European Journal of Psychology of Education1990, Vol. V, n? :!, 191-206© 1990, l.S.P.A.

A Process Theory of Inductive ReasoningTested by the Teachingof Domain-Specific Thinking Strategies

Karl Josef KlauerUniversity of Aachen, Federal Republic of Germany

Inductive reasoning can be conceived as the process of discoveringregularities by finding out identity and difference with respect toattributes of and relations between objects. This assumption gives riseto the definition of a set of inductive tasks consisting of six subsets,all of which can be solved by variantsof a basic strategy. Such a theorycan be tested by teaching subjects the strategy, ie. by trainingexperiments: Inducing the postulated processes should lead to predictableimprovements in certain tasks and to no improvements in other tasks.The article provides an account of the main results of about 30experiments. The theory seems to be sound and the training approachproved to be a powerful research method: A greatnumber ofdifferentialeffects, partly considerable in amount, have been predicted andempirically tested, most of them even by several replications. Transfereffect of an inductive thinking training on intelligence test performanceis about twice as great as an average test coaching effect.

The cognitivist turn in psychology led to an increased interest in attempts at improvinghigher-order cognitive processes. More or less comprehensive and critical summaries of differentapproaches are given by Chipman, Segal, and Glaser (1985), Detterman and Sternberg (1982),Nickerson, Perkins, and Smith (1985), Resnick (1987a, 1987b), Schwebel and Maher (1986),Segal, Chipman, and Glaser (1985), and Sternberg (1983). The purpose of this article is toinform about a recently proposed process theory of inductive reasoning and its applicationin training experiments. Whereas an earlier publication concentrated on the theoretical aspectsof inductive thinking and particularly on the paradigmatic approach of the training procedure(Klauer, 1989d), the stress of this contribution lies on experiments designed to test hypothesesderived therefrom. The main aspects of the theory, nevertheless, have to be sketched briefly.

A process theory of inductive thinking

Inductive thinking is called for whenever a rule, a law, or, more generally, a regularityhas to be discovered. Though factor analytic research was able to show that certain kinds

Theoretical, methodological, and educational implications are briefly discussed.

192 K. 1. KLAUER

of tasks constitute factors like Reasoning or Induction or Inductive Reasoning, it was, dueto the methodology used, unable to reveal the processes underlying such factors. The coreof our theory is very simple. Its basic assumption is that regularities are discovered by certaincomparison processes. More specifically, it is assumed that the comparison process consistsin the processes of discovering identity or difference or both with respect to attributes ofobjects or relations between objects. Discovering identity of attributes is required by taskslike classifications or similarities, whereas discovering identity of relations is demanded by

Table 1Inductive reasoning items - attributional

GENERALIZATION (GE)

Discovering classes: Underline those 3 items which have one feature in common that theother two do not have.herring finch raven trout parrot

20 50 42 18 10

Adding to classes: Underline the optimal answer fitting best to the given items.

socks slipper stocking sandal a) eye b) boot c) toe d) shirt50 25 30 45 a) 57 b) 13 c) 60 d) 24

D 0 .0 d al!l1 b) 0 co) D 0) ((J)Similarities: Underline that one which has most in common with the given item.

fir a) oak b) ivy c) rose d) pine

7 a)6 b)15 c) 12 d)5

, alO hl~ dl OlO

DISCRIMINATION (DI)

Underline that one which does not fit in with the others.

Chair sofa stool table bed

12 16 14 18

CROSS-CLASSIFICATION (CC)

The fourfold table shows the possible combinations of two attributes (+ +, + -, -+, --).Find the field in which the right hand item fits in best.

daisy

picture-book

(5)

dandelion

Tableau 1Taches de raisonnement inductif - attributives

A PROCESS THEORY 193

tasks like series or analogies. Finding out differences between attributes is needed when onehas to detect an item not belonging to a group of others, and between relations, when onehas to rearrange a disturbed series (of numbers, or symbols, or words). Recognizing bothequality and difference is required with respect to attributes when solving tasks like cross­classifications, and with respect to relations, when solving items like matrices. Illustrativeexamples of test items are given in Thble 1 and 2.

Table 2Inductive-reasoning items - relational

RECOGNIZING RELATIONS (RR)Series: Order the following items in a meaningful waydressing, waching, getting up, having breakfast, going to school9 6 12 3 15

o o •Adding to a series: Complete the following series according to the rule.Sweden Denmark Germany Austriaa) Czechoslowakia b) Italy c) Spain d) Great Britain18 20 16 18 14 a) 11 b) 16 c) 8 d) 21

A 0 A 0 A AI6 b) 57 e) 0 4"~.Simple analogy: Find out the item which completes the second row so that between thetwo items of the second row the same relation holds as holds between those of the first row.

hands : soapteeth ?

