Running head: INDUCTIVE REASONING TRAINING Inductive ...Inductive Reasoning 2 Abstract For several decades, researchers have been engaged in examining inductive reasoning in order

Running head: INDUCTIVE REASONING TRAINING

Inductive Reasoning: A Training Approach

Karl Josef Klauer Gary D. Phye

Technical University of Aachen Iowa State University

Germany USA

Revised manuscript # 354

Inductive Reasoning 2

Abstract For several decades, researchers have been engaged in examining inductive reasoning in order to identify different cognitive processes participants use when they are dealing with inductive problems. In many cases the processing observed is unique to the problem encountered. The present article presents a different approach. A prescriptive theory of inductive reasoning is presented that identifies cognitive processing which basically consists of a procedural strategy for making comparisons (i. e., of looking for similarity and difference). Based on the prescriptive theory of inductive reasoning, it is hypothesized that training in the use of the procedural inductive reasoning strategy will improve cognitive functioning in terms of, (a) increased fluid intelligence performance, and (b) better academic learning of classroom subject matter. The following review and meta-analysis summarizes the results of seventy-four training experiments based upon nearly 3,600 children. Both hypotheses are confirmed. Further, two moderating effects were observed, (a) training effects on intelligence test performance increased over time, and (b) positive problem-solving transfer to academic learning is greater than transfer to intelligence test performance. Moreover it is shown that the results cannot be explained by placebo or test coaching effects. It can be concluded that the proposed strategy is theoretically as well as educationally promising and that children of a broad range of age and of intellectual capacity benefit when participating in such training.


Inductive Reasoning: A Training Approach Empirical research in inductive reasoning began about a hundred years ago in the

context of intelligence research when Spearman found that his g factor of general intelligence was mainly determined by inductive processes “eduction of relations”, (Spearman, 1923). Later, dimension analytic research also identified inductive processes as central intellectual factors identified as Reasoning (Thurstone, 1938), or Fluid Intelligence (Cattell, 1963). Using modern linear structural equations, Gustafsson (1984; Gustafsson & Undheim, 1992) came to comparable conclusions.

Meanwhile, in psychology and education the research focus has evolved to the analysis of cognitive processing when students solve inductive reasoning and other types of problems. Many researchers in the cognitivistic tradition have been engaged in exploring inductive processes (Goldman & Pellegrino, 1984; Pellegrino & Glaser, 1980; Sternberg & Gardner, 1983). More specifically, research has focused on the cognitive processing involved in series completion (Holzman, Pellegrino, & Glaser, 1983), analogies (Alexander & Willson, 1987; Gitomer, Curtis, Glaser, & Lensky, 1987; Pierce, Duncan, Gholson, Glen, & Kamhi, 1993), classifications, (Coley, Hayes, Lawson, Moloney, 2004; Tennyson, Youngers, & Suebsonthi, 1983; van de Vijver, 2002), categorizations (Heit & Hayes, 2005; Sloutsky & Fisher, 2004), and matrices (Carpenter, Just, & Shell, 1990).

Moreover, educational psychologists have studied ways of fostering inductive reasoning and its transfer (Phye, 1989; 1990; 1997). Other studies have focused on the use of special inductive measures in teaching and learning, such as analogies as instructional tools in teaching science (Chen, 1999; Gentner, 1989; Gick & Holyoak, 1983; Robin & Mayer, 1993) or other subject matter (Bean, Searles, Singer, & Cowen, 1990; Reed, Dempster, & Ettinger, 1985; Vosniadou & Schommer, 1988).

In addition, researchers in the field of artificial intelligence have constructed computer programs based upon process models that aim to solve certain kinds of problems in order to test their theories of inductive reasoning (Ernst & Newell, 1969; Holland, Holyoak, Nisbett, & Thagard, 1986; Kotovsky & Simon, 1973). Even sophisticated mathematical models have been developed and tested that are able to predict how people process inductive problems, for instance causal models (Rehder, 2003; Rehder & Burnett, 2005) or Bayesian models (Heit, 2000). Recent cognitive process research has highlighted the impact of general principles that seem to strongly influence subjects’ inductive processes (Heit & Feeney, 2005; Heit & Hahn, 2001; Medin & Heit, 1999). This line of research shares some important features with the research to be reported here by stressing principles such as similarities and diversities.

In contrast to most of the research mentioned, the following prescriptive theory does not claim to analyze how learners proceed cognitively when they solve inductive problems. For example, which processes are activated, or in what way processes are modified by properties of the given problems. This line of research is particularly demanding because processes employed can vary depending on the participants and their special experiences as well as the influence of different kinds of problems. Our focus is comparably modest in that the prescriptive theory delineates a rather simple strategy that in principal should enable subjects to solve any inductive problem. And it is rather easily tested by teaching participants to make use of the recommended strategy. A Prescriptive Theory of Inductive Reasoning

At the outset it is useful to distinguish between inductive reasoning and inductive inferring. Inductive reasoning is aimed at detecting generalizations, rules, or regularities. For example, if a number of objects is given and if it is found that all of these are toys made of wood, a generalization or regularity has been discovered. Should we extend this generalization to the totality of toys by stating that all toys are made of wood, then we would have made an inductive inference, although a false one in this case. An inductive inference extends the generalization


beyond the scope of experience by asserting something about a non-observed or even non-observable universe of objects. Drawing inductive inferences is much more demanding but also much more critical than inductive reasoning that might precede it.

The main purpose of this article is to describe a recent prescriptive theory of inductive reasoning (not inductive inferring) and to test this theory for its usefulness in educational research, teaching, and training. The theory was developed some years ago (Klauer, 1989; 1991; 1993; Klauer & Phye, 1994; Klauer, Willmes, & Phye, 2002) and since a number of experiments have been performed by different authors, it seems reasonable to review and empirically evaluate the basic assumptions.

The first step of the theory is to define inductive reasoning. A useful formulation has been provided by Glaser and Pellegrino (1982, p. 200) who stated, “All inductive reasoning tasks have the same basic form or generic property requiring that the individual induce a rule governing a set of elements.” There is general agreement that tasks such as, (a) classifications, (b) analogies, (c) incomplete series, and (d) matrices require inductive reasoning and that they are widely accepted as typical inductive reasoning tasks (Büchel & Scharnhorst, 1993). It is commonly accepted that these four types of tasks require the detection of a rule or, more generally, of a regularity. However, is this list of the four types of tasks an exhaustive one? Is there a plausible reason why only these four tasks are identified as inductive reasoning tasks? In addition, is inductive reasoning characterized by individual instances of (a) its product, (b) the detection of a rule, or (c) characterized by a certain kind of process? Or, is it defined by some combination of the three dimensions? Figure 1 suggests some answers and in some respects, a more specified definition (Klauer, 1989; Klauer & Phye, 1994).

Inductive reasoning consists of detecting regularities and irregularities by finding out

A B

a1 similarity b1 attributes

a2 difference of

a3 similarity & b2 relations

difference C

c1 verbal

c2 pictorial

with c3 geometrical material.

c4 numerical

c5 other

Figure 1. Definition of inductive reasoning.


According to Figure 1, inductive reasoning not only reveals regularities but also

irregularities and diversities. For instance, in cases where a rule only partially governs a set of elements, the assumed rule has to be rejected and, possibly, replaced by a better fitting one. Moreover, using three facets A, B, and C, Figure 1 specifies by which means a rule can be detected or rejected, namely by a comparison process. Comparing is defined as finding out similarities and differences, or both (Tversky, 1977). Hence, facet A is the comparison facet. The comparison process produces regularities consisting of at least one commonality among all the objects. According to facet B that commonality refers either to attributes of the objects or to relations between objects. We call facet B the category facet. Looking at modern logic, another aspect can be introduced since attributes are identified as predicates with one argument, while relations are identified as predicates with two or more arguments. Since no other predicates are possible, the distinction implies that attributes and relations exhaust all possibilities for characterizing objects. This fact demonstrates the far reaching impact of inductive reasoning. In Figure 1, facet C of the definition is the materials facet. Facet C specifies the nature of the inductive reasoning materials. It is, of course, possible to replace the categories of facet C with school relevant material such as types of subject matter taught in school.

The central facets of the definition are facets A and B. They clearly constitute six classes of inductive reasoning, not considering all possible combinations. The six classes are specified in Table 1, where item formats are given as they are identified in current intelligence tests. The first three classes are varieties of classification tasks, while the remaining can be identified as analogies, series, and matrices. Thus, it becomes clear that the traditional item format possibilities reflect all inductive reasoning tasks. It is evident from Figure 1 why this is the case.

Table 1 specifies the names attributed to the six classes, the facet identifications, the item formats as found on intelligence tests, and the cognitive processes required to solve these items. The relationships among the six basic varieties of inductive reasoning tasks are depicted in the genealogy of Figure 2.

SYSTEMCONSTRUCTION

RELATIONSHIPS RELATIONSHIPS

Similarity Difference Similarity Difference

Attributes Relationships

CROSSCLASSIFICATION

STRATEGY OF INDUCTIVE REASONING

GENERALIZATION RECOGNIZING DIFFERENTIATINGDISCRIMINATION

Figure 2. Genealogy of tasks in inductive reasoning.


Table 1. Types of Inductive Reasoning Problems

Process

Facet

Identification

Item

Formats

Cognitive Operation

Required

Generalization a1b1 class formation

class expansion

finding common

attributes

similarity of

attributes

Discrimination a2b1 identifying

disturbing

items

discrimination of

attributes (concept

differentiation)

Cross

Classification

a3b1 4-fold scheme

6-fold scheme

9-fold scheme

similarity &

difference in

attributes

Recognizing

Relationships

a1b2 series completion

ordered series

analogy

similarity of

relationships

Differentiating

Relationships

a2b2 disturbed series differences in

relationships

System

Construction

a3b2 matrices similarity &

difference in

relationships Depending on the problem given, the strategy to reason inductively requires a person

to scrutinize either attributes of the objects or the relations among them. Hence, Figure 2 shows two branches, which are divided again into two branches depending if one is looking for similarities or for differences. In some cases, both similarities and differences are called for, bringing the two branches together again. A symmetrical figure results because the attribute and the relations branches are similarly differentiated.

From the definition portrayed in Figure 1, it should be possible to design an analytic strategy that enables one to solve every kind of inductive reasoning problem. Its basic core would be a comparison procedure. The objects (or, in case of relationships, the pairs, triples etc. of objects) would be checked systematically, predicate by predicate (attribute by attribute or relation by relation), in order to find out commonalities and/or diversities. Presumably, a computer program could be developed to solve any problem of inductive reasoning.


However, human beings may prefer to make use of a heuristic strategy, as depicted in Figure 3. In this case, a participant starts with a more global inspection of the task and builds a hypothesis. This can then be tested so that the solution might be found more rapidly, depending of the quality of the hypothesis. In a training program, participants might be advised to first use the heuristic strategy and, if some attempts do not lead to a solution, to then apply the analytic strategy.

Start

Compare the objects(pairs of objects) globally

Build a hypothesis

Test the hypothesisby directed comparisons

Rule discovered?

yes

no

Already triedseveral times ? no

Try again

EndApply the analytical

strategy

yes

Figure 3. Heuristic or hypothesis – guided strategy of inductive reasoning.

Hence, Klauer’s theory of inductive reasoning first offers a definition of inductive reasoning. This definition leads to an exhaustive classification of inductive reasoning tasks. Moreover, it specifies processes by which these task types can be solved. Finally, the cognitive process analysis leads to two comprehensive strategies that problem solvers might use when solving inductive problems.

