the role of mental I n e r t i a i n producing error. In the foregoing review of experimenter's conclusions, " r i g i d i t y " and "mental'inertia" have been named repeatedly as being antecedents to erroneous hypotheses. Grudden found that "that-whioh-is-to-be-avoided" was an important ante-cedent to successful abstraction. Why was i t helpful? I t s value lay i n i t s a b i l i t y to upset the t r a n q u i l i t y of an ' erroneous hypothesis and so) to overcome "mental i n e r t i a " and " r i g i d i t y " . What i s Crudden's "that-which-is-to--be-avoided" but a negative instance! According to Crudden's conclusions, therefore, a positive-negative presentation should be super-i o r to a purely positive method, due to the influence of the negative instances i n preventing "mental i n e r t i a " or " r i g i d i t y " . The conclusion that negative instances assist toward 84 correct abstraction i s supported by s t i l l another l i n e of • reasoning. Sengerelli (28) found that i t i s more d i f f i c u l t to conceive an object a second way after having learned to conceive i t a f i r s t way. The section on "Impetus to Caution" shov/ed that the influence of the negative instances was toward a tendency of suspended judgment; i . e . , a tendency not to have conceived an hypothesis hard and fast i n a " f i r s t way".' This tentative attitude would soften the effect of having had an incorrect hypothesis. Accordingly, i t i s to be expected that the Introduction of negative instances w i l l lessen the d i f f i c u l t y of concept. Table 21 shows the number of Recognitions achieved for each concept by each method. TABLE XI.- ORDER OP DIFFICULTY 01? TEE CONCEPTS Order of Positive Po s i t i ve-Ne gat i ve Both D i f f i c u l t y Prase ntation • Pre sentation Pre sentati ons Hardest to Number lumbe r Number Easiest Name Correct" ; Name Correct* Name Correct" (out of .50) (out of- (out of 25) (out of 25) 50) 1*5 Wez 0 • Tov 10 Tov 11 1 .5 Tov 1 Pog 9 Pog 11 5 Z i f "' 5 Wez 18 Wez 18 4' Pog 1 2 . Z i f 24 Z i f 29 5 Mib 11 ;ffief 25 Mib' 55 6 M e f : 15 Yec 25 Mef; 58 7 Zum 22 Mib 24 Zum 47 8 Yec 22 Zum 25 Yec 47 TOTALS: 78 I58 . Some concepts, ?/hile being achieved by a high percentage of the subjects who saw both positive and negative C r i t e r i a of "correct" was the, successful Recognition of the 16 test cards f o r each concept. instances,were learned "by-only a small f r a c t i o n of the subjects who saw only positive examples. [These r e s u l t s , therefore, corroborate the conclusions of those experimenters who suggest that mental i n e r t i a and r i g i d i t y were factors of d i f f i c u l t y i n concept formation. These results also strengthen the hypothesis that introducing negative instances tends to develop an attitude of suspended judgment, which, i n i t s turn, increases concept achievement by preventing definite acceptance of an incorrect hypothesis. (b) The Acceptance by the Subject of Incomplete Hypotheses and the Influence of Negative Instances: In nearly a l l cases where the concept was not achieved, part of i t , but not a l l of i t , was accepted as the whole of the concept. P a r t i c u l a r l y was th i s glaringly evident i n the group where generalization was done from positive examples only. Any factors which can be shown to encourage the acceptance of common factors less than the highest common fac t o r , become major factors of d i f f i c u l t y . The l o g i c a l analysis submitted i n Chapter 7 suggests that because the presence of the characteristics oomposing an incomplete hypothesis can be abstracted from every positive, instance, positive examples tend toward being antecedent to incomplete hypotheses composed of part of the correct hypothesis, but not a l l of i t . Further, the l o g i c a l analysis to be found i n Chapter V shows that a negative instance can exist to eliminate d i r e c t l y any and a l l incomplete hypotheses. Therefore, the inclusion or 86 exclusion of negative instances along with positive examples i s a major factor related to d i f f i c u l t y in concept formation. (c) Complexity of Concept: The differences between the number of Recognitions achieved by the positive and by the positive-negative presen-tation are different for each concept. Since the Inclusion or exclusion of negative instances constituted the experi-mental variable, these results would suggest that the efficacy of introducing negative examples varies with the concept. The l o g i c a l analyses of negative instances submitted i n Chapter ¥ support this conclusion. Table XC shows that when the results of both presen-tations are combined, the concepts "Tov" and "Pog" were recognized least frequently. Why were these generalizations harder than the others? A "Tov" was defined as "a square with an X near each of the four sides". The writer suggests that i n the "Tov" there were more probable combinations of common factors than i n any other concept. Consequently, a greater number of hypotheses could be formulated regarding "Tov" than could be with the other concepts. In pointing to the number of possible hypotheses as a factor of d i f f i c u l t y , the present study i s adding supporting evidence to one of Tyler's suggested factors. On the other hand, however, there i s a serious 8? objection to speaking of "the number of elements and relations". The present study does not give a psychological analysis of i t s figures into a number of elements and r e l a t i o n s , for that would be extremely d i f f i c u l t i f not impossible. Who i s to say whether a subject sees a triangle as one area,or as three straight l i n e s intersecting to form three angles? . Is a segment of a o i r c l e one element or area, or i s i t two r a d i i and one arc enclosing a space? KVho i s to say how many elements or relations there are i n concepts such as were employed i n the present experiment*. Crudden stated that "knowledge of the figure-to-be-abstracted" increases 1 the ease of abstraction. The writer would suggest that the explanation of t h i s i s that "knowledge of the figure-to-be-abstracted" knits what would otherwise be several elements and r e l a t i o n s into a unit and so reduces the "number of elements and r e l a t i o n s " to be contended with. (d) Abstractness of the Concept: A "Pog" was defined as "two unequal l i n e s " . Table U l i s t s "Pog" as being one of the two hardest concepts. Why should "Pog" be hard? The writer suggests that the r e l a t i o n -ship of inequality i n length i s quite abstract when applied to an element which can be varied i n as many ways as " l i n e " can be. This evidence, therefore, supports another of Tyler's factors of d i f f i c u l t y , namely, the abstractness of the elements and relationships involved. 88 (e) "Minimum Number of Words Required": Tyler suggests that "the minimum number of words required to express a ru l e " i s a factor of d i f f i c u l t y . The writer would encounter two obstacles i n attempting to use this suggested c r i t e r i o n of d i f f i c u l t y . F i r s t , how could "the minimum number of words required" be determined? Secondly, how can the number of words'be counted? F i r s t , how i s "required" to be defined? Required by whom? The experimenter? Webster? Or the subject? I f the answer i s "required by the subject", how i s the experimenter to know whether a given subject's vocabulary would have permitted him to define a "Dax" as "a triangle enclosing a dot", or whether that d e f i n i t i o n was beyond him and his vocabulary "required" him to define a "Dax" as "a triangle with a dot i n i t " ? Secondly, after the d i f f i c u l t y of defining "minimum number of words required" has been overcome, another obstacle i n counting "the number of words" i s encountered. Are "a's" and "the's" to be counted as words? I f so, how would we deal with the de f i n i t i o n s of two subjects one of whom' said, "Dax i s triangle with dot inside" and the other of whom said, "a Dax i s a triangle with a dot inside"? In other words, the subject's optional inclusion or omission of "a's" and "the's" would present d i f f i c u l t y . I f "a's" and "the's" should not be included, should one count words which could be replaced by "the" without obscuring the meaning of the definition? For 8? example, i f "the" i s not to be counted as a word, should " i t s " be counted i n the following p a r t i a l d e f i n i t i o n , "a c i r c l e touching a tr i a n g l e on i t s shortest side"? After considering the perplexities inherent i n trying to use as a c r i t e r i o n of d i f f i c u l t y the number of words required to express a concept, the writer would not attempt to u t i l i z e i t . However, the author i s w i l l i n g to concede that to the extent that the number of words indicate the complexity of the concept, i t may be a c r i t e r i o n of d i f f i c u l t y . 5. Relationship of Presentation Method and Time Both Haught (36) and Tyler (71) are agreed that i n studies l i k e the present one, "time" i s not an important measure of learning. Smoke (67) found no sign i f i c a n t difference between the time required to learn concepts from a positive-negative presentation and the time necessary when the presentation was from p o s i t i v e instances only. Table XIX compares the time factor i n the two methods used i n the present study. TABLE XII.