3 126 ?

\l ~~6: ?

a) towelc) watera) 16c) 22

A)~ b) Vc) AA d)~~

b) dish-clothd) tooth-pasteb) 24d) 18

DISCRIMINATING RELATIONS (DR)

Disturbed series: Underline the item which disturbs the given order.Mouse cat lion worm elephant

14 21 42 28 35

o 6 ~ <3 8)SYSTEM FORMATION (SF)Complete analogy: Between the items of the first row a certain relation holds, another holdsbetween the items of the left hand column. Find out the item which fits in the open fieldso that in both rows the first relation holds and in both columns the second one.

garden furniture

garden

garden chair

?

a) garden table

c) balcony

b) lawn

d) flowerbed

MatrixA) 0 b) (j}

clO dl 0

Tableau 2Taches de raisonnement induetif - se referaru aux relations

194 K. J. KLAUER

Inductive reasoning items are used in nearly every intelligence test. This is one reasonwhy modern cognitive research stresses the experimental analysis of the processes going onwhen solving items of that kind (Glaser, 1984; Goldman & Pellegrino, 1984; Putz-Osterloh,1981; Shye, 1988; Snow, 1980; Sternberg, 1977). But instead of analyzing the processes ofsolving single item forms descriptively and looking later for «unities in inductive reasoning»(Sternberg & Gardner, 1983), I try to begin with the assumption of such unities. The assumedunities are components of the comparing processes just mentioned.

The postulated comparison process requires abstract and analytic thinking because objectsare not compared as wholes but with respect to features and to relations holding betweenthem. Moreover, it can be shown that the comparison process, if it is both effective andefficient, requires metacognitive components and strategies like these: Keeping in mind thestructure of the superordinate goal and the results of past comparisons, choosing more orless systematic strategies when comparing different features or relations in order not to overlookthe relevant ones or, alternatively, establishing hypotheses and testing them successively,checking one's own solution by an inverse process, and so on.

Experimental analysis of such process components encounters several well-knownmethodological drawbacks. This is one reason why we tried an alternative approach, thetraining experiment. The rationale of such an experiment is that specifiable transfer effectsare predictable if subjects can effectively be trained to perform certain of these processcomponents.

Methodological aspects

Until now, about 30 experiments have been performed to test hypotheses derived fromthe theory or to replicate our own experiments. In most cases we used pretest-posttest designswith twoor morerandomized groups, the groups differing in treatment. The teaching methodsvaried from a more or less directive cognitive-behavioral procedure of verbal self-instruction(Meichenbaum & Goodman, 1971, Meichenbaum, 1985) to more indirect procedures of guideddiscovery or of self-reflection. Based upon these experiments, we recommend a kind ofparadigmatic teaching which is sketched in Klauer (1989d) and which is elaborated in themanual of our first training program for 5- to 7- year-old children (Klauer, 1989a).

Defining effect size

We did not confine ourselves to significance tests but added information about the effectsizes found, because most of our hypotheses consisted in expectations about the differentialeffect sizes of the treatments involved. Therefore, it seemed advisable to assess the effectsizes directly. We decided in favor of Cohen's (1977) measure of effect size d = (xE-xC)IsO where xE and xC represent the means of the experimental (E) and control (C) group,respectively, and Sc the standard deviation of the control group. This measure is very oftenused in meta-analysis, is simply computed and easily understood. Thus, d = 1 means thatthe experimental group outperformed the control group for one standard deviation. Cohen(1977) terms d = 0.2 a small effect, d = 0.5 a medium effect, and d = 0.8 a large effect.

Using small-group experiments, as we did, considerable random variation of d is tobe expected. Whenever pre-experimental differences made it advisable, we used a correctedd (d* = dpost - dpre)'

Defining transfer distance

Within the present theoretical framework it is expected that the transfer effect, measuredby d, will decrease as transfer distance increases. Quantitative measures of transfer distancehave recently been developed and empirically tested (Klauer, 1989 c).

A PROCESS THEORY 195

According to the theory sketched earlier, inductive reasoning is influenced by three facets.