However, as was mentioned earlier, it is not claimed that all learners always proceed according to the analytic or the heuristic strategy. Actually, one can assume that people make use of innumerable ways of solving different varieties of inductive tasks. What follows from the definition of Figure 1 concerning the solving process is not a description of what commonly occurs but a prescription of how to proceed in order to effectively and efficiently solve inductive problems (i.e., the theory is basically a prescriptive one). Consequently, an adequate test of this kind of theory is to teach participants to apply it and to see whether they are able to solve inductive problems more adequately than those that have not had the opportunity to learn how to proceed. Thus, training experiments are appropriate means for testing the theory. Training Programs According to the theory introduced, training to reason inductively provides an opportunity for participants to acquire the basic strategy of inductive reasoning, to modify it appropriately for the six varieties of inductive tasks and to experience sufficient opportunities through practice


to internalize the strategy. Actually, participants should be able to recognize an inductive problem whenever they meet one. More precisely, they do not have to be able to Table 2. Instructional Objectives of the Ten Lessons

Lesson Training objective Comment 1

Solving the problems naively The children should get familiar with

the material and the training situation

2 Distinguishing attributes and relationships

Introduction of the terms “attribute” and “relationship.” Sorting all items of lesson 1 appropriately

3 Recognizing the three attribute classes

Distinguishing the three classes. Sorting all of the attribute items thus far

4 Recognizing the three relationship classes

Distinguishing the three classes. Sorting all of the relationship items thus far. Recapitulation of the attribute problems

5 Solving and checking procedures with similarity problems

Learning how to solve and check generalization and recognizing relationship problems. Recapitulating sorting of items

6 Solving and checking procedures with difference problems

Learning how to solve and check discrimination and differentiation of relationship problems. Recapitulating sorting of items

7 Solving and checking procedures with similarity & difference problems

Learning how to solve and check cross-classification and system construction problems. Recapitulating sorting of items

8 Repeating and practicing problems of the attribution branch

Rehearsing all of the processes with attribution problems

9 Repeating and practicing problems of the relation branch

Rehearsing all of the processes with relation problems

10 Mixed repetition of all kinds of problems and procedures

Practicing all types of identifying, solving, and checking processes with all types of problems

classify a given inductive problem as belonging to one of the six varieties. It is enough when they are able to identify a problem as one similar to a familiar problem and then assign the adequate solving strategy. Ideally, the application of the inductive strategy should be


automatized so that whenever the problem solver comes across an inductive problem, he or she automatically chooses the adequate strategy.

Three training programs and their corresponding manuals have been developed, • Program I for children of the ages 5 – 8, • Program II for children aged 11 – 13, and • Program III for youth of the ages 14 – 16

(Klauer, 1989; 1991; 1993). Program I is basically nonverbal so that it can be used in all language environments. For this reason an American version of the manual has been published (Klauer & Phye, 1994) as well as a Dutch version (Klauer, Resing, & Slenders, 1996). The first two programs are appropriately used with regular classroom children, gifted children and learning disabled children. The cognitive development of the child would determine whether Programs I or II were to be used for training. Program III was designed to be used with mildly learning disabled youth, with weak performances in school and who are at risk for vocational integration. Training Format

Each of the programs I, II, and III consist of 120 items, that is, 20 items for each of the 6 basic classes of inductive reasoning tasks. Further, programs II and III offer forty verbal, forty figural, and forty numerical problems adapted to children’s everyday life experiences and to the problems they might meet in school. Only program I differs a bit from this scheme since it is not anticipated that these children are able to read. Also, at the beginning of program I a few problems with real blocks are included so that the children can manipulate the blocks when solving the problem at hand.

According to recommendations by Belmont, Butterfield and Ferretti (1982), during training children should receive ample opportunities to acquire the appropriate metacognitive aspects of the solving procedure which are mentioned in Table 2. As a rule, a complete training episode is made up of 10 lessons with 12 items each. With programs II and III, trainers are advised to adopt the plan outlined in Table 2 which specifies objectives for each of the ten lessons. Beginning with lesson two, metacognitive aspects are at the center of attention. In lessons two and three, problem classes are defined by attributes while in lesson four problem classes are defined by relationships. Children learn the terms for attributes and relationships and they are provided the opportunity to classify all of the training problem tasks they have encountered. Lessons five to seven repeat what has been learned so far but in a different order. This way the children are provided the opportunity to realize that problems can differ with respect to the category involved (attributes or relations) but can require identical processes (looking for similarity or for difference or for both). The last three lessons provide review and practice to help students to consolidate what they have learned.

Various kinds of verbal self-regulating instructions are helpful and it is useful to give participants tips and hints such as, “COMPARING means looking for SIMILARITIES and DIFFERENCE". During the last three lessons, children are encouraged to acquire a habit of monitoring themselves and their solution processes. Three procedural processing questions identified below should be asked and students should be expected to answer appropriately to all three queries for each new problem. QUESTION ANSWER

1) What do I have to look at? Similarity or difference or both with attributes or relationships.

2) What should I do to find the solution? Compare, (i. e. look on similarity Or difference or both). I do it according to an assumption or systematically. 3) How can I check my solution? By the opposite comparison.*


*The opposite comparison is a favored checking procedure. When, for instance, all objects are characterized by a certain attribute, no difference must be found with respect to that attribute. Meta-analysis

Currently, 74 experiments (Appendix A) have been performed where at least one training group participated in a training of inductive reasoning using one of the three training programs and where at least one other group did not receive such a training but continued regular classes or another activity. Under these circumstances it is advisable to use meta-analysis in order to gain an overview of the most important results. Based upon the prescriptive theory of inductive reasoning and a review of the research literature cited, it is possible to derive certain hypotheses which can be tested meta-analytically using the available data base. Hypotheses

As already mentioned, a strong research tradition has shown that inductive reasoning is a central part of general intelligence. Snow, Kyllonen, and Marshalek (1984) were able to clearly demonstrate this fact. They used the data set of Thurstone (1938) and reanalyzed it via multidimensional scaling. This reanalysis found inductive and deductive reasoning to make up the core of fluid ability. Consequently, today tests of fluid intelligence contain at least some inductive subtests [e g Cattell Culture Fair Tests (Cattell & Cattell, 1963) or Raven Progressive Matrices (Raven, Court, & Raven, 1994)]. It is worth noting however that the inductive training programs and these intelligence tests are quite different in terms of test items. The training programs offer meaningful material and incorporate problems that children may encounter in their daily lives. In contrast, the intelligence tests consist of abstract, isolated and more or less meaningless material. Our first and central hypothesis deals with the effect of the training on intelligence test performance. It is necessary for theoretical reasons to test whether the training improves intellectual functioning. However, because intelligence has a positive impact on learning in school, academic learning is also of interest from a practical point of view.

Hypothesis 1. It is expected that inductive reasoning training results in positive transfer to tests which measure fluid intelligence (effectiveness hypothesis). According to this hypothesis a positive transfer effect of the training program to a standardized adequate g factor intelligence test can be viewed as evidence of the effectiveness of inductive reasoning training. As is usually the case in meta-analyses, possible moderator variables will also be addressed. A case in point is in reference to the comparison of the effectiveness of the three programs. If the three programs are valid constructs of the same theoretical conception, then one expects their effects do not differ substantially from one another. However, the results concerning the three programs are not independent of several potential moderator variables.

Primary examples are the age or level of cognitive development of the children being trained which may exert special influence. Program I is used in kindergarten, school kindergarten and primary school. School kindergarten is a special German institution. It is designed for children old enough to enter school but who are not yet ready for regular schooling. Thus, they are generally fostered for another year in a kindergarten–like environment in the school but without exposure to the three R’s. For instance, these mildly learning disabled or otherwise exceptional children may be less responsive to a cognitive training than the learning disabled but older children in special education settings in the primary school. Program II is used in secondary schools whereas Program III is used with even older but mildly learning impaired youths. Thus, Program III results are confounded not only with age but also with a slightly reduced level of general ability. One would expect that both the chronological age and the differing levels of cognitive development of the students across programs may account for differences in mean effect sizes. This is particularly the case


with respect to possible aptitude by treatment interactions (Goska & Ackerman, 1996). Thus, it can be assumed that participant differences play a role in moderating the effect of the inductive training on intelligence test performance. Despite confounded variables and with respect to possible future research, it makes sense to check whether age and/or participant differences modify the effectiveness of the training.

The social condition of the training may also play a moderating role. One can assume that a one–to–one training is the most effective because the contact between trainer and trainee is most intense and because the trainer can adapt his or her interventions optimally to the child’s individual needs. However, one-to-one teaching has not always been found to be the most effective approach with every subject matter or skill (Elbaum, Vaughn, Hughes & Moody, 2000). The training of pairs of children might be both effective and efficient and is advantageous for several reasons (Lochhead, 1985). For example, if one of the children is asked to solve a given problem and comments loudly on his or her attempts, then the other partner can be asked to check whether all of the relevant information has been correctly considered. Thus, both children are cooperatively involved in the solving process, but each has different roles. According to Lochhead’s recommendation, children can change their mutual roles with the next problem. This way a child learns to apply techniques and strategies he or she did not previously know and both acquire metacognitive vocabulary and a habit of reflecting metacognitively on their own inductive reasoning processes. Lochhead’s principles can also be applied when one deals with small groups of trainees (Palincsar & Brown, 1984) or even with whole classes. For practical purposes it would be advantageous if small groups or intact classes could be trained simultaneously and effectively.

Finally, a fourth moderator variable should be taken into consideration, the authorship of the experiments. Nearly half of the training studies are published by Klauer. These experiments were conducted by Klauer’s staff members or by his students of psychology or education in fulfilling their requirements for a master’s degree. While none of Klauer’s students received different instruction other than that which is available to anyone else reading the handbook, one cannot rule out the assumption that the experiments published by Klauer show differing effect sizes. All of the other experiments were conducted and published by different persons and hence are not subject to the same criticism.

Hypothesis 2. The effects of inductive training on intelligence test performance equals an effect due merely to participation in training irrespective of what is trained (placebo hypothesis). Actually, it has been suggested that the positive results of inductive training may result from a variation of the placebo effect (Hager & Hasselhorn, 1995; Hager, Hübner, & Hasselhorn, 2000). These authors assume that a close bonding between trainer and trainee is developed if a single child or a small group of children is trained. This special relationship and the individual attention children experience during training may account for the cognitive training effects, irrespective of the kind of cognitive activity the children are experiencing. According to this assumption, the decisive agent is not the special training but the close personal relationship between trainer and trainee which results when children participate in any training. Hence, it is necessary to determine whether the positive performance effects of inductive training can be attributed to non-inductive reasoning factors encountered during training.

Hypothesis 3. The effect of inductive reasoning training on intelligence test performance does not disappear after a few weeks (durability hypothesis). As Lipsey and Wilson (1993) demonstrated meta-analytically, placebo effects (if observed) disappear after a few weeks. Given our stance with reference to hypothesis 2, we expect a much longer lasting effect of inductive training. Otherwise such training would be a waste of children’s time if it does not lead to a lasting improvement in cognitive functioning. This is especially the case with respect to positive transfer of training to academic learning. A rapidly diminishing effect of the training would not be of great value to educational practice. Thus, for theoretical as


well as practical reasons, an important question is whether training effects will last for some time or whether they will rapidly disappear.

Hypothesis 4. Training in inductive reasoning will result in positive transfer to the learning of academic subject matter (transfer hypothesis). However, the transfer effect will be smaller than the effect of the training on intelligence test performance. One can assume that inductive reasoning training improves learning to the extent it improves intellectual functioning and information processing. Moreover, because nearly all regular classroom subject matter requires the acquisition of generalizations (be it in the form of concepts, classes, rules or laws), one could anticipate that inductive reasoning training would improve learning of many kinds of subject matter. Such a line of reasoning is encouraged by Csapó’s (1997) cross–sectional research, where he found a close relationship between inductive reasoning and science learning in school. However, because intelligence test performance correlates with scholastic achievement only to a moderate degree, the transfer effect on learning of regular subject matter in school is anticipated to be smaller than the effect of the training of intelligence test performance.