- RELATION OF TIME FACTOR TO METHOD OF PRESENTATION Po s i t i v e (min.) Total time for 25 S's 1 Mean time 1275 51 Positive-Negative (min.) C r i t i c a l Ratio 1340 54 174 (57 chances i n 100) 90 The positive-negative took s l i g h t l y longer than the positive presentation. Comparison of the mean time per. subject, however, shows only three minutes difference. This gives a c r i t i c a l r a t i o of .174, i . e . , 57 chances i n 100, that there i s a r e a l difference i n the time required. The c r i t i c a l r a t i o of 1,4 shows that there are 92 chances i n 100 that the time taken i n the positive-negative presentation w i l l be less variable than the time required for the positive presentation. The results of the present study, therefore, support the view that i n experiments l i k e t h i s one, time i s not an important measure of learning. 6. Summary and Conclusion 1. There i s no s i g n i f i c a n t difference between the two methods i n the tendency toward description rather than general-i z a t i o n . 2. The evidence supplied by t h i s experiment supports the hypothesis that concepts are formulated gradually rather than suddenly. 3. The introduction of negative, i n addition to po s i t i v e , examples increases the attitude of suspended judgment and thus gives an impetus to caution. 4. " R i g i d i t y " or "mental i n e r t i a " tend to be antecedent to erroneous hypotheses. Negative instances tend to distrub the " r i g i d i t y " and "mental i n e r t i a " and thus contribute to greater achievement. 5. Many errors are made by the acceptance of incomplete hypotheses. The introduction of negative instances lessens t h i s d i f f i c u l t y . 6. The d i f f i c u l t y of a concept increases with -(a) Complexity, (b) Abstractness. 7. I t i s very d i f f i c u l t to count the number of elements and relations i n a geometrical concept. 8. I t i s very hard, i f not impossible, to determine the '"minimum number of words required" 1 i n the d e f i n i t i o n of a concept. Thus t h i s measure cannot be used as an experimental c r i t e r i o n of the d i f f i c u l t y of a concept. 9. In an experiment l i k e the present one, time i s not an important measure of learning. CHAPTER 7. THE RELATIVE ROLE OE POSITIVE MP NEGATIVE INSTANCES 1. In the Pre sent Experiment , Ihieh Me th od of Pre sent ati.on, the . Po s i t i ve Or The Po s i t i ve -Se gat i ve, Pro duce & 'fixe Ore at er~ AchTevement ? (a) Comparison of the two methods as to the achievement on each concept and also on the totals of a l l eight concepts Table XII I exhibits experimental results which are c r u c i a l to the problem stated, above. In the column headed L i s shown the c r i t i c a l r a t i o between the achievements for each concept by the positive and by the positive-negative methods of presentation. The c r i t i c a l r a t i o of t o t a l s , also, i s shown. Garrett's short formula for the standard error of differences between percentages was used. A more accurate formula gives c r i t i c a l r a t i o s greater than the results of Garrett's short formula. I t w i l l be noted that the c r i t i c a l r a t i o s of four concepts are s i g n i f i c a n t , while the remaining c r i t i c a l r a tios show that on the average, In at least 99.77 , 99.45, 96.5 and 96,5 chances out of 100, respectively, the efficiency of learning i s greater, on each of the given concepts by the positive-negative than by the positive presentation. The c r i t i c a l r a t i o of t o t a l s (5.3) shows that, under present experimental conditions, i t i s v i r t u a l l y certain that .subjects w i l l , on the average r always learn these experimental concepts with greater efficiency i n the present positive-negative sit u a t i o n than i n the experimental positive s i t u a t i o n . o CQ O H H B3 ri O *H ffi O , • g 3 • •ft 44 HO 96,5 chances 99.45 ohanoes 99.77 chances Significant " . Significant Significant Significant Significant :> vo vo ir\ Lf\ <=t to u\o t-OJ to CO CO IAOO <xt* CO O LT\ H H CNJOJ to 00 co to OJ « to OJ •• • 0 0 ^ H C-~e-'co.H Lf\LC\0 OJ Lf\MD Ox OX .0 0 e « •© © « VOM3 1—1 H O OCOCO H H H H CO NO « OJ H oj ojeo OJNO oj ojvo H i-i <M CO to ir\c--tr~ H r4 Posi-tive Nega-tive O 0 O to O CM CO OJ O O NO sj> CO ON ON ON • * • • 1* 4 ©0-0 O O CTN tr\ CK to 00 to t-i 0 CO r4 ! •ri CO CO f» O -ri f4 43 • . 0 0 to 0 OJ to 0 0 tr\ir\^co ONONO O • * © © 0 4 -« O « NONO ir\ONtO ONOCO H • ON i H M o 1 © CD J> [> •rf'rl •H «3 CQ 60 O CD OO NO OJ O NO OJNO OOtOOs^ONC~-ON H H ON e-i H M o 1 •ri © CQ f> O >H P4 -P COCOCOO^^OO OOOD NO <3- OJ 00 , to CQ oto O fxj O P> r & ft H OM O I CD CD t> > •ri -ri 43 43 •H CO CQ 60 O CD lALOxONtOOsJ-CO^ OJ OJ OJ H OJ H OJ CO H CQ oto O fxj O P> r & ft H OM O 1 •ri CD CQ |> O <H fl) 43 OJ OJ OJ Lf\H HO tf\ OJ OJ H H NO c~-CQ E-i 0 Ogc!3ftl>PqtS3!i) NO c~-CQ E-i 0 93 CQ pi o o o -p -ri © © 60 i> co © fl Pi © © F-l'ri CD 60 cd 03 CQ «H © o 0 •ri FH-P O F-I«H J4 O © © <d 60 14 03 co<P ri © 03 o +3 FH CQ 0 a a ri ts © OJ CQ o •H .43 CQ CQ CD iH. CQ += CO CO O P CQ «H O CQ t-i-43 © © 43 FH CO I •P44 p CQ «H CQ •ri Pj co •ri © © FH F-l (D © 14 ^ 6-o CO 0 14 o © © © © ft !=• p p P ri © © p © © o ri © ri © •ri © 44 o (4 o © f-i co ^ H co CQ © 44 43 CQ •rl OJCQ VPJ © ^ 60 + CO H-P CD =- O . H U © is fH -P - © 44 OJ © ri co © o © © •ri 44 o © 43 o p '.•© • f-i © •ri . CQ td ri © O o •H ri CQ 60 -P fH P-l © >> 2 H ri -P 0 o O CD u 03 FH o - o U © © P FH CD • is CQ FH G3 o 44 o CQ •H 44 43 •P tH CQ O CD •P CQ CD NO Cfl H o P1 *o3 ."••PI FH '© ft ^ to (b) Comparison of the achievement of the whole positive group-with the achievement•of the whole positive-negative group: Shi oh method i s the more e f f i c i e n t ? Table. XIV shows further s t a t i s t i c s relevent to the question^ TABLE XIV,- CRITICAL RATIOS BE TWEES' THE MB AH SCORES ACHIEVED BY EACH METHOD 94 Positive Positive-Negative •No, 'Of Subjects 25 25 A.H. of concepts learned 1 by each subject 3.12 6.32 S.D. of concepts learned by each subject 1.31 1 .09 S.D. of Mean (^M) .27 .22 (fj) = .33 -^P-N-P s 3.20 ^%-N-P = 9.7 (a sign i f i c a n t ~^ =g ~ difference) Those subjectswho received the positive-negative presentation had a mean achievement (6.32) more than double that of the subject who saw only positive instances (3.12). The c r i t i c a l r a t i o of the difference between the means (3 . 2 ) , and the standard error of thei r difference (.35), i s s i g n i f -icant ( 9 . 7 ) . In other words, i t i s " v i r t u a l l y certain" that under present experimental conditions a pupil exposed to the positive-negative teaching cards w i l l always score above a pupil learning from the positive instances alone. Furthermorethe S.D.'s of each group (1,31 and 1 .09) and the S.D.^s-of the mean (.27 and .22) . T See footnote 3 of previous page. 95 suggest tliat In the group where negative instances were introduced there i s l e s s spread In achievement and consequent-l y a greater s t a b i l i t y of the mean. Providing- we can generalize from t h i s experimental attack, these two conclusions have great significance to pedagogy. They indicate a two-fold superiority of the posi-tive-negative over the positive method of presentation; i . e . , ( l ) the positive-negative method produces an increased achievement; and (2) a greater uniformity of achievement i n the group taught. \ This f i r s t factor i s of direct assistance to the learner, while the second factor, without retarding any 'bright learner t gives the teacher the advantage of producing a homo-geneous achievement with a l l learners. This second advantage accrues from the r e l a t i v e l y greater assistance rendered by the negative instance to the duller learner. This l a t t e r state-ment w i l l be considered i n following sections' of the chapter. (c) Comparison of the achievement of the group having both the highest I/4»Ts and the positive presentation, with-the group having-both the lowest I.Q.'s and the positive-negative presentation: How do the number of concepts learned by the highest positive I.Q. group compare with the achievement of the lowest pesitive-negative L..Q. group? Table XY shows the s t a t i s t i c s relevant to t h i s question. TABLE XT.