Facet A: Kind of comparison (identity, or difference, or both),Facet B: Kind of units to compare (attributes or relations),Facet C: Kind of material (verbal, numerical, figural etc).

Transfer of training may occur when training and test materials differ with respect toone or more of the facets. It is, however, also possible if training and test items are differentbut characterized by the same facets. In this case we speak of nominally parallel tests andexpect maximal transfer of training. Thus, the number of facets varying between trainingand test items is a measure of transfer distance D. In its simplest form transfer distanceD between a training and a test item is defined as

vD = E <XI' d,

1'=1

where dr equals 1 if both tasks differ with respect to facet r and equals 0 if both tasksdo not differ with respect to that facet and where <XI' is the weight attributed to facet r.The weights are to be determined theoretically or must be estimated empirically. For moredetails and more complex formulas see Klauer (1989 c).

Selected results of research

Question 1: Can inductive thinking be trained?

The first question to be answered is whether inductive thinking can effectively be taughtat all, particularly since authors like R.M. Gagne (1980) doubt that learning and problemsolving strategies can be subjected to intentional teaching. It is clear that the improvementof thinking processes cannot be shown by an improvement in solving the tasks incorporatedinto the training program but only by transfer of training. This implies that training andtest items must not be identical. The largest transfer effects, however, are to be expectedif training and test items are different but nominally parallel, i.e. if they belong to the samesubset of inductive tasks.

In order to show that training one kind of inductive tasks transfers to different tasksof the same kind, Herbrand & Henze (see the short version in Klauer, 1989a) performeda three group experiment. The first group (N = 10) was trained to solve figural cross­classification tasks (see Table 1). The second group (N = 10) was trained to solve otherinductive thinking tasks, whereas the control group (N = 20) participated in the normalclassroom activities. One of the posttests consisted of different figural cross-classificationtasks. We expected the median of the first group to be greater than the median of the secondgroup and the latter greater than that of the control group. The means were Xl = 19.5,x2 = 14.2, and x3 = 12.65. The Yonckheere trend test (Lienert, 1978) yielded a significantresult (p < 0.01). For the first group an effect size of d = 1.54 resulted.

Six other experiments have been performed which at least once tested the hypothesisof trainability of inductive thinking in a comparable way (Table 3). A. median effect sizeof d = 1.54 and a mean effect size of a = 2.04 resulted. It can be concluded that traininga certain kind of inductive tasks yields considerable transfer on new items of the same kind.Trained subjects outperformed control subjects on the average for more than one standarddeviation.

Question 2: Does a training of discovering identity improve the discovering of differences,and inversely?

The theoreticallyassumed comparison processesinvolve discoveringidentity and difference.Because both results are mutually exclusive, one result can be checked by the other: If, for

196 K. 1. KLAUER

Table 3Transfer effect size «d» when training and test items are parallel, i.e. are different but havethe same facet components

Project 1 Training and test material d Significant ?

Maihack (1984) Figural discrimination 1.89 +N = 20 Figural generalization 4.48 +

CMM2 1.38 +

Meiss & Rakowski (1984) Recognizing figural relations 1.37 +N = 50 Discriminating fig. relations 2.07 +

Theine-Schule (1986) Figural & verbalN = 21 system formation 1.40 +

Herbrand & Henze (1987) Figural cross-classificationN = 40 1.54 +

Arns & Stock (1987) Figural cross-classificationN = 48 2.88 +

Hols & Dreier (1987) Verbal cross-classificationN = 30 2.91 +

Tarraber & Perret (1985) Recognizing figural relations 1.00N = 48 Discriminating fig. relations 1.54 +

a = 2.04 (SD = 1.02)

Note. I For more information see the abridgment in Klauer (l989a), or Masendorf (1988), Masendorf & Klauer (1986),and Masendorf & Maihack (1986); 2 Different forms of the Columbia Mental Maturity Scale

Table 3Grandeur «d» de l'effet de transfert quand les tiichesd'entrainement et de test sont paralleles,c-a-d. quand elles sont differentes mais ant les memes composantes de facette

instance, identity with respect to a certain feature is the rule looked for, no difference withrespect to this feature must be found unless the solution was incorrect. Hence, wheneversubjects are instructed to control their own solution appropriately, both of the processesare made use of during training. In this case, a transfer effect is to be expected when facetA varies between training and test, that is when training and test tasks call for differentcomparison processes. We expect an effect size d greater than zero but smaller than themean of Table 3, where no facet varies.