The four moderator variables that potentially modify intelligence test performance (hypothesis 1) can also be checked for impact on positive transfer to academic learning. It is possible that across the three programs, the age or cognitive development of the children, the social condition of the training, or the group of authors might also moderate the transfer effect on academic learning (hypothesis 4).

Hypothesis 5. The training effects are not due to procedures of coaching or teaching to the test (coaching hypothesis). Hager, Hübner, and Hasselhorn (2000) have suggested the possibility that the positive training effects can be the result of teaching to the test or coaching procedures. Coaching to a test is an old and widespread practice, particularly where test performance determines admission to certain careers (Anastasi, 1981). However, participants in Klauer’s training programs are instructed to solve six item classes, which are found in many intelligence tests. During training participants are not taught only to solve specific items but a general strategy “compare and contrast,” which has to be adapted to the six classes of inductive items.

Hasselhorn (1995) recommended distinguishing between coaching or training effects according to the nature of the effects. According to Hasselhorn, coaching results only in improvement of performance, while training results in improvement of the underlying competence. He proposes two indicators of improvement in competence, namely transfer to other variables and durability of the effects. Hence, the coaching hypothesis will be tested within the context of two preceding hypotheses, the durability and the transfer hypothesis. The Meta-Analysis Data Pool

Klauer’s theory of inductive reasoning and the training programs have attracted the attention of many researchers. Actually, the theory of inductive reasoning and the first training experiments caused some controversies and discussions. As a result, by the end of 2004, a total of 74 experiments were available which used one of the three previously described training programs (references can be found in Appendix A). Note that in some of the 71 published articles, more than one experiment is reported. Unfortunately, only a few of the articles were published in English language journals.

The probability is rather high that all European evaluations published are included in the analysis because the community of interested researchers is well known. In order to identify additional relevant research, systematic internet searches were performed, mainly using the database PsychINFO and labels such as “Inductive reasoning AND training,” “Klauer AND training,” and “Denktraining,” the German label of the programs. These searches produced 180 hits. However, none of these searches led to the identification of even one additional paper not already included in the data pool.


Only three of the experiments in the data pool (see Appendix A) were not published, the studies by Brünken (# 56), Bussas (#7), and Favre (#55). These experiments were theses and were not published mainly because they did not add new insights or results to the body of research which was available at that time.

Method For a study to be included in the meta-analyses testing hypotheses 1-5, one of two

kinds of experiments had to have been employed. Studies either had to be: (a) a test of the positive transfer of one of Klauer’s inductive reasoning training programs to intelligence test performance, or (b) studies had to be a test of the positive transfer of one of Klauer’s training programs to learning of academic subject matter. Training Study Designs

Designs to test hypotheses 1-3 focus on transfer to intelligence test performance. The central hypothesis (1), predicts transfer of inductive reasoning training to performance on intelligence tests which include measures of fluid intelligence. All of the studies included in this review employed a two-group design. Frequently, this took the form of a training group contrasted with a no–training control group. These comparison groups continued with regular kindergarten work or schooling (i.e., they received academic training, but not the specific inductive training). In these studies, the effect of the special training was compared with the effect of regular schooling.

Sometimes the two-group design involved two treatment groups. In these cases a group trained inductively was contrasted to a group trained with a non-inductive program, (i. e., with an alternative training program). Thus, the effect of the inductive reasoning training program is compared with the effect of a different training program. Here both treatment groups share the experience of participating in a training program. However, such a two training groups design without a no-training control group sometimes turns out to be disadvantageous. When there is no difference between both treatments, one cannot decide if both treatments were equally effective or equally ineffective. Fortunately, a number of studies made use of a three-group design to assess the effect of the treatments by adding a regular no-training control group to the two training groups. If both treatments yield more or less the same effects, comparisons with the no–treatment control group enables one to decide whether both treatments are equally effective or ineffective.

Furthermore, the three-group design enables one to assess the amount of effect that may be attributable specifically to the training situation. Hypothesis 2, the placebo hypothesis, states that the experience of participating in any training can, in and of itself, produce positive effects on intelligence test performance. As a test of hypothesis 2, different kinds of alternative non-inductive training programs were used, [training of spatial cognition with program Tetris (Masendorf, 1994; Souvignier, 1997), training of metacognitive strategies using problem-solving with non-inductive problems (Bornemann, 1989; Klauer, 1992; Kolmsee, 1989), arithmetical training (Angerhoefer et al., 1992), training in reading strategies (Klauer, 1996), training in other academic learning strategies, social games (Sonntag, 2004), and a motivational training (Fries, Lund & Rheinberg, 1999)]. Training Episode

Most of the training studies lasted for several weeks. In a typical training episode, two lessons are given per week, requiring a training period of five weeks. As a rule, subjects were tested a week before training and a week after training (pretest – posttest design), resulting in a total training study duration of seven weeks. A few of the training studies needed less time, while others needed more time, depending on the given circumstances.

All of the training experiments used such a pretest–posttest design. Additionally, in order to test hypothesis 3 concerning the durability of the training effects, after the posttest was administered a second follow-up posttest was administered some weeks or even several months later. Very often, although not in every case, pretest, posttest and follow-up tests


were identical. This design element leads to considerable retest effects. However, in cases where a no–training control group or an alternatively trained control group was available for comparative purposes, specific training effects are not confounded with retest effects.

Following training, intelligence tests were administered that consisted entirely of inductive reasoning items such as Raven Coloured Progressive Matrices (CPM), Standard Progressive Matrices (SPM), or Advanced Progressive Matrices (APM). Others included subtests of inductive reasoning items , Cattell Culture Fair Tests (CFT), the German version of the Cognitive Ability Test (CAT), or the German version of the Columbia Mental Maturity Test (CMMT) for learning disabled children. In some studies only those subtests which require inductive reasoning were administered whereas others included the complete test. Thus, the data upon which the meta-analysis is based refer to intelligence tests which in part, or in their entirety, measure inductive reasoning. Further, the overwhelming majority of the intelligence tests made use of abstract, more or less meaningless material so that the stimulus tasks for training (real world ) and transfer (abstract materials) were quite different in terms of similarity and familiarity.

Designs to test hypothesis 4 that focuses on the transfer to academic learning. Of the 74 training experiments available, 38 studies tested the effect of the training on learning of an academic subject matter. These studies consisted of two phases. During the first phase, children in a class were randomly assigned to one of two groups, a training group and a no-training control group. Most training groups participated in inductive training for two sessions a week over a five week period while the control groups continued regular classes during these sessions.

In the second phase of these studies, a lesson followed involving a subject matter that belonged to the regular curriculum that had not yet been taught. In participating classrooms, these lessons were administered to both the training and control group together. This second phase was experienced as regular classroom activity by both experimental group and control group students. As a rule, after choosing an appropriate subject matter, an informal criterion-referenced test was developed and used as both pretest before and as posttest after the common lesson. This way it was possible to measure how much the children already knew and how much they acquired during the lesson. Specifically, it was possible to determine whether the inductive training and the no-training control groups differed in academic learning.

Across studies, a variety of academic topics were chosen: mathematics, biology, geography, physics, as well as reading, spelling, grammar, and learning of foreign languages or learning and problem solving in ecology. In Appendix B, the disciplines are listed in column DV 2 (dependent variable 2) as numbers 1 - 7. The numbers 8 – 13 deal with cognitive variables, which do not include learning of a subject matter. The verbal descriptors for variables coded 1 – 13 in Appendix B are provided in the description of the table.

Typically, data were analyzed using an analysis of covariance with the pretest as covariate, training as the independent variable, and the posttest as the dependent variable. Some authors preferred, however, t-tests to ascertain significance of posttest performance and, following this, significance of differential pretest-posttest increase for the training and control groups. Research Design Shortcomings

The overwhelming majority of the training experiments included only small samples of children or youth because it is more efficient to conduct the training of inductive reasoning in small groups rather than the entire class. This is a trade-off. While training can be more effectively administered to small groups, statistically significant findings may be less likely to result. Fortunately, the information provided by effect sizes will help determine if there is a coincidence of small N and small effect size that inevitably leads to insignificant results. Actually, across studies one would not expect all of the trainers to be equally effective.


Consequently, if many small groups are trained by many trainers who differ in effectiveness then a relatively large range of results is anticipated.

In a few cases whole classes were assigned to the treatments. Here we are dealing with quasi-experiments even when the classes were randomly assigned to the conditions. However, because pretest-posttest designs were used it was possible to take the most important pre-experimental differences into consideration. Calculating Effect Sizes

There are differing opinions on whether it makes sense to calculate an effect size when the effect is not statistically significant (Cahan, 2000; Levin & Robinson, 2000; Robinson & Levin, 1997; Wainer & Robinson, 2003). It is clear that with small sample sizes only large effects can reach the level of statistical significance. Regardless, for these meta–analyses it seems meaningful to estimate all of the effect sizes. Furthermore, because of their theoretical and practical importance, in the following analyses, we added to each mean effect size its confidence interval (Thompson, 2002).

Due to differences among research designs, different effect size estimates were generated and are discussed below. Since the early efforts of Cohen (1968) and Glass (1976), effect sizes have typically been estimated as standardized mean differences. Also, following suggestions by Hedges and Olkin (1985) the difference of the means is divided by the pooled standard deviation of both groups.

Calculating g. For all g-measure comparisons (Hedges & Olkin, 1985), g was calculated as:

MT – MC g = ─────

sp

Because we are often dealing with small sample sizes and because pretest means can vary considerably in this case, even when the subjects were randomly assigned to the treatments, we decided to improve the effect size estimations by correcting for pretest differences. Thus, gcorr is calculated for each effect size estimation.

gcorr = gposttest – gpretest The three g columns of the Appendix B contain gcorr values with the following

headings: g11 refers to the effect size on the first dependent variable (an intelligence test) as posttest; g12 refers to the same variable as follow–up some months later; and g2 represents the transfer effect on a second dependent variable (often school relevant learning).

Calculating d. Hedges (1981), however, showed that g overestimates the true effect size a bit if one deals with small samples. Therefore d is used instead of g when further calculations were computed,

3 d = (1- ───────) g (4N – 2) - 1

where N refers to the number of subjects involved. Primarily dependent on sample size N, d is somewhat smaller than g. Moreover, when mean effect sizes are estimated, this is done using the weighted integration method by Hedges and Olkin (1985, p.112). This means the d values are weighted according to their sample sizes so that studies with larger samples get a higher weight than studies with smaller samples. This procedure generally leads to lower mean effect sizes. Hedges and Olkin also developed correcting procedures in order to account for a lack of test reliability. Since applying these corrective procedures would lead to higher means, corrections for attenuation were not employed.


When Effect Sizes are Dependent. If one compares the results of one experimental group with the results of one control group per experiment, no dependency exists among the contrasts. However, in our case we have 74 experiments but 89 contrasts as can be seen in Appendix B or in Table 3 below. In order to avoid overlap as much as possible, one should differentiate among three types of contrasts. In Appendix B, the three types are depicted in column “Contrast” and denoted by 1, 2, or 3. Here are the explanations. Contrast type 1: An inductively trained group is contrasted with a no – training control group. Contrast type 2: An inductively trained group is contrasted with an alternatively trained group. Contrast type 3: An alternatively trained (non-inductive reasoning training) group is contrasted with a no – training control group.

Contrast 1 is the primary contrast for providing credible results. For contrast 2 an inductive training group is tested against a different but non-inductive training group. Contrast 3 enables one to directly test hypothesis 2, the placebo effect. Arguably, if this contrast yields significant training results it is merely the result of participation in any training of any type that accounts for the observed improvement in cognitive performance. This would suggest that the special attention trainees receive during training is the agent of change.