- COMPARISON OF THE NUMBER OF CONCEPTS LEARNED BY THE POSITIVE HIGHEST I .Q„ GROUP AND THE POSITIVE-NEGATIVE LOWEST I.Q. GROUP.. • Positive Positive-Negative No, of cases 6 9 .A'JT. of concepts learned 4.0 6.0 S.D. of concepts per subject 1.0 .82 S.D. of Mean .45 .29 S.D. of Difference =. .535 Difference • = between means S.D. of D i f f , 5.7 (significant) The table above shows that under the present experi-mental conditions, i t i s v i r t u a l l y certain that a group of d u l l normals (I.Q. 95 plus or minus 7.5) taught by the positive-negative cards, w i l l on the average always have a higher Recognition achievement on t h i s test than a superior group (I.Q. 125 plus or minus 7.5) exposed to positive instances only. The number of cases contributing these data was very small, only 6 i n the one presentation and 9 i n "Wie other. The s t a t i s t i c s exhibited i n Table, XV, therefore, must be regarded only as barely suggestive. With t h i s reservation, we may say that these resul t s indicate that i t may be that, within the I.Q.. range" considered, achievement i n learning the kind of concept here presented depends more upon method of presentation than upon I.Q. The lowest I.Q. group i n t h i s experiment when given positive-negative presentation was on 91 the average more e f f i c i e n t at generalizing than was the highest I.Q. group when given the positive presentation only. (d) Comparisons of the amount of advantage received, from the introduction of negative instances "by pupils of different I .Q. level s : ' " : : : In the following sections, the evidence i s analysed i n twat ways: -A. In each of the three I.Q. l e v e l s , the pupils receiving the positive-negative, presentation had higher achieve-ments than those having the positive presentation. Section A compares, for each of the three I.Q. l e v e l s , the difference i n achievement by each of the two presentation methods. This comparison i s intended to determine whether i t i s the brighter pupils or whether i t i s the duller children who received the most advantage from the introduction of negative instances, B. Section B deals with the same question as Section A, and analyses the same data, also, but i t attacks the problem from a different angle. In both methods of presentation the gusnup of bright pupils had a greater achievement than the group of d u l l pupils taking the same type of presentation. Section B compares the difference between the achievement of the bright and d u l l groups seeing the positive instances only, with the difference between the schievement of the bright and the d u l l groups exposed ta both positive and negative instances. The purpose of th i s comparison i s 98 to determine which method of presentation tends to give the more, uniform amount of achievement. I f high I.Q;„ i s associated with the a b i l i t y to evaluate hypotheses c r i t i c a l l y , and i f the introduction of negative instances i s also an antecedent of the c r i t i c a l evaluation of hypotheses (as has been suggested both i n this chapter and i n the section on "Impetus to Caution"), then both -high I.Q. and negative instances tend to be antecedent to the same, thing. This "same thing" ( c r i t i c a l , evaluation of hypotheses) may be antecedent to achievement i n t h i s experiment. I f these assumptions are correct, the negative instances compensate the d u l l learner f o r that which he otherwise lacks, and for that which the bright c h i l d enjoys. Accordingly, the introduction of negative instances into the learning si t u a t i o n would tend to obscure, the influence of the difference i n the I.Q.'s of the d u l l and the bright c h i l d . . A. Which groups, the d u l l or the bright, received the mora advantage from the introduction of "~ negative instances? and why"? ~~ The folloxving table exhibits s t a t i s t i c s showing i n which of the three I.Q.. groups (low, middle or superior) the introduction of negative instances made the greatest difference to achievement:-99 TABLE XYI.- COMPARISOT OS THE I.Q. GROUPS SHOWING ^ HE . . ;. J ' AMOUNT.OF ADVANTAGE. IN EACH GIVEN BY THE; INTRODUCTION 01 NEGATIVE INSTANCES I.Q. 95±7.5 i.Q. LI at. 7.5 Pos. Pos.-Neg. Pos. Pos.-Neg. A.M. f of group .92 .525 6,00 .82 .29 3.40 1.28 .45 6.40 1.11 .57 : <% "' .436 . .567 G r i t i o a l Ratio' ' V " 8.7 (sign i f i c a n t ) 5.3 (significant) I.Q. 125I7.5 I.Q. 110122.5 POS. Pos.-leg. Pos. Pos.-Neg. (Tof group 4.00 1.00 A3 6.67 1.23 5.12 1.51 .27 6.52 1 .09 .22 .71 ,55 •Critical Ratio 5.8 ( s i g n i f i c a n t 9.7 ( s i g n i f i c a n t ) Table XVI shows that subjects i n the low I.Q. group learning from positive Instances only, learned an arithmetic mean, of 2.22 concepts. The group having corresponding I.Q.'s but seeing negative as well as positive instances, achieved •'-Garret, H.E. " S t a t i s t i c s i n Psychology and Education" ,p.201. Formula to apply i f N<30. 100 an arithmetic mean of 6.00 concepts learned. The c r i t i c a l r a t i o of 8.7 shows the existence under experimental conditions of a s i g n i f i c a n t difference between the means achieved by the two methods of presentation,. In the lowest I.Q. group, the difference between the means of the positive and positive-negative methods i s 5.78 concepts. The corresponding s t a t i s t i c for the middle I.Q. group i s 3.0 concepts, and for the superior group i s 2.6? concepts. These figures suggest that the advantage enjoyed by introducing negative examples diminishes as the i n t e l -ligence increases. Whereas i n the loxvest I .Q. group the c r i t i c a l r a t i o between the achievement- produced by the two methods i s 8 . 7 , t h i s s t a t i s t i c dwindles to 5.3 for the middle I ,Q.. groups, and to 3.8 with the highest I.Q. group. This suggests the conclusion that the higher the I.Q. group the less s i g n i f i -cant i s the difference between the number of concepts learned by the two methods. In other words, the higher the i n t e l l i g e n c e , the le s s useful are the negative instances, o r vice versa, the lower the intelligence (within the l i m i t s of t h i s experiment) the more useful are the negative cases. These results strengthen the argument advanced else-where i n t h i s thesis that the chief role of the negative instance i s i t s direct attack on incomplete hypotheses. Pupils with lower I.Q..Ts have less a b i l i t y for s e l f -c r i t i c i s m than those with higher I.Q.'s. The imposition of an external check on the hypothesis of a pupil with a low 101 I.Q,. supplies one of the missing factors necessary to a modified hypothesis. The d u l l c h i l d , given a positive presentation only, lacks t h i s check. Accordingly, while the positive-negative presentation elevates the performance of a, subject with a low I.Q. to proximity with the subject having a higher I.Q., the positive presentation leaves the low group with l i t t l e achievement. The high group supplies i t s own s e l f - c r i t i c i s m and so i n the higher levels the negative instances are less needed. The conclusion i s , therefore, that i n this, experiment the lower the I.Q. group, the more advantageous was the introduction of negative instances. . B„ . Which Method of Presentation, the Positive or the Pps'it'ive-negative, i s Antecedent £o the more Uniform Amount of Achievement? Ana" why? A second avenue of attack on this question i s supplied by comparing the c r i t i c a l r a t i o of the lowest and the highest I.Q. groups given the positive presentation with' the corresponding c r i t i c a l r a t i o for the pos i t i v e -negative method. 102 TABLE XVII.- COMPARISON 03? THE ACHIEVEMENT MADE BY TWW LOWEST 17ITH THE HIGHEST I.Q, GROUPS - BY EACH TYPE OE PRESENTATION Positive Positive-Negative 87 - 102 118 - 132 87 - 102 118 - 132 A.M. A^.M. 2,2 2 .325 4.00 .45 6.0 .29 6.67 ^ S.D. of %-%-N 0621 ;**'Mp. " Mp_N S.D. o f ' B i f f . 3.2 (significant) 1.078 (06 chances out of 100) In Table XVII the c r i t i c a l r a t i o of 3.2 shows that when only p o s i t i v e instances are present i t i s v i r t u a l l y certain that the mean achievement of the highest I.Q. group of the experiment would be superior to that of the lowest I.Q, group. ."When negative instances were introduced, however, the chances dropped to 86 out of 100 ''"that the highest I.Q. group would show superiority over the lowest. In other words, when negative instances are absent, differences i n I.Q. l e v e l are more l i k e l y to produce d i f f e r -ences i n achievement than when negative instances are shown. This result substantiates the conclusion that negative instances introduce an element which tends to obscure the influence of differences i n I.Q* l e v e l , i s A.M. of p o s i t i v e presentation. M P-N 1 3 A , M * o f P°sitive-negative presentation. 103 2 • The Relative Roles of Positive and Negative Instancies. ' ~" (a) Positive Instances: In a series of po s i t i v e instances, the oonoept to be formulated i s the greatest aggregate of characteristics found i n . a l l p o s i t i v e instances, i . e . , the highest common factor of the instances. The concept to be formulated i s composed of more than one element and of the relati o n or relations between these elements. Every pos i t i v e instance i s composed, therefore, as follows:-where Ip represents any given positive instance; a means " i s composed of" and has no reference to equality of magnitude; Fhc is., the abstracted concept (the highest factor or ~' greatest aggregate of characteristics that the given p o s i t i v e instance has i n common with a l l other p o s i t i v e instances); C a i s any characteristic of the given instance, which characteristic i s acceptable i n , but not necessary to, the concept. The Ga may vary from r e l a t i v e s i m p l i c i t y through many successive advances to great complexity. I t i s found at i t s simplest i n the po s i t i v e example requiring the smallest aggregate of characteristics comprising the medium from which an i n t e l l e c t can abstract the concept. I t i s found in i t s highest complexity i n the medium containing F h c and having the greatest aggregate of characteristics. 104 The writer suggests that, i n addition to the concept (^ ho).