In a rather complex design Tarraber and Perret (Klauer, 1989a) trained 48 mildly retardedchildren according to four different treatments (each treatment N = 12). Four dependentvariables were given, RR, DR, and two variants of SF (see Table 2). Training and test materialwas figural in nature if not stated otherwise. Six conditions called for a shift between trainingand test from recognizing identity to recognizingdifference or in the reverse order. The observedeffect sizes d are as follows.

A PROCESS THEORY 197

Training Test d

RR DR 1.13RR SF 1.56RR SF (verbal) 0.94DR SF (verbal) 0.18DR SF 0.66DR RR 0.63

For each of the four dependent variables a specific trend between the group means waspredicted. Only one of the predicted trends failed to reach statistical significance when testedagainst an adjusted Ci* = 0.05/4 = 0.0125.

Three other experiments allowed us to test the same hypothesis (Hols & Dreier, Dorna& Stroter, Winkelmeier & Latsch, cf. Klauer, 1989a). Five of the eight significance tests yieldedsignificant positive results. With eight significance tests and p = 0.05 only three significantresults can be expected by chance (p < 0.05). Hence, a transfer effect has taken place. Witha mean (J = 0.82 (SD = 0.48), its amount is greater than zero and less than that of Table3, as was expected. The conclusion is that learning to solve inductive thinking by itemsrequiring one type of comparison process transfers to solving such items requiring the othertype of comparison process - at least if there is no shift in facets B or C.

Question 3: What is learned during our training, structures of inductive thinking or piecesof declarative knowledge?

This question is, in a sense, a crucial one. Transfer of training can consist in the transferof declarative: knowledge or in the transfer of procedural knowledge, or in both. If, forexample, a number of tasks are solved which deal with garden plants, a body of declarativeknowledge about garden plants will be acquired or become more retrievable so that newtasks about such plants might more likely be solved. If, however, such a training rendersthe solution of, say, numerical or geometric-figural tasks more probable, the situation isquite different. In this latter case we can speak of improved thinking and problem solvingprocesses because transfer can only consist in transferring procedures instead of declarativeknowledge. In order to test whether or not the inductive-reasoning training enabled the subjectsto apply the acquired thinking processes in areas of different declarative knowledge, a shiftin the material facet C between training and test tasks was realized. This is a very strongtest. Normally it would be sufficient to remain within the same class of material, e.g. verbalmaterial, and to shift to another topic, e.g. from a biological to a historical topic. Becauseof the importance of the present question we preferred to shift to quite a different classof material.

Duda-Schreyer (Klauer, 1987a) trained N = 30 children in a kindergarten setting tosolve discrimination tasks (see Table 1) with verbal material. Tho discrimination posttestswere given, one with pictures, the other with geometric figures so that no declarative knowledgebut only thinking procedures acquired during training could be transferred to the posttest.Nevertheless, the training group outperformed the control group significantly and yieldedeffect sizes of d = 0.98 and d = 1.88, respectively.

Table 4 gives a complete picture of the replications being done thus far. It containsall of the experiments in which at least the kind of material used in training and test varied.The mean effect size of this transfer is about one standard deviation, an astonishingly highvalue. Yielding 11 significant results when 15 tests at a significance level of p = 0.05 areperformed, cannot beexplained by chance (p < 0.01). Hence, the conclusion is that the studentsreally learned to transfer thinking processes into new contexts.

198 K. 1. KLAUER

Table 4Transfer effect sizes when thinking structures are to be applied to different material (i.e. whenat least facet C varies)

Project Training material Test material d Significant ?

Stegmann verbal & geometric- 0.70 +(Klauer, 1987b) numerical figuralN=45

Kolmsee verbal & geometric- 0.30 +(Klauer, 1987b) numerical figuralN=35

Rudol verbal & geometric -0.14(Klauer, 1987b) numerical figuralN=30

Duda-Schreyer verbal pictorial 0.98 +(Klauer, 1987a) geom.-fig. 1.88 +N=30

Rink verbal pictorial 3.48 +(Klauer, 1987a) geom.-fig. 2.26 +N=30

Arns & Stock figural verbal 1.27 +(Klauer, 1989a) -0.30 +N=48

Hols & Dreier figural verbal 1.08 +(Klauer, 1989a) verbal figural 1.21 +N=30

Dorna & Stroter figural verbal -0.23(Klauer, 1989a) verbal figural 0.16N=44

Mailandt figural verbal & 1.45 +(Klauer, 198ge) numericalN=33

Biirstinghaus real objects(Klauer, 1989d) pictures figural 0.28 +N=30 words

a = 0.96 (SD=1.04)

Tableau 4Grandeur «d» de l'efjet de transfert quand des structures de raisonnement doivent etreappliquees a des matieres differentes (c.-a-d. quand, au mains, facette c varie)

A PROCESS THEORY 199

Question 4: Does comparing attributes improve comparing relations, and inversely?