Table 3 Frequency of Contrasts Used in the Meta-Analysis (In parentheses experiment reference numbers according to Appendix B) ________________________________________________________________________ Type of Frequency of Frequency of contrast experiments effect sizes Comment ________________________________________________________________________ 1 only 49 49 nonproblematic* 2 only 13 13 nonproblematic 1+3 6 (39, 33, 23, 8, 5, 3) 12 nonproblematic 1+1 3 (64, 34, 22) 6 problematic** 1+2+3 1 (73) 3 problematic 1+1+3 2 (52, 9) 6 problematic

Sum 74 89 * Nonproblematic: The estimates of the effect sizes are independent of each other. ** Problematic: The estimates of the effect sizes are not independent of each other.

With respect to dependency, no problems arise when only one contrast per experiment is tested, be it contrast 1, 2, or 3. When two dependent variables were employed in a single experiment, for instance an intelligence test and a criterion-referenced subject matter test, both contrasts were never included in the same meta-analysis because they referred to different hypotheses. So, no dependency problem occurred in these cases. The same holds true when contrasts 1 and 3 were made. Contrast 3 deals with a different research question.

However, when both contrasts 1 and 2 were performed in one experiment, there is a problem of dependency because the same control group is used twice. The same is true when two type 1 contrasts are calculated (e. g., when two different varieties of inductive training were compared to a control group that did not receive training). Again, in these cases, the effect size estimations refer to the same control group and, hence, are not independent from each other. Yet, such research is of practical importance because it helps provide evidence concerning the effectiveness of particular types of inductive training programs. To eliminate these results from analysis would be shortsighted from an educational perspective. Because only six experiments and 15 effect size estimations were affected, it was decided to keep them, while including only half the number of subjects in the control groups. This procedure


has the following ramifications: (a) the d values as well as the corresponding means receive lower estimations, (b) d values are corrected for (larger) sampling errors, and (c) the means are based upon correct instead of inflated sample sizes so that their confidence intervals are not overestimated.

Results According to hypothesis 1 it was predicted that inductive training would result in

positive transfer effects to tests measuring fluid intelligence. The results of the 74 experiments are summarized in Appendix B. Omitting experiment number seventy because no intelligence test was administered, 73 experiments are available where the effect of an inductive training on intelligence test performance can be ascertained. Based upon these experiments, 79 contrasts could be performed using an intelligence test as the dependent variable. The effect sizes g11 ranged from -0.05 to 1.30 with an unweighted mean of Mg = 0.59 ± 0.31 (n = 79, N = 3595). Figure 4 complements these data by presenting a visual representation of the frequencies for the various effect sizes observed and the shape of the distribution of frequencies.

Freq

uenc

y of

Eff

ects

Figure 4. Distribution of the g effect sizes of training transferring to intelligence test performance.

Figure 4 shows a rather symmetrical distribution. As expected, there is considerable variability among the effect sizes. Some are quite small, while others are rather large. However, the bulk of the data clusters about the mean. Nevertheless, the effect sizes are not normally distributed about their mean (p = 0.048, Kolmogorov - Smirnov test with Lilliefors' correction). There were too many relatively large effect sizes. If one eliminates the three largest effect sizes as possible outliers, the effect sizes are normally distributed. Regardless, the following analyses are based upon the whole data set.

Hedges and Olkin (1985) have shown that effect measure g slightly overestimates the actual effect sizes, particularly when dealing with rather small samples. Effect measure d gives an unbiased and typically a somewhat lower estimation of the effect size. Using the above mentioned weighted method by Hedges and Olkin, several means d+ were calculated which weigh the single d values according to the respective sample sizes N. Table 4 provides an overview of the results with respect to the effect of the training of inductive reasoning on intelligence test performance. These results are disaggregated in terms of various moderator variable influences.

According to Table 4, the overall weighted mean of the 79 effect sizes d+ equals 0.52. As expected, this value is a bit smaller than the above mentioned unweighted mean g (Mg = 0.59). Nevertheless, one can conclude that on average an inductive training improves


intelligence test performance by about half a standard deviation. This corresponds to an improvement of about 20 percentile ranks for the average participant. Moreover, all of the average d+ effect sizes in Table 4 differ significantly from zero (p < 0.01). The same is true for the average d+ values of Table 5.

Also, the coefficient Q of homogeneity was calculated and its probability ascertained. If this probability lies beyond a significance level, then the effect sizes, combined to produce a common estimation, are heterogeneous. If this is the case, it makes sense to look for variables moderating the effects. As shown in Table 4, all of the mean effect sizes are accepted as being based on a homogenous body of data. This suggests that the considerable variability observed can, possibly, be explained by sampling errors. In any case, there is no requirement to analyze further the influence of moderator variables.

Nevertheless it is not unusual in meta-analyses to refer to anticipated possible moderator variables. In our case the three Klauer programs are of interest as were the type of students involved, the training conditions, and the two varieties of authorship. None of these moderators taken as a whole seem to have a particular impact on the results. The only disaggregated exception involves the nine studies that were performed in kindergarten that show a tendency to produce heterogeneous results within the group.

Table 4. Weighted Means d+ of the Effects of the Inductive Training on Intelligence Test Performance: Summary of Meta – Analyses (n: Number of Contrasts, N: Number of Subjects) _____________________________________________________________________ Variable d+ 95 % Confidence Interval n N p (Q)* ______________________________________________________________________ All experiments 0.52 0.46 – 0.59 79 3 595 0.80 ______________________________________________________________________

Possible Moderator Variables Programs Program 1 0.57 0.49 – 0.66 42 2 004 0.65 Program 2 0.43 0.32 – 0.55 24 1 144 0.63 Program 3 0.50 0.31 – 0.67 13 447 0.99 79 3 595 Subjects Kindergarten 0.47 0.24 – 0.70 9 306 0.09 School kindergarten 0.43 0.11 – 0.75 5 153 0.95 Primary school 0.61 0.50 – 0.72 19 1 274 0.63 Secondary school 0.42 0.30 – 0.54 24 1 148 0.78 Special education 0.54 0.39 – 0.69 22 714 0.98 79 3 595 Training Conditions One-to-one 0.34 0.15 – 0.53 11 432 0.70 Pairs 0.59 0.41 – 0.78 15 466 0.64 Small groups 0.57 0.46 – 0.67 36 1 422 0.84 Classes 0.51 0.40 – 0.62 17 1 275 0.50 79 3 595 Authorship Staff Klauer 0.57 0.47 – 0.68 35 1 386 0.79 Other authors 0.49 0.40 - 0.57 44 2 209 0.80 79 3 595 _______________________________________________________________________ * Probability of the coefficient Q of homogeneity


Hypothesis 2 (placebo effect) assumes that the effect of inductive training is due

simply to the special social conditions of any training. In order to test this hypothesis nine experiments were planned as three group designs. The first group received the regular inductive training, the second group was alternatively trained (but not inductive reasoning), and the third group did not participate in a training at all but continued regular classes. As was reported in the method section, the alternative training sessions made use of a broad range of different materials and activities so that the tests are not restricted to a single set of conditions. Hypothesis 2 is tested by comparing the alternatively trained group with the no–training control group (i. e., by a type 3 contrast). A meta–analysis on these nine effect sizes leads to a mean effect size estimation of d+ = 0.004 (n = 9, N = 230) which is not significantly different from zero. Hypothesis 2 is clearly rejected. One can conclude that the non–inductive training procedures had no significant effect on intelligence test performance.

Testing Hypothesis 3 is an attempt to determine how long training effects on intelligence test performance will last. What about its durability? In order to address this question, 22 experiments involving 1094 students were administered a follow-up posttest. As a rule, the first posttest was administered a few days after the end of the training. Follow–up posttests were administered between 3 and 15 months later (see column Month in Appendix B). The correlation between (a) the follow-up posttest and (b) the months between first posttest and follow-up posttest when (c) the pretest values were partialed out is r12.3 = 0.44 (df = 19), p = 0.045). Unexpectedly, this result means that training effects do not diminish over time and even increase slightly when the dependent variable is performance on fluid intelligence test items. Academic Learning As previously mentioned, in 38 experiments inductive training was followed by a lesson on a new subject matter that was a part of the regular curriculum. Training and control groups participated in the same lesson, and the amount of learning could be ascertained by criterion-referenced pre- and posttests. Effect sizes are displayed in the last column (g2) of the table in Appendix B. The following analyses refer to this column. The mean effect on academic learning was Mg = 0.74 ± 0.36 (n = 38, N = 1723) and thus larger than the mean effect on intelligence (Mg = 0.59 ± 0.31). In Figure 5 the distribution of the effect sizes on academic learning are depicted. It conveys the impression that there are a few outliers with unusually large effect sizes. Nevertheless, the analyses were performed with the whole data set.

Under these circumstances it again makes sense to look for possible moderator variables. This was done using the more adequate d measure of effect size and its means calculated with the weighted method of Hedges and Olkin (1985). The results of the meta–analysis used to examine hypothesis 4 are summarized in Table 5.


Freq

uenc

y of

Eff

ects

Figure 5. Distribution of the g effect sizes of training transferring to academic learning performance.

Table 5 shows an overall mean effect size d+ = 0.69. This is significantly larger than

the corresponding mean effect d+ = 0.52 for the transfer of training effects on intelligence test performance (p < 0.05, which is in contract to expectations. Obviously, inductive reasoning training improves academic learning of school–type subject matter more than it improves measured intellectual functioning. Moreover, with p(Q) = 0.35, one can maintain the hypothesis that the whole body of effect sizes is homogeneous and that it is not necessary to look further for moderator variable effects. However, upon closer inspection, one moderator variable effect requires additional consideration. Within program III, eleven experiments did not produce homogeneous effect sizes (p(Q) = 0.04). The largest outlier effect sizes on learning were found in studies with older students in special education who were trained using program III. Table 5. Weighted Means d+ of the Effects of the Inductive Training on Learning: Summary of Meta – Analyses (n: Number of Contrasts, N: Number of Subjects) _______________________________________________________________ Variable d+ 95 % Confidence Interval n N p (Q)* ______________________________________________________________________

All experiments 0.69 0.59 – 0.79 38 1 723 0.35 ______________________________________________________________________

Possible Moderator Variables Programs Program 1 0.64 0.49 - 0.80 11 663 0.89 Program 2 0.64 0.49 – 0.79 16 698 0.87 Program 3 0.84 0.62 – 1.06 11 362 0.04 38 1 723 Subjects Primary school 0.63 0.47 – 0.80 8 594 0.71 Secondary school 0.59 0.43 – 0.75 15 650 0.90 Special education 0.94 0.74 – 1.14 13 434 0.20 36 1 678 Training Conditions


Small groups 0.73 0.60 – 0.86 22 969 0.38 Classes 0.62 0.46 – 0.79 11 612 0.76 33 1 581 Authorship Staff Klauer 0.67 0.54 – 0.81 20 966 0.79 Other authors 0.71 0.57 – 0.86 18 757 0.80 38 1 723 _______________________________________________________________________ * Probability of the coefficient Q of homogeneity

Prior to analyzing the social conditions of the training, five experiments are excluded

from the analyses because of too few subjects (three studies with single children and two with pairs of children) so that 33 experiments were subjected to analysis. Results indicate that training in small groups of three to five children turns out to be a bit more effective, with training of whole classes close behind. In terms of effectiveness and practical utility, this is a noteworthy result. Finally, it is of some interest to again look at the authorship of the publications. This time the other authors slightly outperformed Klauer’s staff members although the difference is negligible.

Discussion With hypothesis 1 it was predicted that training in inductive reasoning would result in

positive transfer performance to tests of fluid intelligence. Results support this hypothesis. Looking at Figure 4, one can assume that training in inductive reasoning does no harm and often benefits children’s intellectual development.