* s o m e c a l s necessary i n order to have a positive instance. I f no 0 a were present, the concept could not he expressed. No instance could be formed. No communication of the concept from one person to another would be possible. To i l l u s t r a t e t h i s point, l e t us consider the concept "Dax" i n the present experiment. Many methods of producing positive instances of this concept may be employed. The method used i n the experiment was to draw a picture of a triangle with a dot inside i t . The idea "triangle-enclosing-dot" was the F ^ Q . The actual l i n e s and dot composed part of the 0 a. These l i n e s and dots were of different lengths, widths, and i n t e n s i t i e s i n each individual instance. These l i n e s and dots were characteristics which were acceptable i n pos i t i v e Instances, but at the same time no given set of them was necessary to a l l p o sitive instances - various sets o them could be used. Thus the l i n e s and dots of a 'given instance are recognized as being part of the 0 a for that instance. Although no given set of l i n e s and dots was necessary to a l l pos i t i v e instances, nevertheless i t i s necessary to have some C a i n order that an instance of the concept could be present. Thus i t i s established that i n order to have a positive-instance, a medium must be presented from which an i n t e l l e c t might abstract the F ^ . At the same time,the very nature of medium requires some 0 a as an inte g r a l part. 105 In no positive example i s less than jy, present.... « o » • • • * e • c (2) Each different p o s i t i v e instance varies from every other p o s i t i v e instance by—and only by—differences In the Oa term. The most simple complete series of positive instances which contained every possible positive instance would be formed as follows:-. ^p " Ipt f Iptt * ..... f Ipp ............... (3) where represents the most simple complete series of ' positive instances = means " i s composed of" and has no reference to equality of magnitude; and the Ipt* Iptt * .... * Ipr series represents every possible p o s i t i v e Instance from the most simple (I-,-,?) to the most complex (Ipr). The analysis of a positive instance given i n formula (1) and the discussion thereafter, established that F^o may be found in a l l p o s i t i v e instances of a given concept, I t i s the Ga that varies i n each different positive example, Accordingly, in the Sp series, every C a which can be an inte g r a l part of a po s i t i v e instance of a given concept w i l l be exhibited i n association with that concept,, In other words, a complete series of po s i t i v e instances displays every situation i n which the concept Is present (4) I f statement (4) Is correct, then one of the impor-tant roles of the positive instance i s to enrich. Positive examples a s s i s t the student to orient and to recognize his 106 conceptin the whole g e n e r a l f i e l d of whion the concept may be a part. (b) Negative Instances: Any given negative instance could be represented-as follows: I n = JTC • 0 a * 0 n a (5) where: l n represents any given negative instance; = means " i s composed of" and has no reference to equality of magnitude; -F 0 represents any factor common to the given negative instance and the concept to be formulated but 0 i ^ c < Fhc; F c i s necessary to, but not suffic i e n t for Fh 0; C a i s any characteristic of the given instance; which characteristic i s acceptable in., but not necessary to, the concept. C n a i s any characteristic neither necessary to the concept nor acceptable i n a positive instance, and varies between the l i m i t s 0 < 0 n a < Z, where Z i s the most complex aggregate of characteristics, i n which the complete concept ( j % 0 ) i s not found. Values can be assigned to the variables i n formula (5) such that I n becomes F c either by i t s e l f or with any other char a c t e r i s t i c . Thus an instance corresponding to any ^ p a r t i a l concept can be displayed as not being the concept.(6) Formula (5) demonstrates that i n a negative example both 0 a and 0 n a factors may be present. Thus from negative 'instances themselves, a subject cannot know whether a given characteristic may, or may not, be associated with the concept, Consequently, experience with negative instances can not ^O^Fc-s^F^c i s a common mathematical symbol meaning that F G i s equal to, or i s larger than, 0 , but i s less than Fh c; and that F c may vary within these l i m i t s . 107 enrich, knowledge of characteristics associated with the concept* On the other hand, a complete positive series displays every situation i n which the concept may be found (4). /We conclude, therefore, that the positive rather than the negative instances as s i s t i n orientation and enriching. Any instance may be a negative instance i f i t does not contain the abstracted concept. A complete negative series would, therefore, contain a l l combinations of terms except FftQ, and could be represented thus: SJI = I j^l I J I " * • . . £ 1^2 . . . . . o (7) where Sn represents the most simple complete series of negative instances; =. means " i s composed of" and has no reference to equality of magnitude; and the X^, * In„ 4 . .... .V * I n z series represents every possible negative instance from the most simple ( I n ? ) to the most complex ( I ^ z ) . Formula (7) indicates that a complete negative series contains a l l c h a r a c t e r i s t i c s , acceptable or not acceptable, necessary or unnecessary, except that.no instance may contain a l l of the necessary factors; i . e . , F ^ (8) F G was l i m i t e d thus: 0< F c < F h c#. Many subjects shown the p o s i t i v e cards only, recognized F c as being common to a l l p o s i t i v e examples. F 0 i s not only common to, but also i s necessary to a l l p ositive instances. Many subjects accepted an F c as being the F ^ Q . I f these did not recognize the remainder of the concent (Fh c-F 0), nothing i n the positive fSee footnote on previous p-arge. ~~~~ 108 series could d i r e c t l y point out the omission. As proof of th i s argument, we examine formula (3): Sp ~ IpT * Ip•* *• *• Ipr• • • . . . . . . . . . . ( 3 ) Factor F ^ Q i s found i n every instance; Factor F c i s present i n F^Q by d e f i n i t i o n . Therefore, the subject can f i n d F c i n every po s i t i v e instance and continue to think that • F c i s the t o t a l concept. Positive examples used to v e r i f y generalization hypotheses allow p a r t i a l concepts to be accepted for the whole. In (2) the observation on the nature of po s i t i v e instances fore-shadowed t h i s conclusion. Compare the p o t e n t i a l i t i e s of the negative instance with the impotency of the p o s i t i v e i n the role of rejector of p a r t i a l conceptual hypotheses. Formula (5) shows that for any incorrect hypothesis (including every F c alone or i n combination with any other characteristic) a corresponding negative instance can be created. Such a negative instance can make a direct attack on any incomplete or incorrect hypothesis by showing d i r e c t l y that the instance corresponding to the hypothesis i s not a pos i t i v e example. In other words, a complete negative series would make possible the direct elimination of a l l incorrect hypo-theses. On the other hand, as was shown i n statement (2), a complete p o s i t i v e series can not d i r e c t l y eliminate any 109 incomplete (?<-,) hypothesis. Furthermore, a subject who has accepted a F c hypothesis can point to that common factor i n every positive instance. The positive series i s helpless to assist such an erring subject except by damning h i s hypothesis with faint praise and hoping that the subject w i l l soon notice the so-far-unrecognized ( F h c-F c) part of the concept. Thus we conclude that as an hypothesis-testing agent, negative instances can be superior to pos i t i v e examples. This conclusion supports two c o r r o l l a r i e s , (1) that negative instances rather than positive are useful in concept analysis, and (2) that the f i n e r the discrimination necessary, (the more complex the concept), the more necessary are the negative instances, (c) The Process of Concept Formation: Tyler defined induction as "generalization based upon observed faots", as opposed to the deduction used i n demon-strative geometry. "The thinking process uses the two methods alternately, or even i n effect simultaneously, so that i t i s d i f f i c u l t to say at what point the thinking i s deductive and at what point p r i m a r i l y inductive." In the present experi-ment, inductive reasoning produced working hypotheses; deductive reasoning tested them. Inductive reasoning produced further modified working hypotheses, while deductive reasoning tested these i n t h e i r turn. Since the role of the positive examples was to suggest and enrich, positive instances make 110 their greatest contribution to the inductive side of general-i z i n g . Since the role of the negative instances was to test and r e j e c t , the negative examples make their greatest c o n t r i -bution to the deductive aspect of generalizing. Since a completed generalization derived from obser-• M W I I M I H H I I mmiimaii 11 minimal fi n m« | I W I I » I W I I H « L H I mi I I I I T * I — I — >miin»i imw ••n.iwiinii n mi i i • i i n nwnn mn • ••• i w m a i m .