A change in facet B between training and test implies a change between attending toattributes and attending to relations. The expectation is that discovering identity or/anddifference with attributes facilitates discovering identity or/and difference with relations ­and vice versa. For experimental purposes it is, however, necessary to train attending to oneof these units more or less exclusively for a longer period so that a set of the Luchins type(Luchins, 1942) might be originated. Such a set should lead to a deterioriation of the lasttask if it is to be solved by a procedure that differs from the procedure being called forby the preceding tasks. Hence, when one type of inductive tasks has intensively been trainedand a different type of inductive tasks is given as test items, then we expect the superimpositionof a positive transfer effect by a negative set effect so that the resulting effect should besmall - small positive or small negative - but in either case small.

Hiltz (Masendorf, 1988; Klauer, 1989a) trained N = 30 mildly retarded children. Onegroup was trained to attend to attributes and tested with material requiring attention torelations. Hence, a change in facet B between training and test had taken place. A significantpositive effect of d = 0.48 resulted. Using the same kind of children three other experimentswere performed. Arns and Stock (Masendorf, 1988, Klauer, 1989a), included N = 48 children.Two of their groups received a training with tasks requiring to attend to relations whereasthe test tasks were of the opposite type. Small but significant negative effects resulted (d= -0.29 and d = -0.30). In a similar study with N = 44 children two insignificant effectsizes were found, d = 0.05 and d = -0.23 (Dorna & Strater, cf. Masendorf, 1988; Klauer,1989a). Using N = 40 children, Hols and Dreier even found evidence that a pretest requiringthe subjects to attend to relations significantly reduces the effect of a training requiring thesubjects to attend to attributes (Masendorf, 1988; Klauer, 1989a).

laking all this together, one can conclude that the empirical evidence is in accordancewith the expectation, It is possible that in such training experiments a positive transfer anda negative set effect are superimposed. In the educational application it is advisable to avoidthe occurrence of such set effects by mixing the different types of tasks appropriately.

Question 5: Domain-specific effects of a domain-specific training?

It has been shown that the facets A, B, and C play a certain role in determining thetransfer effects of training studies in inductive reasoning. Actually, it is possible to predictthe amount of transfer effect from information about the facet structure of the tasks includedin training and test. Hence, the next step is to combine the information about the threefacets in predicting the transfer effect. The above-mentioned measure of transfer distanceD as the weighted sum of the differences in facet composition has recently been proposed(Klauer, 1989 c). This measure can be applied to our problem.

What kind of relation is expected to hold between transfer effect d and transfer distanceD? If our domain-specific training leads to domain-specific effects, one should expect anegative correlation and hence a linearly decreasing function between transfer effect andtransfer distance. If, on the other hand, the transfer effects have to be traced back to moregeneral improvements, for instance to improved general problem-solving strategies, nocorrelation at all will be expected.

Based upon N = 73 pairs of values, the correlation yielded a significant result of rdD= -0.53. The transfer effect can be predicted by the transfer distance to a considerable amount,and it is clear that the transfer effect decreases as the transfer distance increases (Figure1). One can conclude that the effect of a training of inductive reasoning is basically domain­specific as was expected. The training mainly enables the subjects to better deal with itemsof the domain of inductive thinking tasks.

The existence of the set effect has been confirmed by an additional multiple correlationRd.A,B,C' Its unstandardized b-weights for the three facets were about 1,2, and 1, respectively,indicating the stronger influence of a shift between training and test in facet B.