According to hypothesis 2, it is assumed that the effects of the training are brought about by merely participating in any training activity, irrespective of what activities are trained (placebo effect). The nine experiments in which this issue was specifically addressed leads to the conclusion that unspecific placebo effects do not play a role. Clearly, hypothesis 2 can be rejected. This result is in line with placebo studies which have been reported in educational settings (Adair, Sharpe, & Huynh, 1990) and other contexts (Dush, Hirt, & Schroeder, 1989). Moreover, as Lipsey and Wilson (1993) demonstrated meta-analytically, when placebo effects are observed they disappear rather quickly. All in all, one can conclude that the results reported so far cannot be explained by placebo effects.

Another question pertains to the assumption that the effects of training diminish over time (see hypothesis 3 concerning durability of the effects). Actually, present results suggest that the effects in some of the reviewed studies are stable or increase linearly over time. How should such results be explained? One possibility would be that the control children’s intellectual capacities decrease linearly in time. However, there is no reason for such an assumption. Another possibility would be that the trained children make more and more use of the acquired strategy as a result of its successful employment and we are observing instances of self-regulated learning. Support for the durability of effects hypothesis would be strengthened if future research in this area were designed to include no-treatment control groups. In the set of studies reviewed, no information is available whether the effect might change beyond the time span of 15 months.

Incidentally, in the European research literature not included in the current review and meta-analyses, some authors have assumed long lasting and cumulative effects of similar interventions that have been deemed “snowball effects” (Feuerstein, Rand, Hoffman, & Miller, 1980). Acquiring a general strategy is said to foster future learning, which in turn should improve even later learning so that the gap between trained and untrained participants could get larger and larger. The alleged mechanisms leading to such results are termed “causes of other effects as well” (Clarke & Clarke, 1989; Schweinhart & Weikart, 1980, p. 64).We have not accepted such a position.


As to hypothesis 4, transfer effects on academic learning, the pattern of results are very encouraging. The effects are unexpectedly high and typically larger than the effects on intelligence. The transfer effects were observed over a broad range of academic subject matter One reason for this success could be that the strategy taught during training can be directly applied in many academic situations. For example, each academic subject requires concept formation and every concept is defined through a set of common attributes. Moreover, every academic subject matter contains rules, laws, or regularities which are defined through one or more common relations. Hence, one can assume that the inductive reasoning strategy as it is acquired during training can be applied and transferred to classroom learning performance.

Actually, the prescriptive strategy is a rather simple procedure that can easily be learned. At its center is basically a general procedure of comparing, (i.e., looking for commonalities and diversities). During the ten lessons, teaching deals exclusively with the concepts required, the cognitive and metacognitive processes involved, and the application of this knowledge to new problems in a wide variety of situations. However, these considerations would not necessarily predict that inductive reasoning training fosters learning of a subject matter to the same or to an even larger extent than it improves fluid intelligence test performance. This question should be addressed by new research projects.

As to the teaching to the test or coaching hypothesis (hypothesis 5), it was tested by two criteria, (a) the durability of the effects, and (b) the transfer to academic learning tasks. Both criteria are clearly fulfilled so that the interpretation of positive training results as being due solely to test coaching procedures can be rejected. A look back at the theory of inductive reasoning presented

In summary, it seems appropriate to have a look back on the theory underlying this research. The core of the theory is prescriptive in nature. It states that inductive reasoning can be achieved by a comparison strategy, where attributes of objects or relations between objects are to be scanned with respect to similarity, difference, or both, for commonality and/or diversity. It is not claimed that subjects actually proceed this way when they solve inductive problems. Instead, our contention is only that subjects have a good chance to solve inductive problems more effectively when they make use of the comparing strategy. The results show that this is the case. Moreover, it was found that the comparing strategy not only transfers to intelligence test performance but that it improves intellectual competencies. Furthermore, it also improves problem-solving and learning of academic subject matter.

The theory, however, maintains that the comparing strategy enables one to solve all kinds and varieties of inductive reasoning problems. But the empirical data show that the trained participants by no means are able to solve all types of inductive problems to which they are exposed. To explain the gap between actual and theoretical improvement one could assume that the comparing strategy may be a helpful but not a sufficient condition for solving all inductive reasoning problems. A simple example can demonstrate that the strategy is not sufficient for every problem. If one has to find commonalities between a pan, a lemon, and a microwave oven, then one needs to have some special knowledge, and a reasonable solution is not possible if that knowledge is not available. Also, insufficient knowledge may not be the only problem that can lead to failure in the application of the inductive strategy. Regardless of participants’ cognitive ability level, for successful application of the comparative strategy it must be mastered at a sufficiently high level of proficiency. Support for this contention is provided by Klauer (1996) where it was shown that a number of “above average” children who had not appropriately learned the comparing strategy benefited little from training. One must conclude that a strategy which is effective in some cases will not lead to success for everybody in all situations.

Finally, if the prescriptive theory of inductive reasoning works as expected, one can assume that teachers should be able to apply it in their regular classes. The basic principle “compare and contrast” is very concrete and teachers should be able to adapt it to their regular


lessons instead of relying on published training programs. This way they would have the opportunity to adapt the strategy according to their student’s level of cognitive development as well as to the subject matter being taught. The majority of the training studies were conducted by educationally inexperienced graduate students of psychology or education and one can assume that experienced teachers would be able to teach the comparing strategy and its applications with much greater effectiveness.

Research, of an experimental or quasi-experimental nature, seeking to replicate these inductive reasoning training effects in U.S. schools, is encouraged. In principle, one should expect both an improvement of children’s intellectual competencies and more efficient learning of regular subject matter as has been found in the experiments reviewed.


References Adair, J. G., Sharpe, D., & Huynh, C. I. (1990). The placebo control group: An analysis of its effectiveness in educational research. Journal of Experimental Education, 59, 67-86. Alexander, P. A., & Willson, V. L. (1987). Analogical reasoning in young children. Journal of Educational Psychology, 79, 401-408. Anastasi, A. (1981). Coaching, test sophistication, and developed abilities. American Psychologist, 10, 1086-1093. Angerhoefer, U., Kullik, U., & Masendorf, F. (1992). Denk- und Rechenförderung lernbeeinträchtigter Kinder: Multivariate Änderungsbeurteilung mittels Prädiktions-KFA [Fostering thinking and math performance with learning impaired children: Multivariate evaluation of change by prediction CFA]. Psychologie in Erziehung und Unterricht, 39, 190-195. Bean, T, W., Searles, D., Singer, H., & Cowan, S. (1990). Learning concepts from biology text through pictorial analogies and an analogical study guide. Journal of Educational Research, 83, 233-237. Belmont, J. M., Butterfield, E. C., & Ferretti, R. P. (1982). To secure transfer of training instruct self-management skills. In D. K. Detterman & R. J. Sternberg (Eds.), How and how much can intelligence be increased? (pp. 147-154). Norwood, NJ: Ablex. Bornemann, K. (1989). Erprobung des Denktrainings in Zweiergruppen [Testing the Training to Reason with pairs of children]. In K. J. Klauer, Denktraining für Kinder 1 (p. 73-74). Göttingen: Verlag für Psychologie. Büchel, F., & Scharnhorst, U. (1993). Training des induktiven Denkens bei Lern- und Geistigbehinderten [Training of inductive reasoning with mildly or severely mentally retarded children]. In K. J. Klauer (Ed.), Kognitives Training (pp. 95-123). Göttingen: Hogrefe. Cahan, S. (2000). Statistical significance is not a “Kosher” certificate for observed effects: A critical analysis of the two – step approach to the evaluation of empirical results. Educational Researcher, 29, 31-34. Carpenter, P. A., Just, M. A., & Shell, P. (1990). What one intelligence test measures: A theoretical account of the processing in the Raven Progressive Matrices test. Psychological Review, 97, 404-431. Cattell, R. B. (1963). Theory of fluid and crystallized intelligence: A critical experiment. Journal of Educational Psychology, 54, 1-22. Cattell, R.B., & Cattell, A.K.S. (1963) Culture Fair Intelligence Test. Champaign, Illinois: Institute for Personality and Ability Testing , Inc. Chen, Z. (1999). Schema induction in children’s analogical problem solving. Journal of Educational Psychology, 91, 703-715. Clarke, A. M., & Clarke, A. D. B. (1989). The later cognitive effects of early intervention. Intelligence, 13, 289-297.


Cook, T. D., Appleton, H., Connor, R., & Schaffer, A. (1975). Sesame street revisited: A case study in evaluation research. New York: Russel Sage. Cohen, J. (1968). Weighted kappa: Nominal scale agreement with provision for scaled disagreement or partial credit. Psychological Bulletin, 70, 213-220. Coley, J. D., Hayes, B., Lawson, C., & Moloney, M. (2004). Knowledge expectations and inductive reasoning within conceptual hierarchies. Cognition, 90, 217-253. Csapó, B. (1997). The development of inductive reasoning: Cross – sectional assessments in an educational context. International Journal of Behavioral Development, 20, 609-626. Dush, D. M., Hirt, M. L., & Schroeder, H. E. (1989). Self-statement modification in the treatment of child behavior disorders: A meta-analysis. Psychological Bulletin, 106, 97-106. Elbaum, B., Vaughn, S., Hughes, M. T., & Moody, S. W. (2000). How effective are one-to-one tutoring programs in reading for elementary students at risk for reading failure? A meta-analysis of the intervention research. Journal of Educational Psychology, 92, 605-619. Ernst, G. W., & Newell, A. (1969). GPS: A case study in generality and problem solving. New York: Academic Press. Feuerstein, R., Rand, Y., Hoffman, M. B., & Miller, R. (1980). Instrumental enrichment: An intervention program for cognitive modifiability Baltimore, MD: University Park Press. Fries, S., Lund, B., & Rheinberg, F. (1999). Lässt sich durch gleichzeitige Motivförderung das Training des induktiven Denkens optimieren? [Can training of inductive reasoning be optimized through fostering simultaneously achievement motivation?]. Zeitschrift für Pädagogische Psychologie, 13, 37-49. Gentner, D. (1989). The mechanisms of analogical learning. In S. Vosniadou & A. Ortony (Eds.), Similarity and analogical reasoning (pp. 199-241). Cambridge, MA: Cambridge University Press. Gick, M. L., & Holyoak, K. J. (1983). Schema induction and analogical transfer. Cognitive Psychology, 15, 1-38. Gitomer, D. H., Curtis, M. E., Glaser, R., & Lensky, D. B: (1987). Processing differences as a function of item difficulty in verbal analogy performance. Journal of Educational Psychology, 79, 212-219. Glaser, R., & Pellegrino, J. (1982). Improving the skills of learning. In D. K. Detterman & R. J. Sternberg (Eds.), How and how much can intelligence be increased? (pp. 197-212). Norwood, NJ: Ablex. Glass, G V. (1976). Primary, secondary, and meta – analysis of research. Educational Researcher, 5, 3-8.