• i um vatlons i s the result of a whole series of inductions and deductions, the presentation of both positive and negative examples could contribute more e f f i c i e n t l y to the formulation of a generalization than could the presentation of instances a l l of which were p o s i t i v e . The superiority of a learning situation embracing both positive and negative instances i s demonstrated by the results of the present experiment. In Chapter I i t was shown that generalization i s commonly i d e n t i f i e d with concept formation. We conclude, therefore, that a positive-negative, rather than a purely p o s i t i v e , presentation i s of the greater assistance i n concept formation. J. Summary and Conclusions 1 0 The results with every concept employed i n the present experiment demonstrated the superiority of the po s i t i v e -negative learning situation over the purely positive presentation. 2. The harder the concept, the greater was the demonstrated value of the negative examples« I l l Under experimental conditions, the positive-negative presentation was v i r t u a l l y certain to be antecedent to a higher Recognition achievement than was the purely positive presentation. 1WI thin experimental l i m i t s , the lower the intelligence, the more useful were the negative instances. Within the l i m i t s of t h i s experiment, the presence of . negative instances proved to be a greater determiner of Recognition achievement than did difference i n i n t e l -ligence. The positive-negative learning situation,.rather than the purely p o s i t i v e , i s antecedent to the greater group homogeneity of achievement. In the generalizing process, the ro l e of the positive instances i s two-fold'(a) to suggest hypotheses, and (b) to orient the concept i n the whole f i e l d where i t i s to be found. In the generalizing process, the r o l e of the negative instance i s to assist i n the rejection of incomplete and incorrect hypotheses by being direct evidence that any such generalization i s not the required concept. Since the generalizing process i s both inductive and deductive i n nature, the roles of positive and negative instances are complementary, not overlapping. Any experiment, such as the present one, i s based on the assumption that a concept i s the highest common factor of characteristics to be found i n the positive examples exhibited and that such an abstraction i s intangible® 113 CHAPTER 71. SUMMARY AND CONCLUSIONS The Present Experiment In t h i s experiment, the general problem attacked was concept formation. The part i c u l a r aspect studied by this investigation was the part played by positive and negative' examples i n the process of generalization. A survey of the experimental f i e l d reveals a great variety i n opinion as to what constitutes a concept. The author's conclusion was that i t i s quite proper to use the term concept to designate a wide variety of psychological phenomena, but that he would l i m i t t h i s investigation within the confines of Smoke's experimental d e f i n i t i o n , that "By 'concept formation', 'generalization', and 'oonoept learning', we r e f e r to the process whereby an organism develops a symbolic response (usually, but not necessarily l i n g u i s t i c ) which i s made to the members of a class of stimuli patterns but not to other s t i m u l i " . Accordingly, the type of materials and method employed i n t h i s experiment was influenced by the t a c i t assumptions that concepts are intangibles, and that Verbal-i z a t i o n , Recognition and Reproduction, as defined i n t h i s study, are methods of communicating the nature of the concept. For the present experiment, f i f t y twelve-year-old boys, selected so that i n t e l l i g e n c e , grade l e v e l , native language, and socio-economic status were controlled, were tested i n d i v i d u a l l y . The apparatus was composed of eight sets of concept cards; each set made up of eight positive examples of the concept, four negative instances and sixteen test examples, together with individual record books in which were recorded each subject's responses* In the pos i t i v e presentation, the eight teaching examples were a l l p o s i t i v e instances, while i n the positive-negative presentation alternate exposures were negative examples constructed to be systematic variations from their p o s i t i v e counterparts, but also made as nearly similar as possible to their corresponding positive oards. A l l instructions and explanations were given to the subject before the experimental concepts were exhibited, A preliminary concept "Dax'1 was presented and administered to acquaint the subject with the experimental situation. The experimental concepts were not introduced u n t i l the subject understood the procedure thoroughly. The experiment was conducted "without memory" as a l l the teaching instances for a given concept were l e f t i n the subject's sight during a l l test responses for that learning s i t u a t i o n . The teaching cards for each concept were given s e r i a l l y , the subject being asked to make a " t r y " as soon as he thought he might know what the concept was, as well as every time he changed his mind as to what the concept might 115 be. Three types of response, Verbalization, Recognition and Reproduction, were recorded for each " t r y " . After Cards 4 and 8, the subject was required to make an attempt regardless of whether he had achieved the concept or not. At no time was any clue given to the subject as to whether his responses were acceptable or not. Word-for-word Verbalizations were recorded by the experimenter. Recogni-tions were recorded. The subject drew his Reproductions i n appropriate rectangles i n the record booklet. 2. Results and Conclusions This experimental method produced both quantitative and qualitative r e s u l t s , among the most important of which were (1) the quantitative comparison of the achievement by the two methods, and (2). both the qualitative and the quantitative comparisons of the excellence of Verbalization with Reproduction as the c r i t e r i o n of concept formation. I t was found that Verbalization was not a higher " l e v e l " of achievement than was Recognition. The results of t h i s experiment corroborated Heidbreder's conclusions, that while certain concepts can be expressed more easil y through one c r i t e r i o n , other concepts may be expressed more easily through other c r i t e r i a . Some graphical concepts, l i k e Fisher*s "Zalof", are composed of "elements" and "relations" for which there i s no concise expression i n a twelve-year-old boy's vocabulary. For such concepts, a r i g i d l y accurate 116 Verbalization by a young boy would be nearly impossible even when he recognized the concept correctly. Usually, for such a concept, Recognition would precede Verbalization. In such cases, scores for Recognition achievement would be higher than scores for Verbalization achievement. On the other hand, i n the present experiment, some graphical concepts l i k e "Mef* (positive presentation) and "Pog" (positive-negative situation) seem to lend themselves more ea s i l y to Verbalization than to Recognition. Accordingly, the subject's achievement of the various c r i t e r i a i s more closely related to the nature of the referent and to the breadth of the subject's vocabulary than to any alleged difference i n the inherent d i f f i c u l t i e s of the " l e v e l s " themselves. Verbalization and Recognition often give c o n f l i c t i n g evidence as to the nature of the subject's concept. Verbal-i z a t i o n i s highly subjective, while Recognition i s objective. Recognition i s the more sensitive of the two measures. This study corroborates Graham's findings that Verbalization lacks the a b i l i t y to produce part-scores for analysing concept components. Recognition, i n contrast, can be used to measure concept formation at any stage and y i e l d s numerical data convenient for s t a t i s t i c a l treatment. Accordingly, Recognition i s the c r i t e r i o n used for computing the quantitative results of t h i s experiment. As a c r i t e r i o n of concept formation, neither the 117 minimum number of words required to define a concept, nor time, i s of experimental value. The d i f f i c u l t y .of concepts varies with complexity and abstractness. Many of 'Smokers conclusions in_ h i s a r t i c l e on negative Instances are p a r t i c u l a r l y clear sighted and penetrating. He did,.hewever,. miss the great role played by the negative instances. This oversight was due to an experimental error of introducing,into an assumed purely positive learning s i t u a t i o n , the important negative instance, "You have some of i t , but not a l l of i t " . The introduction of negative instances appears to combat both r i g i d i t y ; i . e . , mental i n e r t i a , and the acceptance of incomplete hypotheses. With every experimental concept the'positive-negative presentation was antecedent to greater Recognition achievement than was the positive presentation. The experimental variable was the introduction of negative Instances. The group which saw both- positive and negative examples scored s i g n i f i c a n t l y higher than the group which saw the positive only. While the role of the positive instance i s to suggest hypotheses and orient the concept i n the whole f i e l d where the concept i s to be found, the role, of the negative i s to reject d i r e c t l y a l l incorrect hypotheses. Since the generalizing process requires both induction and deduction, the roles of the positive and negative are complementary, 118 "both are necessary, neither i s s u f f i c i e n t . 