200 K. 1. KLAUER

Figure J. Effet de transfer en tant que fonction de la distance du transfert (N 73)

2.0

1.8

1.6

1.4

Transfer1.2

Ettec td 1.0

0.8

0.6

0.4

0.2

1.0 2.0 3.0 4.0 5.0

Transfer Distance D

Figure 1. Transfer effect as a function of transfer distance (N 73)

Another point, however, seems to be of interest. In the present context, the transferdistance measure D roughly varies between zero and five. With D = 0 we are dealing withtransfer to a nominally parallel test, i.e. transfer to different items of the same type. Thiskind of transfer occurs in experiments of test coaching. Comprehensive meta-analyses ontest coaching yielded mean effect sizes of about a = 0.25 (DerSimonian & Laird, 1983;Kulik, Bangert-Drowns, & Kulik, 1984; Samson, 1985): Coaching effects are normally notgreater than a quarter of a standard deviation. As Figure 1 shows, with D = 0, an effectof d = 1.9 can be expected in our studies. At the other extreme, D = 5, every facet variesbetween training and test. Even in this situation of the maximum of dissimilarity - withinthe framework given - between training and test tasks, transfer effect does not drop tozero. With D = 5, in our experiment a d = 0.3 can be expected, i.e. about as much asoccurs in a normal coaching situation. This difference can, possibly, be explained by ourstress on training special thinking processes.

Question 6: Does our inductive-reasoning training improve intelligence test performance?

Because inductive reasoning is a major factor contributing to intelligence test performance,it can be hypothesized that a training of inductive thinking leads to an improvement inintelligence test scores as compared to untrained control subjects. Several experiments wererun, throwing light on this question. Table 5 provides an overview of these studies.

A PROCESS THEORY 201

Table 5Transfer to intelligence test performance

Project Subjects Training Test d Significant?

Masendorf & 20 children with a) OI (v) & (p) CMM 1.38 +Maihack (1986) speech discorders b) GE (v) & (p) CMM 1.79 +

Hiitz (Masendorf, 1988; 30 mildly retarded a) OI, GE (f), (v), & (n) CMM 1.39 +Klauer, 1989a) children b) RR,DR (f), (v), & (n) CMM 1.79 +

Homann (Klauer, 1987c) 88 sec. school children GE, 01, RR (f), & (n) CFT 0.36 +

Schmeer 22 students of a cf. Homann CFT 2 0.42(Klauer, 1987c) vocational track

Stegmann 45 elementary verb. & numerical(Klauer, 1987b) school children tasks of all types CFT I 0.70 +

Kolmsee 35 elementary cf. Stegmann CFT I 0.30 +(Klauer, 1987b) school children

Rudol 30 elementary cf. Stegmann CFT 2 -0.14(Klauer, 1987b) school children

Winkelmaier 40 mildly a) RR, DR (v) CMM -0.21(Masendorf, 1988) retarded b) RR, DR (n) CMM 0.42(Klauer, 1989a) children c) RR, DR (f) CMM -0.77

Mailandt, 33 elementary figural tasks of(Klauer, 198ge) school children all types KFT 1.16 +

Biirstinghaus 30 mildly cf. Mailandt,(Klauer, 1989b) retarded children diff. types of mat. CFT 2 0.28 +

Kaftan 30 elementary cf. Biirstinghaus CFT 2 0.95 +(Klauer, 1989b) school children

Masendorf I 44 mildly a) RR, DR, SF (f) & (p) CMM 0.34(Klauer, 1989a) retarded children b) GE, OI, CC (f) & (p) CMM 0.04

Masendorf 2 21 mildly Via computer(Klauer, 1989a) retarded children a) RR, DR, SF (f) & (p) CMM 0.99 +

b) GE, OI, CC (f) & (p) CMM 1.09 +

Sonntag 164 mildly cf. Burstinghaus CFT 2(Klauer, 1989a) retarded children mean 0.75 +

Bornemann 20 children from the new training KFT-K(Klauer, 1989a) 3 kindergartens program (Klauer, 1989a) mean 1.60 +

(J = 0.71SD = 0.67

Note. Abreviations: GE, OI, CC, RR, DR, SF see Table 1 & 2; (I), (n), (p), (v): figural, numerical, pictorial, verbalmaterial; CMM: Columbia Mental Maturity Scale; KFT: German version of the Cognitive Abilities Test; KFT-K:Kindergarten form of the KFT, CFP. Culture Fair Test

Tableau 5Transfert sur la performance au test d'intelligence

202 K. J. KLAUER

The results are quite clear. In 19 out of 22 comparisons a positive effect was obtained,a result which cannot be explained by chance (P < 0.01, sign test). Moreover, 15 of the 19experiments with positive effect signs reached statistical significance but none of the threewith negative effect signs. The mean effect size amounts to about two thirds of a standarddeviation. No reasonable doubt is possible that the inductive-reasoning training improvesintelligence test performance much more than it is improved by an average test coachingprocedure, although with coaching, the training and test material are of the same type.