Goldman, S. R., & Pellegrino, J. W. (1984). Deductions about induction: Analysis of developmental and individual differences. In. R. J. Sternberg (Ed.), Advances in the psychology of human intelligence (Vol. 2, pp.149-197). Hillsdale, NJ: Erlbaum. Goska, R. E., & Ackerman, P. L. (1996). An aptitude – treatment interaction approach to transfer within training. Journal of Educational Psychology, 88, 249-259. Gustafsson, J. E. (1984). A unifying model for the structure of intellectual abilities. Intelligence, 8, 179-203. Gustafsson, J. E., & Undheim, J. O. (1992). Stabilty and change in broad and narrow factors of intelligence from ages 12 to 15 years. Journal of Educational Psychology, 84, 141-149. Hager, W., & Hasselhorn, M. (1995). Zuwendung als Faktor der Wirksamkeit kognitiven Trainings für Kinder [Effects of special attention directed to children as a determinant of the effectiveness of cognitive training programs]. Zeitschrift für Pädagogische Psychologie, 9, 163-179. Hager, W., Hübner, S., & Hasselhorn, M. (2000). Zur Bedeutung der sozialen Interaktion bei der Evaluation kognitiver Förderprogramme [The meaning of social interaction in evaluations of cognitive training programs]. Zeitschrift für Pädagogische Psychologie, 14, 106-115. Hasselhorn, M. (1995). Kognitive Trainings: Grundlagen, Begrifflichkeiten und Desiderate [Cognitive training: Basis, concepts, and desiderata]. In. W. Hager (Ed.), Programme zur Förderung des Denkens bei Kindern (pp. 14-40). Göttingen: Hogrefe. Hedges, L. V. (1981). Distribution theory for Glass’s estimator of effect size and related estimators. Journal of Educational Statistics, 6, 107-128. Hedges, L. V., & Olkin, I. (1985). Statistical methods for meta-analysis. New York: Academic Press. Heit, E. (2000). Properties of inductive reasoning. Psychonomic Bulletin and Review, 7, 569-592. Heit, E., & Feeney, A. (2005). Relation between premise similarity and inductive strength. Psychonomic Bulletin & Review, 12, 340-344. Heit, E., & Hahn, U. (2001). Diversity-based reasoning in children. Cognitive Psychology, 43, 243-273. Heit, E., & Hayes, B. K. (2005). Relations among categorization, induction, recognition, and similarity: Comment on Sloutsky and Fisher (2004). Journal of Experimental Psychology: General. 134, 596-605. Holland, J. H., Holyoak, K. J., Nisbett, R. E., & Thagard, P. R. (1986). Induction. Processes of inference, learning, and discovery. Cambridge, MA: MIT Press. Holzman, T. G., Pellegrino, J. W., & Glaser, R. (1983). Cognitive variables in series completion. Journal of Educational Psychology, 75, 603-618.


Klauer, K. J. (1989). Denktraining für Kinder I [Training to reason for children 1]. Göttingen & Seattle: Hogrefe. Klauer, K. J. (1991). Denktraining für Kinder II. [Training to reason for children II]. Göttingen & Seattle: Hogrefe. Klauer, K. J. (1992). Problemlösestrategien im experimentellen Vergleich: Effekte einer allgemeinen und einer bereichsspezifischen Strategie [Comparing problem solving strategies experimentally: Effects of a general and a domain specific strategy]. In H. Mandl, & H.F. Friedrich (Hrsg.), Lern- und Denkstrategien, (pp. 58-78). Göttingen: Verlag für Psychologie. Klauer, K. J. (1993). Denktraining für Jugendliche [Training to reason for youths]. Göttingen & Seattle: Hogrefe.

Klauer, K. J. (1996). Teaching inductive reasoning: Some theory and three experimental studies. Learning and Instruction, 6, 37-57.)

Klauer, K. J., & Phye, G. D. (1994). Cognitive training for children. A developmental program of inductive reasoning and problem solving. Hogrefe & Huber: Seattle.

Klauer, K. J., Resing, W. C. M., & Slenders, A. P. A. C. (1996). Cognitieve training voor kinderen [Cognitive training for children]. Göttingen: Hogrefe.

Klauer, K. J., Willmes, K., & Phye, G. D. (2002). Inducing inductive reasoning: Does it transfer to fluid intelligence? Contemporary Educational Psychology, 27, 1-25.

Kolmsee, R. (1989). Erprobung des Denktrainings I im ersten Schuljahr [Testing Training to Reason I in a first class]. In K. J. Klauer, Denktraining für Kinder 1 (pp. 64-65). Göttingen: Verlag für Psychologie. Kotovsky, K., & Simon, H. A. (1973). Empirical test of a theory of human acquisition of concepts for sequential patterns. Cognitive Psychology, 4, 399-424. Levin, J. R., & Robinson, D. H. (2000). Rejoinder: Statistical hypothesis testing, effect – size estimation, and the conclusion coherence of primary research studies. Educational Researcher, 29(1), 34-36. Lipsey, M. W., & Wilson, D. B. (1993). The efficacy of psychological, educational, and behavioral treatment. Confirmation from meta –analysis. American Psychologist, 48, 1181-1209. Lochhead, J. (1985). Teaching analytic skills through pair problem solving. In J. W. Segal, S. F. Chipman, & R. Glaser (Eds.), Thinking and learning skills (Vol. 1, pp. 83-108). Hillsdale, NJ: Erlbaum. Masendorf, F. (1994). Förderungstypen des induktiven Denkens und des räumlichen Vorstellens bei lernbeeinträchtigten Kindern [Types of improvers of inductive reasoning and of spatial ability with learning impaired children]. Psychologie in Erziehung und Unterricht, 41, 14-21.


Medin, D. L., & Heit, E. (1999). Categorization. In Bly, B. M. & Rumelhart, D. E. (Eds.), Cognitive Science (pp. 99-143). San Diego, CA: Academic Press. Palincsar, A. S., & Brown, A. L. (1984). Reciprocal teaching of comprehension - fostering and comprehension – monitoring activities. Cognition and Instruction, 1, 117-175. Pellegrino, J. W., & Glaser, R. (1980). Components of inductive reasoning. In R. Snow, P. A. Frederico, & W. Montague (Eds.), Aptitude, learning, and instruction: Cognitive process analyses of aptitude (Vol. 1, pp. 177-217). Hillsdale, NJ: Erlbaum. Phye, G. D. (1989). Schemata training and transfer of intellectual skill. Journal of Educational Psychology, 81, 347-352. Phye, G. D. (1990). Inductive Problem solving: Schema inducement and memory – based transfer. Journal of Educational Psychology, 82, 826-831. Phye, G. D. (1997). Inductive reasoning and problem solving: The early grades. In G. D. Phye (Ed.), Handbook of Academic Learning (pp. 451-471). New York: Academic Press. Pierce, K. A., Duncan, M. K.,Gholson, B., Ray, G. E., & Kamhi, A. G. (1993). Cognitive load, schema acquisition, and procedural adaptation in nonisomorphic analogical transfer. Journal of Educational Psychology, 85, 66-74. Raven, J.C., Court, J. H., & Raven, J. (1994). Raven Progressive Matrices: Oxford England: Oxford Psychologist Press Ltd. Reed, S. K., Dempster, A., & Ettinger, M. (1985). Usefulness of analogous solutions for solving algebra word problems. Journal of Experimental Psychology: Learning, Memory, and Cognition, 11, 106-125. Rehder, B. (2003). A causal model theory of conceptual representation and categorization. Journal of Experimental Psychology: Learning, Memory, and Cognition, 29, 1141-1159. Rehder, B., & Burnett, R. C. (2005). Feature inference and the causal structure of categories. Cognitive Psychology, 50(3), 264-314. Robin, S., & Mayer, R. E. (1993). Schema training in analogical reasoning. Journal of Educational Psychology, 85, 529-538. Robinson, D. H., & Levin, J. R. (1997). Reflections on statistical and substantive significance. Educational Researcher, 26, 21-29. Schweinhart, L., & Weikart, D. P. (1980). Young children grow up: The effects of the Perry Preschool Program on youth through age 15. Ypsilant, MI: High/Scope Press. Sloutsky, V. M., & Fisher, A. V. (2004). Induction and categorization in young children: A similarity-based model. Journal of Experimental Psychology: General, 133, 166-188. Snow, R.E., Kyllonen, P.C., Marshalek, B. (1984). The topography of ability and learning correlations. In R.J. Sternberg (Ed.), Advances in the psychology of human intelligence. Vol. 2 Hillsdale, N.J.: Lawrence Erlbaum Assoc.


Sonntag, W. (2004). Experimentelle Untersuchungen zum Einfluss des Klauerschen Denktrainings auf mathematisches Denken und Lernen von lernbehinderten Sonderschülern [Experimental studies on the impact of Klauer’s training to reason on mathematical thinking and learning with slightly retarded students]. Zeitschrift für Pädagogische Psychologie, 18, 101-111. Souvignier, E. (1997). Die Förderung des räumlichen Denkens bei lernbeeinträchtigten Schülern [Fostering spatial reasoning with learning impaired students]. In F. Masendorf (Ed.), Experimentelle Sonderpädagogik, S. 379-420. Weinheim: Deutscher Studien Verlag. Spearman, C. (1923). The nature of intelligence and the principles of cognition. London: Macmillan. Sternberg, R. J., & Gardner, M. (1983). Unities in inductive reasoning. Journal of Experimental Psychology: General, 112, 80-116. Tennyson, R. D., Youngers, J., & Suebsonthi, P. (1983). Concept learning by children using instructional presentation forms for prototype formation and classification-skill development. Journal of Educational Psychology, 75, 280-291. Thompson, B. (2002). What future quantitative social science research could look like : Confidence intervals for effect sizes. Educational Researcher, 31(3), 25-32. Thurstone, L. L. (1938). Primary mental abilities. Psychometric Monographs No. 1. Tversky, A. (1977). Features of similarity. Psychological Review, 84, 327-352. Van de Vijver, F. J. R. (2002). Inductive reasoning in Zambia, Turkey, and The Netherlands. Establishing cross-cultural equivalence. Intelligence, 30, 313-351. Vosniadou, S., & Schommer, M. (1988). Explanatory analogies can help children acquire information from expository text. Journal of Educational Psychology, 80, 524-536. Wainer, H., & Robinson, D. H. (2003). Shaping up the practice of null hypothesis significance testing. Educational Researcher, 32(7), 22-30.


Author Notes

Karl Josef Klauer is professor emeritus of education at the Institute of Education, Technical University of Aachen, Germany. He is especially interested in the research of teaching and learning. E-mail: [email protected] Gary D. Phye is professor of curriculum/instruction and psychology in the College of Human Sciences of Iowa State University, Ames, Iowa. He is especially interested in problem-solving transfer and academic learning. E-Mail: [email protected] Gary D Phye N162b Lagomarcino Iowa State University Ames, IA. 50011-3190 Correspondence concerning this article may be addressed to either author at the aforementioned E-Mail addresses.


Appendix A

Meta-Analyses Data Pool

73.-74. Sonntag, W. (2004). Experimentelle Untersuchungen zum Einfluss des Klauerschen Denktrainings auf mathematisches Denken und Lernen von lernbehinderten Sonderschülern [Experimental studies on the impact of Klauer’s training to reason on mathematical thinking and learning with slightly retarded students]. Zeitschrift für Pädagogische Psychologie, 18, 101-111.

70.-72. Sonntag, W. (2002). Fördert ein Training des induktiven Denkens das Lösen

mathematischer Textaufgaben? [Does a training of inductive reasoning improve solving of mathematical word problems?]. Heilpädagogische Forschung, 28 (1), 24-37.

68.-69. Roth-van der Werf, T. J. M., Resing, W. C. M., & Slenders, A. P. A. C. (2002). Task

similarity and transfer of an inductive reasoning training. Contemporary Educational Psychology, 27, 296-325.

67. Klauer, K. J., Willmes, K., & Phye, G. D. (2002). Inducing inductive reasoning: Does

it transfer to fluid intelligence? Contemporary Educational Psychology, 27, 1-25. 66. Möller, J., & Appelt, R. (2001). Auffrischungssitzungen zur Steigerung der

Effektivität des Denktrainings für Kinder I [Booster sessions to foster the effectiveness of the training to reason for children I]. Zeitschrift für Pädagogische Psychologie, 15, 199-206.

65. Sydow, H., & Schmude, C. (2001). Training des analogen Denkens und des

Zahlbegriffs im Vorschulalter [Training of analogical reasoning and of the number concept with preschoolers]. In K. J. Klauer (Ed.). Handbuch kognitives Training (pp. 129-164). Göttingen: Hogrefe.

64. Koning, E. de (2000). Inductive reasoning in primary education. Measurement,

teaching, transfer (Chapter 6). Dissertation Universität of Utrecht. See also Koning, E. de, Hamers, Jo H. M., Sijtsma, K., & Vermeer, A. (2002). Teaching inductive reasoning in primary education. Developmental Review, 22, 211-241.