5. Educational Implications Much stress i n education has "been placed upon the ad v i s a b i l i t y of teaching from positive instances^ Teachers should reali z e that direct evidence necessary for generaliz-ation i s supplied by negative instances also. To i l l u s t r a t e t h i s , the following problem may be help f u l : -Is the combination of l e t t e r s "RSTT" a member of the same "class" as the'following combination of l e t t e r s , "1MHL", "%Gm" , "BODB"? The answer i s that there i s i n s u f f i c i e n t evidence from which to give an answer. Evidently the three examples given are not the complete series of positive instances, because the question i s asked as to whether or not "RSTT" i s an additional positive instance belonging to the "class". In solving the.problem, the following l i n e of reasoning might be used. We note that the given examples have the following characteristics in common:-(1) They are a l l c a p i t a l l e t t e r s ; (2) There are four l e t t e r s i n each group; (3) In each group one l e t t e r occurs twice, but th i s repeated l e t t e r varies from group to group; (4) The repeated l e t t e r appears at each end of the group; (5) The f i r s t two l e t t e r s are i n alphabetical order; (6) The middle two l e t t e r s are i n alphabetical order; (7) The f i r s t three l e t t e r s are i n alphabetical order. 119 Tie example "RSTT" oontains characteristics ( 1 ) , (2), (3), ( 5 ) , (6) and ( 7 ) . Characteristic (4) i s the only one l i s t e d which "RSTT" does not have i n common with the examples given. I f t h i s characteristic i s not only accept-able i n , but also necessary to, any member of the "class", then "RSTT" i s not a member. I f , on the other hand, characteristic (4) i s acceptable but not necessary, then "RSTT" i s a member of the "class". . I f i t had been shown that (a) "1MNL" , "EGHE"ana "BCDB" are members of the "class" and (b) "EEGCx" i s not, the problem could have been solved. Since "EEGG" and "RSTT" are s i m i l a r l y constructed, having a l l l i s t e d characteristics but (4), "RSTT" i s not a member of the "class". This problem demonstrates that both negative and positive instances give direct evidence necessary i n the process of generalizing. One application of the use of both positive and negative examples i n the classroom may be found i n teaching the solution of any l i n e a r equation /in one unknown. By the use of positive examples demonstrating a l l the necessary thought processes i n solving such a problem as i f 7 Y a 21 then Y = 3, teachers attempt to. lead pupils to the follov^ing generaliza-tion : to solve for the unknown, get r i d of a l l other numbers or l e t t e r s associated with i t by undoing the operations which associated them with the unknown; that i s , by applying 120 the processes which are the inverse (opposite) of those which hind these l e t t e r s or numbers, to the unknown. Even after a thorough presentation of a l l the positive examples necessary to demonstrate a l l of the processes involved i n such a problem, pupils make mistakes. A pupil might make the error of thinking that since the "7" on the l e f t side of the problem above did not appear i n the last' l i n e , i t must have been "taken away". Accordingly, i t should be "taken away" from the right side also. In working out another problem; such a pupil might make the following type of mistake:-I f 8x = 52, then x = 24 ("taking away" 8 from both sides). In such a situation as t h i s , i t would be advisable to inform the pupil that his "solution" was incorrect, i . e . , I f 8x = 52 then x X 4. The example just shown i s a negative instance. When teachers mark a pupil's solution incorrect, end then ask .the pupil to correct h i s work, the teacher i s pointing out a negative instance to the learner and then asking him to produce a positive example. Re-teaching after testing usually combines the presentation of negative instances with the presentation of positive instances. Though many teachers have given l i p 121 service, to the elimination of negative teaching and to the adoption of purely positive teaching, few of them have ceased e n t i r e l y from pointing out to the younger generation tike error of i t s ways. Accordingly, our teachers have not discarded a l l negative instances, even when pledging l o y a l t y to the cause of the purely positive. One great aim of education i s the establishment of the attitude, of suspended judgment. The positive-negative presentation has a great contribution to make to learning by supplying an impetus to caution. The use of the negative instance should be exploited to break up the r i g i d i t y of mental set. I f we can generalize from experimental procedure to classroom teaching, the value of the negative Instance to the pu p i l of low I.Q» demands that the teacher give attention to t h i s factor, The greater eff i c i e n c y of the positive-negative presentation, over the purely positive^ i n assisting toward geometrical generalizations,, warrants a very d e f i n i t e , persistent, and searching scrutiny of the educational p o t e n t i a l i t i e s of t h i s method. A negative example should be introduced at this point i n the discussion. As defined by t h i s experiment, rote learning, suclh as s p e l l i n g achievement and mastery of foreign language vocabulary, does not come int© the c l a s s i f i c a t i o n of concept formation. Accordingly, t h i s thesis and i t s conclu-sions have not any necessary bearing on the pedagogy of such subjects. 4. Suggestions for Further Research Before any great "body of research into the process of concept formation can be undertaken, certain preliminary techniques must be perfected. The two most important among these are the development (a) of group testing techniques; and (b) of concepts for use with a wide range of both chronological age and i n t e l l e c t u a l a b i l i t y . The attempt to develop a group technique could be directed along two l i n e s ; namely ( l ) the use of f i l m s l i d e s , and (2) the use of large sheets of cardboard on each of which are drawn individual, instances. In designing procedure and materials to hold the attention of the subject, f i l m slides are l i k e l y to prove useful for older pupils, while the large cards may be more suitable f o r the less mature children. For the young subjects, a l i g h t e d , rather than a darkened, room minimizes errors i n recording answers and makes supervision more easy. Each change of card at the front of the room can be employed to recapture wandering attention. Older subjects, requiring les s a l e r t supervision and having a longer attention span, could have the materials administered by f i l m s l i d e . The same type of record book could be used with both types of presentation. Ho make i t interesting, each page might be devoted, t© the Recognition responses for one concept only; each page should b© of a d i s t i n c t i v e colour; and each should contain generously spaced c e l l s designed for 123 as many response attempts as desired. (a) "With Memory" The present experiment excluded the memory factor and found that the introduction of negative instances increased Recognition achievement. I f memory had "been introduced by removing the teaching instances before the administration of the test series, would the negative instances have proved as useful? "With memory", perhaps the negative instances would have caused confusion. Both the lecture method (auditory) and moving pictures ( v i s u a l ) , as used i n teaching., are a "with memory" type of presentation. The usefulness of negative examples i n a "with memory" learning s i t u a t i o n should be determined before making generalizations from the laboratory resul t s to classroom procedures. (b) Sex Differences Is there any sex. difference i n the type of learning studied In t h i s experiment and as suggested i n (a) above? (c) Readiness to Generalize In the present experiment, i t was found that negative instances gave an impetus to caution. Test responses were required, however, at Oard No. 4 and Card No. 8. I f subjects had been allowed to wait as long as they pleased before they volunteered a response, the Recognition achievement curves might have been of a much different shape. 124 Yihat Is the influence of positive and negative instances on readiness to generalize? An experiment to answer this question would include no compulsory t r i a l s l i k e those of t h i s experiment and might incorporate several arrangements of instances other than the alternate positive and negative arrangement. (d) Incorrect Hypotheses and Achievement How does the number of previous iscorrect t r i a l s a f fect the speed of learning the concept? She answer to t h i s question has a direct hearing upon the amount.of teaching that pupils should receive before they are- required to try to solve problems. (e) Order and Frequency of Positive and Negative Instances What are the principles l i n k i n g optimal achievement with order and frequency of positive and negative instances? So determine the best order i n which to present the positive and the negative examples,-a number 'of learning situations should be prepared i n each of which the orders of the instances can. be arranged in a number of ways, Concepts such as those used i n the present experiment could be employed. (f) Maturity and Negative Instances E i i s experiment has shown that i n formulating concepts under experimental conditions, twelve-year-old boys receive assistance from the introduction of negative instances, the amount of assistance varying inversely with i n t e l l i g e n c e . 