Another point deserves attention. The effect sizes of Table 5 vary considerably abouttheir mean, indicating that there is, beyond random variation, probably no single homogeneouseffect at work. Hence, more research is needed to analyze the overall improvements intospecifiable components. One such component can obviously be given by the above-mentionedset effect. Others will be dealt with in the next paragraphs.

Question Z· Can the improvements be explained by warming up and similar effects?

The experiments mentioned so far were performed to test by an intervention strategyspecial aspects of the theory that inductive reasoning consists in certain comparison processes.There remain, however, some alternative explanations about the nature of the improvementswe yielded. The most important of them already gave rise to special studies.

Warming up is a well known phenomenon in transfer research. Such effects can resultafter a relatively short training period. As most of our training sessions lasted only aboutfour hours on four days, an explanation of the transfer effects by unspecific warming updid not seem to be completely out of the question. Another alternative explanation is givenby taking the Hawthorne or novelty effect into consideration: Introducing any new conditionsometimes leads to a more or less general improvement in performance and it is clear thatthe training procedure can function as such a new condition. Finally, it is possible thatparticipating in a small group guided by an appreciative adult and occupied with stimulatinggames may exert a generally stimulating influence.

One of the first experiments was designed to test alternatives of this kind. Masendorfand Maihack (1986) used two control groups, one traditional no-training group and onegroup playing different games with an adult person. With the Columbia Mental MaturityScale, the means of the two groups were 8.6 and 8.8 respectively, the difference not beingstatistically significant (p > 0.05). Hence, it can be concluded that the group playing differentgames under the guidance of a teacher was not superior to the not trained group. The sameprocedure was replicated by Masendorf and Klauer (1986) with the same result. There isadditional evidence that warming up and similar effects do not improve transfer on taskslike those we used (Lohaus, 1988; Phye, 1987). Based upon these results, the decision wastaken to dispense with a special warming up (etc.) group in comparable experiments.

Question 8: Can the results be explained by improved metacognitive components of a moregeneral nature?

Other alternative explanations seem to be more important. It is possible that, duringtraining, the subjects acquired metacognitive and/or general problem-solving strategies.Moreover, it is equally possible: that they acquired an analytic instead of a global inspectionstrategy or even that they moved, due to the training, on the impulsivity-reflexivity dimensionin the direction of the reflexivity pole. Influences of this kind could have amounted to theeffect that the trained subjects are superior to nontrained subjects in solving any type ofthinking problem. The evidence concerning the domain-specifity of our training effects,however, allows us to refuse an explanation of all of our effects by such rather generalimprovements. On the other hand, it is still possible that some more general componentsplay a certain role.

An experiment has been performed to throw some light on this question (Klauer, 198ge).

A PROCESS THEORY 203

N = 33 about ten-year-old students of an elementary school were randomly allotted totwo treatments and one no-treatment control condition. The first treatment consisted in ananalytic-systematic training of inductive-reasoning tasks according to our training procedure.The second treatment consisted in a similarly analytic-systematic problem-solving trainingwith non-inductive intelligence test items, for example with labyrinths. Two dependent variableswere given, one with inductive thinking tasks, the other with non-inductive thinking tasks,both taken as whole subtests from the German version of the Cognitive Abilities Test.

With respect to inductive-reasoning performance we expected the inductively trainedgroup to outperform the group trained to solve other problems, and the latter to outperformthe control group. The medians were 32.0, 25.5, and 24.0, respectively (p = 0.01, Yonckheeretrend test). With respect to non-inductive thinking performance we did not expect a significanttrend because there is no reason why one of the two kinds of training should turn out tobe more effective than the other. The corresponding trend test yielded no significant result(p = 0.12). Additional information is given by the effect size measure d. The problem-solvingtraining with non-inductive intelligence test items yielded not significant values of d = 0.30and d = 0.35 for both kinds of posttest, a result which can, possibly, be interpreted astest-coaching effects. The inductively trained group, however, yielded a value of d = 1.45for the inductive, and of d = 0.63 for the non-inductive items. This training seems to leadto a more general transfer effect, too.

The conclusion is that the transfer effect of our inductive thinking program is composedof at least two partial effects, of a larger domain-specific effect and of a smaller more generaleffect of knowing how to solve any intelligence test problem, i.e, of a metacognitive type.It is possible, however, that this preliminary result has to be further differentiated by futureresearch.