63. Fries, S. (2001). Ein Training zur gleichzeitigen Förderung des Leistungsmotivs und

des induktiven Denkens [A training to foster simultaneously achievement motivation and inductive reasoning]. Münster: Waxmann.

62. Hager, K., Hübner, S., & Hasselhorn, M. (2000). Zur Bedeutung der sozialen

Interaktion bei der Evaluation kognitiver Trainingsprogramme [On the impact of social interaction on the evaluation of cognitive training programs]. Zeitschrift für Pädagogische Psychologie, 14, 106-115

61. Braun, J., Weyhreter, H., Köhnlein, O., Storck, M., & Bode, H. (2000). Kognitives

Training: Ein Programm zur Förderung von Vorschulkindern mit intellektuellen Defiziten [Cognitive training: A program to foster preschoolers with intellectual deficits]. Psychologie in Erziehung und Unterricht, 47, 10-17.


60. Klauer, K. J. (1999). Induktives Denken oder elementares Wahrnehmen? Ein Entscheidungsexperiment [Inductive reasoning or perception?]. Empirische Pädagogik, 13, 97-122.

58-59. Strathmann, A. (1999). Denktraining bei Lernbehinderten: Transferiert es auf

Intelligenz und Lernen? [Training to reason with learning disabled subjects: Does it transfer on intelligence and learning?]. Heilpädagogische Forschung, 25, 129-139.

56.-57. Brünken, R. (1993). Auswirkungen eines Denktrainings für Kinder auf intentionales

und inzidentelles Lernen bei Lesetexten [Effects of a training to reason on intentional and incidental learning with instructional texts]. Unpublished master’s thesis, University of Aachen, Aachen, Germany.

55. Favre, M. (1994). Der Einfluss eines Trainings des induktiven Denkens auf die

Leistung im intentionalen und inzidentellen Lernen bei schulischen Lehrtexten [On the influence of an inductive training on intentional and incidental learning with instructional texts]. Unpublished master’s thesis, University of Aachen, Aachen, Germany.

54. Strathmann A. (1999). Über die Effekte eines Strategietrainings bei verhaltensgestörten

Schülern und Regelschülern [On the effects of a strategy training with behavior disturbed and regular students]. Psychologie in Erziehung und Unterricht, 46, 177-186.

53. Möller, J. (1999). Denktraining für Jugendliche: Homogenität der Trainingsgruppen

und Booster-Sessions [Training to reason for youths: Homogeneity of training groups and booster sessions]. Heilpädagogische Forschung, 25, 2-7.

52. Fries, S., Lund, B., & Rheinberg, F. (1999). Lässt sich durch gleichzeitige

Motivförderung das Training des induktiven Denkens optimieren? [Can training of inductive reasoning be optimized through fostering simultaneously achievement motivation?]. Zeitschrift für Pädagogische Psychologie, 13, 37-49.

51. Langfeldt, H.-P., & Schlieper, J. (1999). Aspekte der konvergenten und

diskriminanten Validität des "Denktrainings für Kinder I" von K. J. Klauer [Aspects of convergent and discriminant validity of the „Training to Reason for Children I“ by K. J. Klauer]. Psychologie in Erziehung und Unterricht, 46, 1-6.

49.-50. Klauer, K. J. (1999). Über den Einfluß des induktiven Denkens auf den Erwerb

unanschaulich-generischen Wissens bei Grund- und Sonderschülern [On the impact of inductive reasoning on the acquisition of abstract – generic knowledge with primary and special school students]. Psychologie in Erziehung und Unterricht, 46, 7-28.

48. Tomic, W., & Kingma, J. (1998). Accelerating intelligence development through

inductive reasoning training. In W. Tomic, & J. Kingma (Eds.), Conceptual issues in research on intelligence (pp. 291-305). Stamford, Com.: JAI Press.

47. Souvignier, E. (1998). Effekte kognitiver Trainingsprogramme der

Vorstellungsfähigkeit und des induktiven Denkens auf die Problemlösefähigkeit [Effects on problem solving ability of cognitive training programs to foster spatial


performance and inductive reasoning]. Zeitschrift für Experimentelle Psychologie, 45, 20-28.

46. Klauer, K. J. (1998). Begünstigt induktives Denken den Erwerb der

Gedächtnisstrategie des Kategorisierens? [Does inductive reasoning improve the acquisition of the memory strategy of categorizing?]. Zeitschrift für Pädagogische Psychologie, 12, 73-84.

44.-45. Hamers, J. H. M., De Koning, E., & Sijtsma, K. (1998). Inductive reasoning in third

grade: Intervention promises and constraints. Contemporary Educational Psychology, 23, 132-148.

43. Möller, J., & Köller, O. (1997). Effekte von Leistungsgruppierung und

Ausgangsfähigkeit auf die Wirksamkeit des Denktrainings II [Effects of grouping according to achievement level and of pre-experimental ability on the effectiveness of the training to reason II]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 29, 242-254.

42. Resing, W. C. M., & Slenders, A. P. A. (1997, September). Training inductive

thinking skills in learning disabled children. Paper presented at the 8th European Conference on Developmental Psychology at Rennes, France. (In W. Resing, & W. Tomic [Co-convenors], Teaching higher order thinking skills).

41. Rollett, W., & Wladika, E. (1997, August), The effect of Klauer's inductive reasoning

training. A consequence of trainer-trainee interaction? Paper presented at the 7th European Conference on Learning and Instruction, Athens (In I. Diakidou [Chair]. Problem solving).

40. Klauer, K. J. (1997). Lässt sich die Strategie des induktiven Denkens auf schulisches

Lernen transferierbar lehren? [Can the strategy of inductive reasoning be taught to transfer on learning in school?]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 29, 225-241.

39. Souvignier, E. (1997). Die Förderung des räumlichen Denkens bei lernbeeinträchtigten

Schülern [Fostering spatial reasoning with learning impaired students]. In F. Masendorf (Ed.), Experimentelle Sonderpädagogik, pp. 379-420. Weinheim: Deutscher Studien Verlag.

37.-38. Tomic, W., & Klauer, K. J. (1996). On the effect of training inductive reasoning: How

far does it transfer and how long do the effects persist? European Journal of Psychology of Education, 11, 283-299.

35.-36. Klauer, K. J. (1996). Begünstigt induktives Denken das Lösen komplexer Probleme?

[Does inductive reasoning improve solving of complex problems?]. Zeitschrift für Experimentelle Psychologie, 43, 85-113.

34. Klauer, K. J. (1996). Teaching inductive reasoning: Some theory and three

experimental studies. Learning and Instruction, 6, 37-57.) 33. Klauer, K. J. (1996). Denktraining oder Lesetraining? Über die Auswirkungen eines

Trainings zum induktiven Denken sowie eines Lesetrainings auf Leseverständnis und


induktives Denken [Training to reason or training to read? The effects of an inductive reasoning training and a reading training on reading comprehension and inductive reasoning]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 28, 67-89.

31.-32. Beck, M., Lübking, M, & Meier, U. (1995). Die Bielefelder Studien zum

Denktraining von Klauer [Bielefeld studies on Klauer’s training to reasoning]. In W. Hager (Ed.), Programme zur Förderung des Denkens bei Kindern (pp. 294-308). Göttingen: Hogrefe.

30. Klauer, K. J. (1995). Induktives Denken erleichtert die Konstruktion analoger

Satzstrukturen [Inductive reasoning improves the construction of analogical sentence structures]. Sprache & Kognition, 14, 221-227.

28.-29. Klauer, K. J. (1995). Weitere Erprobung des "Denktrainings für Jugendliche" in der

Oberstufe der Schule für Lernbehinderte [Another test of the „Training to Reason for Youths“ in special education]. Heilpädagogische Forschung, 21, 157- 170.

27. Hasselhorn, M., Hager, W., & Boeley-Braun, K. (1995). Läßt sich die fluide

Intelligenz erwachsener Behinderter durch das Aachener Denktraining nachhaltig verbessern? [Can fluid intelligence of handicapped adults be sustainably improved by the Aachen Training to Reason?]. Heilpädagogische Forschung, 21, 171-179.

26. Hager, W., & Hasselhorn, M. (1995). Zuwendung als Faktor der Wirksamkeit

kognitiver Trainings für Kinder [Attention as a factor of the effectiveness of cognitive training programs for children]. Zeitschrift für Pädagogische Psychologie, 9, 163-179.

25. Tomic, W. (1995). Training in inductive reasoning and problem solving.

Contemporary Educational Psychology, 20, 483-490. 24. Hasselhorn, M., & Hager, W. (1995). Neuere Programme zur Denkförderung bei

Kindern: Wie effektiv sind sie im Vergleich zu herkömmlichen Wahrnehmungsübungen? [Newer programs to foster children’s reasoning: How effective are they in comparison to traditional perceptual training?]. Psychologie in Erziehung und Unterricht, 42, 221-223.

23. Masendorf, F. (1994). Förderungstypen des induktiven Denkens und des räumlichen

Vorstellens bei lernbeeinträchtigten Kindern [Types of improvers of inductive reasoning and of spatial ability with learning impaired children]. Psychologie in Erziehung und Unterricht, 41, 14-21.

22. Klauer, K. J. (1994). Transferiert der Erwerb von Strategien des induktiven Denkens

auf das Erlernen eines schulischen Lehrstoffs? [Does the acquisition of a strategy of inductive reasoning transfer on learning of school type subject matter?]. Zeitschrift für Pädagogische Psychologie, 8, 15-25.

21. Schmude, C., & Sydow, H. (1994, September). Wirkungen kognitiven Trainings im

Vorschulalter [Effects of cognitive training programs with preschoolers]. Contribution at the 39th Congress Deutsche Gesellschaft für Psychologie, Hamburg (Section: Evaluation of programs to foster cognitive development).


20. Hager W., & Hasselhorn, M. (1993). Induktives Denken oder elementares

Wahrnehmen? [Inductive reasoning or fundamental perception?]. Empirische Pädagogik, 7, 421-458.

19. Beck, M., Lüttmann, B., & Rogalla, U. (1993). Wenn Du denkst, Du denkst... Eine

Untersuchung der Effektivität des Klauer´schen Denktraining [If you think you think … A study on the effectiveness of Klauer’s Training to Reason]. Zeitschrift für Enwicklungspsychologie und Pädagogische Psychologie, 25, 297-306.

18. Hager, W., & Hasselhorn, M. (1993). Evaluation von Trainingsmaßnahmen am

Beispiel von Klauers Denktraining für Kinder [Evaluation of training measures with the example of Klauer’s Training to Reason for Children I] . Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 25, 307-321.

17. Klauer, K. J. (1993). Über den Einfluss eines Trainings zum induktiven Denken auf

den Erwerb und die Nutzung der Lernstrategie des "Networking" [Impact of a training of inductive reasoning on the acquisition and use of the learning strategy „networking“]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 25, 333-352.

16. Klauer, K. J. (1993). Induktives Denken beeinflusst das Rechtschreiblernen [Inductive

reasoning influences learning to spell]. Zeitschrift für Entwicklungspsychologie und Pädagogische Psychologie, 25, 352-365.

14.-15. Klauer, K. J. (1993). Denken und Lernen bei Lernbehinderten: Fördert das Training

des induktiven Denkens schulisches Lernen? [Thinking and learning with slightly retarded children: Does a training of inductive reasoning improve learning in school?]. Heilpädagogische Forschung, 19, 55-66.

13. Klauer, K. J. (1993). Über die Auswirkungen eines Trainings zum induktiven Denken

auf zentrale Komponenten der Fremdsprachenlernfähigkeit [On the effects of a training of inductive reasoning on central components of the ability to learn foreign languages]. Zeitschrift für Pädagogische Psychologie, 7, 1-9.