125 The cju.estlox- arises as to the usefulness of negative instances at varying l e v e l s of maturity. Perhaps an immature mind needs negative instances more than a mature mind does. On the other- hand, perhaps the immature are confused "by negative cases. To attack t h i s problem, two groups of 180 subjects each might be employed. One group might be made up of Grade One seven-year-olds, while the other might be made up of Grade Eleven seventeen-year-olds. Each group should be formed so that i t can be paired for intelligence and then s p l i t v e r t i c a l l y to form two comparable experimental groups with mean I.Q. of 100 and range from 70 to 130. The subjects should be such that they can be divided horizontally into three groups of sixty subjects, paired for i n t e l l i g e n c e , the three groups to have I ..Q. ranges of 70 to 90, 90 to 110, and 110 to 130 s respectively. Comparisons of the results of these groups should provide r e l i a b l e and enlightening information. ' /' BIBLIOGRAPHY 126 Ach, N», Uber aie Begriffsbildung, Bamberg: Buchner, 1921, v i i i and 343. ' Alpert, A., "The Solving of Problem Situations by Pre-school Children: An Analysis". T.C. Contr. to Eduo., 192-8, JTo. 323, 69. ~ Arons, L., "S e r i a l Learning and Generalizing Abstrac-tions" j A ^ J ^ ^ f ^ P s y ^ h o l o , XLV (July 1933), 417-432. Barr, A.S., "Educational Research and the Research Worker". Journal of Educational Research, Sept. 1937. Bedell, R.C." "The Relationship Between the A b i l i t y to Recall and the A b i l i t y to Infer i n Specific Learning Situations", Ph. D. Thesis, University of Missouri, 1934. Berger, D,, Unterschiede der Abstraktion sfahigheit nach. Alte r Geschlecht und Mil i e u der Schulkinder. (Age, Sex, and Environmental Differences Among School Children.in the A b i l i t y of Form Abstract Judgments). Z Kinderforsoh, 1937: 4.6, 250-282. — — Berkenblit, Z.M., "The Genesis of Concepts". Trud Inst. Mozga Bekht. 1939, 10, 21-25. Brown, W. and Wait t e l l , F„ , "Yerkes' Multiple Choice Method with Human Adults", J . 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Duncker, K., "Zur Psychologic des Produktiven" Denkins, B e r l i n J u l i u s Springer, 1935, v i i & 135. 19. English, H.-B., "An Experimental Study of Certain I n i t i a l Phases of Abstraction". American Journal of Psychol., 1922,33,305-350. 20. Eggers, "W.J., "An Experimental Study of Children's • Reasoning by The Multiple Choice Method": M.A. Thesis, University of C a l i f o r n i a , May 1933. 21. Ewert, P.H., and Lambert, J.F., Part I I "The Effect of Verbal Instructions upon the Formation of a Concept". J. Genet. Psychol., 1932, 6, 400-413. 22. F i e l d , Paul E., "Studies i n Concept Formation" 1. The Development of the Concept of Triangularity by the 'White Rat. Pomp. Psychol. Monog. 1932, 9 No. 2. 23. Fisher, Sara C. , "The Process of Generalizing Abstraction; and i t s Product, the General Concept". Psychol. Monog. 1920, 28, No. 2 . * 24. Fowler, H.L., "The Development of Concepts": "An Inves-tigati o n into the Methods of Teaching". B r i t . J. Educ. Psychol., 1931, 1, 13-40. 25. Garrett, Henry E., S t a t i s t i c s i n Psychology and Education Longman, Green & Co., Toronto. >? 26. Gellerman, L.W., "Form Discrimination i n Chipanzus and Two-year-old Children". J. Genet. Psychol., 1933, 42, 3-27. -27. Gengerelli, J.A. "studies i n Abstraftion of "White Rat". Ped. Seminar and J? Genet. Psychol., 1930, 38,171-202. 28. Gengerelli, J.A., "Mutual Interference i n the Evolution of Concepts". ,. Amer. J. Psychol., 1927, 38, 639-646. 29. Gibson, E,J,, and McGarvey, H.R, "Experimental Studies of Thought and Reasoning". Psychol. B u l l . 1937? 34, 327-530. 30. Graham, J.L., "Learning to Generalize". Psychol. Monog. 1938, 50, No. 5, 8 4 - I I 5 . 128 Gray, J.S. "A Behavior!sties Interpretation of Concept Formation". Psychol. Rev., 1931, 38, 72. Hamilton, G.U. "A Study of T r i a l and Error Reactions i n Mamals". Journal of Animal Behavior, I (Jan.-Feb., 1911), 33-66. — — Hanfmann, E., "Concept Formation Test i n Schuzophrenia". Psychol. B u l l . , 1936, 33, 296, Abstract. Hanfmann, E., "Personal Patterns i n the Process of Concept Formation", Psychol. B u l l . , 1940, 37, 515 Abstraot, Hanfmann, E., and Kasanin, J. . "A Method for the Study of Concept Formation", J . Psychol., 1937, 3, 521-540. Haught, B.F. , "The Interrelation of Some Higher Learning Processes", Psychol, Monog. Whole No. 139, 1921, 71. H a z l i t t , Y., "Children's Thinking", B r i t . J. Psychol., 1929730, 20, 354-361. " Heidbreder, E.F., "Language and Concepts". Psychol. B u l l . 1 9 3 6,33 , 7 2 4 . — ~~ Heidbreder, E.F., "A Study of the Evolution of Concepts". Psychol. B u l l . , 1934, 31, 673. H u l l , C.L.j "Quantitative Aspects of the Evolution of Concepts". Psychol. B u l l . , 1934, 31, 673. H u l l , C.L., Psychol. Monog., 1920, 28, #123. James W. , P r i n c i p l e s of Psychology, Yol. I , H. Holt, N.Y. , 1905l — • -Kinnanion, A.J. , "Mental L i f e of Two Macacus Rhesus Monkeys i n Captivity". Am. Journal of Psychol. XIII (Jan. & A p r i l , 1902), 98-148, T73-218* Kuo, Z.Y. , "'A Behavioristic Experiment on Inductive Inference". J . Exper. Psychol., 1923, 6, 247-293. Long, L., "Concept Formation i n Children", Psychol. B u l l * , 1939, 36, 550-551 Abstract. Maier, N.R.F., "An Aspect of Human Reasoning". B r i t . J . Psychol. B u l l . , 1936, 33, 724. Matheson, E, , "A Study of Problem Solving i n Pre-School Children". Child Develop, 1931, 2, 242-262. 129 48. MoGeoch, J.A. and Oberachelp, V.J".} "The Influence of Length of Problem and Transfer upon Rational Learning and i t s Retention". General Psychol., 1930, 4, 154-170. 49. M i l l e r , I.E., The Psychology of Thinking, . New York, MacMillan 1917, 192. " "~~ "— 50. Moore, T.V., "The Process of Abstraftion". Univer. of C a l i f . , Publ. i n Psychol. 1910, 1, No. 2. 51. Mott, S.M., "The Growth of an Abstract Concept". Child Develpm., 1939, 10, 21-25. 52. Munn, N . L i , and Stiening, B.R., "The Relative Efficiency . of Form and Background1 i n a Child's Discrimination of Visual Patterns". J". Garret Psychol. 1931, 39, 73-90. 53« Ovsepjan, G.T., "The Evolution of Observation i n Children". Soi. Mlm. Pedog. Inst, Herzen, 1939, 18, 21-59. 54. Patton, E.K., "The Problem of Insig h t f u l Behavior", Psychol. Monog. , 1933, 4-4, No. 197, 198-124. 55. Peterson, J.C., "The Higher Mental Processes i n Learning" Psychol. Monog., 1920, 28 No. 7, 5 6 . Peterson, JVC., "Experiments i n Rational Learning", Psychological Review XKV (Nov, 1918.), 443-467, 57. P r a t t , C.C., "Experimental Studies of Thought and Reasoning". Psychol. B u l l . , 1928, 25, 550-561. 5 8 0 Radlinslsa - Ostaszewska, J , , (On the Nature of so-called Clear but I n d i s t i n c t Concepts). Kwart. Psychol. 1935, 7, 393-470. 59, Rees, H., and I s r a e l , H., "An Investigation of the Establishment and Operation of Mental Sets". Psychol. Monog., 1935, 46, No. 210, 1-26, 60. Roberts, K.E., " A b i l i t y of Preschool Children to Solve Problems i n which a Simple P r i n c i p l e of Relationship i s Kept Constant". Pedagogical Seminary, XL (March, 1932, pp, 118-135)i 61. Roberts, K.E., "Learning in Pre-School and Orphanage Children". Univ. Iowa Stud., Stud, i n Child Welfare, 1933, 7, No. 3 , 94, 62, Roslow, S., "A S t a t i s t i c a l Analysis of Rational Learning Problems", J . Genet. Psychol. 1936, 48, 441-467. 1 F, S e l l s , S.B., "The- Atmosphere Effect; An Experimental Study of Reasoning". Arch of Psychol. 1936, 2 9 , No, 2 0 0 , Sibano, M., ."Concept Formation as Productive Thinking' 9. J. Psychol., 1 9 ? 8 , 1 3 , 389-400. S i i p o l a , E.M., "A Group Study of Some Effects of Prepar-atory -Set". Psychol. Monog.. 1935, 46, No. 210, 2 7 - 3 8 . Smoke, K.L., "Negative Instances i n Concept Learning". J. Exper. Psychol., 1 9 3 3 , 1 6 , 583-588. •Smoke, K.L., "The Experimental Approach to Concept Learning", J . Exper. Psychol., 1935, 42, 2 7 4 - 2 7 9 , Smoke, K.L*, "An Objective Study of Concept Formation". Psychological Monographs XLII Whole No. 191 , 1932, 8. Stevanovic, B.P., "An Experimental Study of the Mental Processes Involved i n Judgment". B r i t . Journal of Psychol. (Monog. Supp.), 1927, XII, 138. Sul l i v a n , E.B., "Attutude i n Relation to Learning". Psychol. Monog. 1927, 3 6 , No. 169, 149. Tyler, F.T., "Generalizing A b i l i t y of Junior High School Pupils: An Experimental Study of Rule Inductions": Unpublished Ph. D. Thesis, Univ. of Oalif. Vedenov, A.V., "On the Question of Experimental Investi-gation of the Structure of Concepts", Bekht. Inst. Brain Res. 2 0 t h Anniv. 