Concluding remarks

The main purpose of this article was to inform about a body of research in inductive­thinking processes. The research is based upon the assumption that inductive thinkingintrinsically consists in comparison processes, in the processes of comparing attributes ofobjects or relations between objects. In this context, comparing means discoveringregularitiesby finding out identity, or difference, or both. The theory is tested by training experiments:Inducing the postulated processes by a systematic training should lead to predictableimprovements with respect to certain tasks and to no improvement with respect to othertasks. In this way, several hypotheses have been deduced and empirically tested.

The main conclusion to be drawn from these results is that the theory seems to be soundand that it can, at least tentatively, be retained. Inductive thinking can obviously becharacterized by the processes in question. Unfortunately, it is not possible here to contrastin detail this process theory with Sternberg's theory- (Sternberg, 1986), according to whichinductive thinking consists in selective encoding and selective comparison processes withrespect to inferring rules. Sternberg describes both, selective encoding and selective comparing,to put it in my own terms, as processes of discovering not further specified commonalitiesand differences, the first between working-memory contents and stimulus inputs, the latterbetween long-term memory and working-memory contents. Consequently, selectiveencodingis required by most of the geometric-figural problems, selective comparing very often byverbal material. Hence, both theories do not contradict each other but can serve assupplements. In a way, the theory presented here specifies in detail what it is that is selectivelyencoded and compared and what has to be done when discovering the regularity.

Another relevant aspect is concerned with research methodology. The training experimentproved to be a powerful and flexible instrument in testing hypotheses about thinking processes.Taking the well-known drawbacks of other methods into consideration, it seems advisableto make use of the training approach, too.

204 K. J. KLAUER

Finally, the educational implications may be of some interest. Two applications seempossible. The first consists in the construction of a formal training program for theimprovement of inductive thinking. One such program has already been developed andempirically tested (Klauer, 1989a) and others will follow. But insofar as inductive thinkingis known to play an important role as predictor of academic achievement, a second applicationcould take place within the normal school setting. If teachers are instructed to systematicallyteach the students to use the above-mentioned comparison processeswithin the normal subjectmatter, an improvement not only in academic achievement but also in thinking and intellectualfunctioning will be expected. In this way, the training approach opens up a number of fruitfulresearch questions and perspectives for educationally relevant investigations and for improvinghigher-order thinking skills.

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Une theorie du raisonnement inductifmise a I'epreuve par I'instruction

de strategies specifiques a un domaine

Le raisonnement inductif peut etre defini comme un processus dedecouverte des regularites en recherchant des similitudes et desdifferences entre attributs ou relations. Cette conception est al'originede la definition de six sous-ensembles de tiiche pouvant toutes etreresolues par une variante de la strategie d'induction de base. Laconception a ete mise iJ l'epreuveen enseignantcette strategie: l'inductiondes processuspostules devant conduireades ameliorationsou al'absenced'ameliorations previsibles. L'article presente un apercu des principauxresultats d'une trentaine d'experiences. La theorie semble solide etl'approche consistant autiliser l'enseignement s'est revelee heuristique:Un grand nombre de differences quantitativement importantes a eteprevu et teste empiriquement, certaines aplusieurs reprises. L'effet denotre entrainement au raisonnement inductifsur la performance obtenue

206 K. 1. KLAUER

iJ un test d'intelligence est iJ peut pres deux fois plus efficace qu'unepreparation ordinaire. Les implications d'ordre theorique,methodologique et pedagogique sont discutees brievement.

Key words: Inductive reasoning, Training studies, Higher-order thinking processes, Intelligence.

Received: December 1989

Karl Josef Klauer. Lehrstuhl fUr Erziehungswissenschaft, Rheinisch-Westfalische Technische Hochschule Aachen,Eilfschornsteinstrarie 7, 5100 Aachen.

Current theme of research:

Higher-order thinking processes. Learning to learn. Theory of teaching.

Most relevant publications in the field of Educational Psycholgy:

Klauer, K. 1. (1989). Paradigmatisches Training induktiven Denkens I. Manual und Aufgabenband. (Paradigmatictraining of inductive thinking I. Manual and program). Gottingen: Verlag fur Psychologie Hogrefe.

Klauer, K. J. (1988). Teaching for teaming-to-learn. Paper read at the American Educational Research Associationconvention New Orleans (ERIC Document Reproduction Service N° ED 293 861, TM 011 428).

Klauer, K. J. (1987). Kriteriumsorientierte 'Tests. (Criterion-referenced tests). Gottingen: Verlag fiir Psychologie.