12. Klauer, K. J. (1992). Teaching inductive thinking to highly able children. European

Journal for High Ability, 3, 164-180. 10.-11. Klauer, K. J. (1992). "Bottom up" oder "top down"? Über die Transferwirkungen

zweier Strategien zum Training des induktiven Denkens [„Bottom up“ or „top down“? On the transfer effect of two strategies of a training to reason inductively]. Sprache & Kognition, 11, 91-103.

9. Angerhoefer, U., Kullik, U., & Masendorf, F. (1992). Denk- und Rechenförderung

lernbeeinträchtigter Kinder: Multivariate Änderungsbeurteilung mittels Prädiktions-KFA [Fostering thinking and math performance with learning impaired children: Multivariate evaluation of change by prediction CFA]. Psychologie in Erziehung und Unterricht, 39, 190-195.

8. Klauer, K. J. (1992). Problemlösestrategien im experimentellen Vergleich: Effekte

einer allgemeinen und einer bereichsspezifischen Strategie [Comparing problem


solving strategies experimentally: Effects of a general and a domain specific strategy]. In H. Mandl, & H.F. Friedrich (Hrsg.), Lern- und Denkstrategien, (pp. 58-78). Göttingen: Verlag für Psychologie.

7. Bussas, K. (1992). Erprobung des Denktrainings II im Gymnasium [Testing Training

to Reason II in a grammar school]. Unpublished master’s thesis, University of Aachen, Aachen, Germany.

6. Igelmund, T. (1990). Erprobung des Denktrainings II im vierten Schuljahr [Testing

Training to Reason II in a fourth class]. In K. J. Klauer, Denktraining für Kinder 1 (p. 64). Göttingen: Verlag für Psychologie.

5. Kolmsee, R. (1989). Erprobung des Denktrainings I im ersten Schuljahr [Testing

Training to Reason I in a first class]. In K. J. Klauer, Denktraining für Kinder 1 (pp. 64-65). Göttingen: Verlag für Psychologie.

4. Johnen, M. (1989). Erprobung des Denktrainings im Kindergarten [Testing the

Training to Reason in kindergarten]. In K. J. Klauer, Denktraining für Kinder 1 (p. 75). Göttingen: Verlag für Psychologie.

3. Bornemann, K. (1989). Erprobung des Denktrainings in Zweiergruppen [Testing the

Training to Reason with pairs of children]. In K. J. Klauer, Denktraining für Kinder 1 (p. 73-74). Göttingen: Verlag für Psychologie.

2. Bornemann, K. (1988). Erprobung des Denktrainings im Kindergarten [Testing the

Training to Reason in kindergarten]. In K. J. Klauer, Denktraining für Kinder 1 (p. 73). Göttingen: Verlag für Psychologie.

1. Bornemann, K. (1988). Erprobung des Denktrainings im Kindergarten [Testing the

Training to Reason in kindergarten]. In K. J. Klauer, Denktraining für Kinder 1 (pp. 72-73). Göttingen: Verlag für Psychologie.


Appendix B Summary Table of Meta – Analyses

Row

Exper.

Author

N

Subj.

Contrast

Progr.

Soc. Cond.

DV 1

g11

Months g12

DV 2

g2

89 74 0 30 5 1 3 3 2 0.64* 6 0.80* 2 0.84* 88 73 0 39 5 1 3 3 2 0.25 2 1.68* 87 73 0 38 5 2 3 3 2 0.49 2 1.50* 86 73 0 20 5 3 3 3 2 -0,22 2 -0,28 85 72 0 36 5 1 3 3 5 0.49* 2 0.82* 84 71 0 29 5 1 2 3 5 1.06* 2 1.33* 83 70 0 40 5 1 2 3 2 0.62* 82 69 0 79 3 1 1a) 2 4 0.24 11 0.16 81 68 0 31 5 1 1a) 2 4 0.22 11 1.31* 80 67 1 166 3 1 1 3 4 0.90* 6 1.05* 2 0.81* 79 66 0 54 3 1 1 3 2 0.83* 78 65 0 62 3 1 1 3 2 0.81* 5 0.34 2 0.77*77 64 0 91 3 1 1a) 4 1 0.69* 15 1.22* 4 0.59* 76 64 0 97 3 1 1a) 4 1 0.59* 15 0.73* 4 0.69* 75 63 0 156 4 1 2b) 4 2c) 0.27* 4 0.23 11 0.44* 74 62 0 32 3 2 1 1 2c) 0.05d) 13 0.51*d)

73 61 0 18 1 2 1 1 2 0.33 8 0.37 72 60 1 48 4 1 2 4 2 0.35* 3 0.35 69 59 0 24 5 1 3 3 5 0.83* 2 0.19 68 58 0 24 5 1 1 1 5 0.47 2 0.72* 71 57 1 46 4 1 2 4 2 0.39* 7 0.53* 70 56 1 25 2 2 1 2 4 0.71* 12 0.73* 2 0.62* 67 55 0 31 4 1 3 3 5 0.83* 3 0.88* 4 0.45* 66 54 0 30 4 1 3 3 5 0.59* 3 0.59* 4 0.19 65 53 0 40 5 1 3 3 2 0.46* 64 52 0 51 4 1 2b) 4 2 0.50* 63 52 0 29 4 1 2 4 2 0.09 62 52 0 39 4 3 2 4 2 -0,14 61 51 0 24 1 1 1 2 3 1.24* 60 50 1 54 3 2 1 3 4 0.30 5 0.46* 59 49 1 40 4 2 1 2 7 0.49* 7 0.54* 9 1.24* 58 48 0 47 3 1 1 4 4 0.67* 4 0.50* 2 0.47* 57 47 0 40 5 1 2 3 5 0.83* 1 1.07* 56 46 1 41 3 2 1 2 2 0.46* 5 9 0.75*55 45 0 331 3 1 1 4 1 0.56* 54 44 0 39 3 1 1 4 5 1.00* 4 0.83* 53 43 0 28 4 1 2 3 2 0.42* 52 42 0 32 5 1 1a) 2 8 0.76* 11 0.70 51 41 0 40 4 1 2 3 2 0.60* 50 40 1 48 4 1 2 3 6 0.48* 4 0.53* 49 39 0 29 5 1 3 4 5 0.45* 7 0.96* 48 39 0 29 5 3 3 4 5 0.26 47 38 1 28 3 1 1 3 4 1.13* 9 1.51* 2 0.80* 46 37 0 43 3 1 1 3 2 0.39* 4 0.54* 2 0.18 45 36 1 60 4 1 2 4 3 1.13* 1 0.74* 44 35 1 84 4 2 2 4 6 0.31* 1 0.42* 43 34 1 22 3 1 1 3 2 0.76* 42 34 1 22 3 1 1a) 3 2 0.59* 41 33 1 22 4 3 2 3 5 -0,17 6 -0,18 5 0.73* 40 33 1 22 4 1 2 3 5 0.80* 6 1.09* 5 0.48* 39 32 0 68 4 1 2 3 2 -0,05 10 0.16


38 31 0 60 5 1 1 1 2 0.49* 37 30 1 32 4 1 2 3 2 0.23 5 0.60* 36 29 1 36 5 2 3 3 5 0.32* 7 1,37* 35 28 1 45 5 2 3 3 5 0.59* 34 27 0 28 5 2 2 1 2 0.61* 6 0.39 33 26 0 34 2 2 1 2 2 0.43 8 0.36 32 25 0 34 5 1 1 3 2 0.74* 4 0.71* 31 24 0 32 2 2 1 1 2 0.28 9 0.21 30 23 0 20 5 1 1 3 2 1.29* 12 1.00* 29 23 0 20 5 3 1 3 2 0.32 12 1.01* 28 22 1 35 4 1 2a) 4 6 0.78* 3 1.13* 27 22 1 34 4 1 2a) 4 6 0.38* 3 0.56* 26 21 0 20 1 1 1 1 2 0.98* 3 0.89* 2 0.97* 25 20 0 30 2 2 1 1 2 0.51* 5 0.51* 9 0.04 24 19 0 140 1 1 1 1 3 0.13 23 18 0 32 2 2 1 1 2 0.34 22 17 1 44 4 1 2 3 2 0.31 3 1.00* 21 16 1 51 4 1 2 3 2 0.59* 5 0.89* 20 15 1 32 5 1 3 2 5 0.76* 10 0.34 2 0.35 19 14 1 36 5 1 3 4 2 0.19 2 1.11* 18 13 1 61 4 1 2 3 6 0.48* 6 0.65* 17 12 1 16 1 1 1 1 4 1.24* 16 11 1 30 4 1 2 3 6 0.80* 15 10 1 24 4 1 2 3 6 0.15 2 0.56* 14 9 0 15 5 1 1 3 2 0.24 13 9 0 15 5 1e) 1 3 2 0,58* 12 9 0 20 5 3 1 3 2 -0,45 11 8 1 20 3 1 1 2 2 1.00* 10 8 1 20 3 3 1 2 2 0.12 9 7 1 56 4 1 2 4 5 0.32* 8 6 1 20 3 1 1 3 3 0.43* 7 5 1 20 3 1 1 2 3 0.45 6 5 1 19 3 3 1 2 3 0.31 5 4 1 19 1 1 1 2 4 1.15* 4 0.99* 4 3 1 22 1 1 1 2 4 1.30* 7 0.34* 3 3 1 22 1 3 1 2 4 0.26 7 0.39* 2 2 1 20 1 1 1 2 4 0.54* 1 1 1 27 1 1 1 2 3 1.12*

*) p ≤ 0.05 a) Modified version of the program b) Combination of the inductive and a motivational training c) CFT subtests 3-5, i.e. the inductive subtests only d) dpost instead of dcorr e) Contrasted to a different control group


Legend for the columns of the summary table Row Number of contrast

Exper. Number of the experiment in the Appendix List

Author 1: experiment was performed by students or staff members of Klauer 0: experiment was performed by other authors N Number of subjects

Subj. Kind of subjects (1: kindergarten, 2: school kindergarten, 3: primary school, 4: secondary school [incl. 9 experiments in grammar schools], 5: special

education) Contrast Kind of contrast 1: inductive training vs. no training control group 2: inductive training vs. another but not inductive training 3: another training vs. no training control group Progr. 1: program I, 2: program II, 3: program III

Soc. Cond. Social condition of the training 1: One – to –one training, 2: Training of pairs of children, 3: Training in small groups of 3-5 children, 4: Training of intact classes DV 1 First dependent variable

1: Informal Test of Inductive reasoning ITIR, 2: CFT by Cattell (German version), 3: Cognitive Abilities Test CAT (German version), 4: Coloured Progressive Matrices CPM, 5: Standard Progressive Matrices SPM, 6: Advanced Progressive Matrices APM, 7: Columbia Mental Maturity Test CMM for mildly retarded children (German version), 8: another intelligence test.

g11 Effect size g of dependent variable 1 immediately after training (corrected for pre-experimental differences).

Months Time interval between g11 and g12. g12 Effect size g of dependent variable 1 the stated number of months after g11

(corrected for pre-experimental differences). DV 2 Second dependent variable 1: Learning and problem solving of ecology, 2: Learning and problem solving

of mathematics, 3: Learning and problem solving of biology, 4: Learning and problem solving of geography, 5: Learning and problem solving in reading or spelling or grammar, 6: Learning of foreign languages, 7: Learning and problem solving of physics, 8: Frostig Test, 9: Memory test, 10: Vocational Counseling Test (BBT 4-6), 11: Nonverbal and /or non-inductive intelligence test, 12: Test of spatial reasoning, 13: Visual Discrimination Test POD.

g2 Effect size g of the dependent variable 2 (corrected for pre-experimental differences).

Documents

Running head: INDUCTIVE REASONING TRAINING Inductive ...Inductive Reasoning 2 Abstract For several decades, researchers have been engaged in examining inductive reasoning in order