1938, 6 5 - 6 6 . Warren, H.C. and Carmichael, L., Elements of Human • Psychology, Houghton M i f f l i n Company, New York, 1 9 3 0 . (The Riverside Press, Cambridge). Welch, L., "A Preliminary Study of the Interaction of Confliction Concepts of Children Between the Ages of 3 and 5 Years". Psychol. Rec. 1938, 2 , 439-459. Welch, L., "The Span of Generalization Below the 2-year Level", J . Genet. Psychol., 1939, 5 5 , 269-297. Welch, L., "The Development of Size Discrimination Between the Ages of 12 and 49 Months", J. Genet. Psychol. 1939, 5 5 , 243-268. Welch, L«., "A Preliminary Investigation of Some Aspects of the Hierarchical Development of Concepts", J . Genet. Psychol. 1940, 2 2 , 359-378. 131 7 8 . Welch, L., "The Genetic Development of the Associational Structures of Abstract Thinking", J , Genet. Psychol. -1 9 4 0 , 5 6 , 1 7 5 - 2 0 6 . ~™ " 7 9 . -Welch, L. and Long, L., "The Higher Structural Phases of Concept Formation of Children", J.- Psychol.., 1940, 9 , 5 9 - 9 5 . ' 8 0 . Welch, L., and Long, L., "A Further Investigation of the Higher Structural Phases of Concept Formation", J. Psychol. 1940, 1 0 , 2 1 1 - 2 2 0 . 8 1 . Ifilhelm, "W. , "Bertrage Zur Psychologie des Schliessens", Arch f.d. ges. Psychol., 1 9 5 3 , 8 9 , 3 7 1 - 4 2 8 . 8 2 . ' Wilkins, M.C., "The Effect of Changed Material on A b i l i t y to do Formal S y l l o g i s t i c Reasoning", Arch of Psychol., 1 9 2 8 , 1 6 , No. 1 0 2 , 8 3 . 83. - Wolff, F.F., Concept, Precept and Reality. P h i l . Rev., New York. 1 9 3 9 , 4 b , 398-414. 8 4 . Woodworth, Experimental Psychology, H. Holt & Co., ' New York, 19 3 « . 8 5 . Yerkes, R.M., "A New Method of Studying the Ideal Behavior of Mentally Defective and Deranged as Compared with Normal Individuals", Journal Comp. Psychol., 1921 , 1, 3 6 9 - 3 9 4 . (i) A P T E N D I X. PROCEDURE (i n detail) On coming for his one experimental period, the subject was given the following verbal instruction: To establish rapport: "Would you l i k e to come over here? I have asked your teacher to l e t you come to help me. You would l i k e to do that, wouldn't you? Here are some interesting puzzles for you to do. They are different from any you have ever done before. I think you w i l l l i k e them. You l i k e working puzzles, don't you? I w i l l show you how to do the f i r s t one. Subject's introduction to the test situation: "I have here the- picture of a Dax. Now you do not know what a Dax i s , nor have you ever heard of one. When I t e l l you to, you w i l l turn these cards over", (pointing to the teaching pack which has been placed face downward i n readiness on the table). "Some are Daxes and some are not. The puzzle i s to figure out what a Dax i s . Turn over as few cards as possible. The fewer cards you have to turn up before you figure out what a Dax i s , the higher your score w i l l be. However, the important thing i s to get i t ri g h t . I f you do not get i t right the f i r s t time you can change your mind and t r y again." (The subject i s seated to the l e f t of the experimenter ( i i ) The cards are placed face downward and i n order from §1 to 8, with #1 on top, and within the subject's reach between him and the experimenter). P 0 SITIYE-N EGAT IT E PRESENTATION "The f i r s t card you turn over i s a Dax. Now turn i t over and place i t here." The cards were then turned over one at a time so that a l l 8 examples were exposed to the subject's view. As the examples were turned over they -were placed i n front of the subject i n two columns of four cards each with odd-numbered (positive) cards i n the left-hand column, and even-numbered (negative) cards i n the r i g h t , cards #1 and #2. farthest from the subject, and #7 and #8 nearest to him. "Now turn over the next card (#2) and place i t here. This i s not a Dax. As you turn over the rest of the cards you w i l l place the next one ($3, a pos i t i v e Instance) here. I t w i l l be a picture of a Dax. The next card you turn up you w i l l place here, because i t i s not a picture of a Dax..." etc, (Using t h i s exact wording, the investigator leads the subject to understand that a l l examples i n the left-hand column WERE Daxes, and that EYERY instance to the right as not a Dax.) (Pointing to where the p o s i t i v e instances go:) " W i l l the cards you place here be Daxes, or not? (The experimenter - ( i i i ) got the answer that they WOULD he Daxes.) "The cards that you place here (indicate the place where the other column would be) w i l l they be Daxes, or not?" (The answer was that they would NOT be Daxes). (1 and 2 were then replaced on the pack and the subject instructed as follows;) "Try to f i n d out what a Dax i s . Do not turn up any more cards than you have to. T e l l me as soon as you think you know what a Dax i s . Now go ahead and turn up the f i r s t card. This i s a Dax." (As soon as the subject thought he knew what a Dax was, the experimenter instructed him as follows:) "The answer that you are going to give me now may be right or i t may be wrong. After you have given me your answer you w i l l be able to look through the rest of the cards, I f you are r i g h t , when you see these cards you w i l l not want to change your mind, but i f you are, wrong, probably these cards w i l l make you want to. Don't be afr a i d to change your mind. The important thing i s for you to have found out what a Dax i s . " (The responses on the Verbalization l e v e l were recorded word-for-word i n the booklet, as already described). (Taking the test pack, arranged i n s e r i a l order, with #1 on top and #1& on the bottom, the experimenter exposed the cards in succession, instructing the subject to say either, "Dax" or "Not Dax". The author noted errors mentally (iv) or I f there were too many he remembered the right responses instead of the wrong, or tipped the cards so that the cards for which incorrect responses were given f e l l out of li n e with those,correctly named. After the subject had responded to every card i n the Recognition t e s t , c i r c l e s were placed i n the booklet around the numbers of the cards incorrectly named. Entry i n the "Number./Wrong" column was deferred u n t i l the subject had finished the test and had l e f t the room, because such recording i n his presence would have given him an external clue to the acceptability of h i s responses.) (Giving the record booklet to the subject, the experimenter said:) "Draw one Dax i n each of these squares", (pointing to the appropriate frames i n the booklet). " I f you can, make each picture different from any other pictures you draw, and make your pictures different from any of these examples" (indicating the p o s i t i v e instances exposed on the table). (After taking a sampling of the subject's ideas by each of the c r i t e r i a , Verbalization, Recognition, and Repro-duction, and regardless of whether the responses were success-f u l or not, the subject was Instructed to inspect the remainder of the teaching pack.) Your answer may be right or i t may be wrong, I am not allowed to t e l l you which. But the rest of these cards w i l l t e l l you. I f the rest of these cards makes you change your mind as to what a Dax i s , t e l l me. Each time you turn up a •(vi-car a , , say either, 'I think the same' or 'I change my mind'. Now turn up these cards," (If after turning up any card, the subject did not spontaneously say whether he had changed his mind or not, the experimenter asked him the question, "Do you think the same, or do you change your mind?" This forced the subject to make a decision and to reveal a modification of his concept on the card at which he recognized the change.) (Test attempts were made on any card at any time the subject wished. In addition to these voluntary testings, compulsory samplings were taken on Card 4 and Card 8 even though (1) the subject had already correctly formulated the concept at the three l e v e l s , and even though (2) he thought he did not know the concept,) (If after exposing a l l 8 cards of the teaching pack, the subject was s t i l l unable to make the successful general-i z a t i o n of the "Dax", the writer told the subject what a Dax was and showed him that each positive instance was a Dax, and that each negative instance was not a Dax, 1/Vhen the experimenter was s a t i s f i e d that the subject understood the experimental s i t u a t i o n , he presented to the subject the 8 experimental concepts.) "Now that you have learned a Dax, you w i l l be shown some more puzzles. This f i r s t one has been used just to show you how to go about doing these others. I f you do not under-stand any part of what you are to do, please ask me about i t ? . . (vl) nowon (After giving any necessary explanations, the 8 experimental concepts were administered similarly.) POSITIVE PRESENTATION In the positive presentation exactly the same instructions were given as i n the positive-negative, except that a l l the Instances i n the teaching pack were po s i t i v e , and a corresponding change of wording was necessitated. As has been stated previously, careful precaution was taken that the experimenter gave the subject no indication as to whether his responses were correct or incorrect. The subject was made to rely upon the eight cards i n the teaching pack to inform him whether or not his concept had been acceptably formed. To give uncontrolled external evidence on t h i s question i s to obscure one of the chief contributions of the negative examples. 

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