Strategy development in a block design task. (Intelligence).

1. Introduction

This study was conducted in the general framework of the cognitive psychology of problem solving, where the processes or strategies underlying performance on psychometric tests are analyzed (Carpenter & Just, 1986; Dickes, Houssemand, & Reuter, 1996; Hunt, 1982, 1983; Hunt, Lunneborg, & Lewis 1975; Huteau, 1995; Jones & Torgesen, 1981, Lansman, Donaldson, Hunt, & Yantis, 1982; Lautrey & Huteau, 1990; Pellegrino & Glaser, 1979; Richard, 1996; Royer, 1977; Royer, Gilmore, & Gruhn, 1984; Rozencwajg & Huteau, 1996; Steinberg, 1988).

One way of analyzing the strategies used on intelligence tests consists of observing subjects' behavior while the test is underway, which generally requires adapting the situation to some extent. This approach was used to detect the strategies that subjects implemented to solve Kohs blocks (Beuscart-Zephir & Beuscart, 1988; Rozencwajg, 1991) or to solve the Passalong test (Richard, 1996; Zamani & Richard, 2000). As Royer (1977, p. 33) said, "The approach is to analyze the task directly by manipulating its structural variables rather than indirectly by factor analysing its relationship to other tests."

1.1. The block design task

The task examined here was derived from Kohs blocks, also called the block design task (Kohs, 1923), in which subjects use red and white colored blocks to reproduce two-dimensional square, red and white designs composed of geometric figures (see Fig. 1). Kohs blocks have given rise to a variety of tasks, all based on the same principle (Alexander, 1950; Bonnardel, 1971; Wechsler, 1974).

[FIGURE 1 OMITTED]

This task is interesting for several reasons. It is usually considered to be a general intelligence test which is highly saturated in factor g. Royer et al. (1984), for example, reported a correlation of .80 between Kohs blocks and IQ assessed on Binet's test. Wechsler uses it as a subtest on his child and adult scales, and its correlation to Weschler's overall score is also high. For Royer et al., "it serves, then, as a very good measure of general intelligence, as well as of performance abilities" (p. 1474).

The block design task is also saturated in the spatial factor (Vernon, 1952). In more recent models on the hierarchical organization of aptitudes, block tests are also used as indicators of a cohort factor called "visualization" (Cattell, 1971; Snow, Kyllonen, & Marshalek, 1984).

Finally -- and of particular interest to us here -- the block task is a test of development. It is sensitive to early development as well as to aging. Normative data (standardizations) obtained for the French population show that performance on the WISC-R block subtest (1981) improves until the age of 16. The results on the WAIS-R block subtest (1989) indicate a plateau between the ages of 16 and 34, after which performance starts declining.

However, the task we used to analyze subjects' strategies is not, strictly speaking, a Kohs block test, but a modified version of it. For this reason, some arguments demonstrating the theoretical validity of the modified task will be presented later in this article.

1.2. Block design task strategies

In classical research on strategies in the block design task, two major strategies are generally observed: an analytic strategy and a strategy called global, syncretic, or holistic (Beuscart-Zephir & Beuscart, 1988; Goldstein & Scheerer, 1951; Ionescu, Jourdan-Ionescu, & Toselli-Toschi, 1983; Jones & Torgesen, 1981; Schorr, Bower, & Kiernan, 1982). Schorr et al. (1982) also used the term "synthetic" to refer to the global strategy, although this term will be used here to speak of another strategy (see below). According to Schorr, in the analytic strategy, "the displayed design is mentally segmented into units corresponding to block faces, then the blocks are directly placed, one by one, to match each unit." In the global strategy, "the design is viewed as a whole and is not differentiated into units corresponding to block faces; instead, the blocks are manipulated until they match the pattern or seem to `click' with adjoining blocks to reproduce the design ... Subjects using the global strategy would attend to the gestalt appearance of the display section under consideration; they would take a block and rotate it in the construction design until it formed the desired pattern. Subjects following the `analytic strategy' would segment the focused area into its crucial sides, noticing the orientation of the colored edges (e.g. red corner north-west, white corner south-east), choose a two-colored block rotated into a matching orientation, and then place it into the target cell" (Schorr et al., 1982, pp. 479-480). Two operations are thus necessary for solving the block design problem analytically: segmentation of the design and orientation of the bicolored blocks. Subjects who use a global strategy do not carry out these operations; the design is adjusted as it is built, by trial and error. When taken to an extreme, the global strategy may not allow the subject to correctly finish reproducing the design.

In an earlier analysis of video recordings of the behavior of 17-year-olds (Rozencwajg, 1991), we found three different strategies: the two classically observed ones, global and analytic, but also a third strategy we called "synthetic." We were able to observe the synthetic strategy in that study because the designs presented to the subjects were made up of gestalts, i.e. groups of blocks that formed a simple geometric figure such as a triangle or a diamond (see Fig. 1). A gestalt is a form or structure that cannot be reduced to the mere juxtaposition of elements; it has a specific quality that is not found in any of its constituents. The modification of a single constituent can modify the entire form (Reuchlin, 1977). The shapes used here to generate the designs obeyed the gestaltist laws of proximity, similarity, continuity, and symmetry. The gestalts did not vary across designs. To our knowledge, this "synthetic" strategy had never been observed before. Unlike the analytic strategy where subjects proceed by cutting up the figure into a grid of n cells and then placing the blocks by rows or columns, the synthetic strategy involves placing the blocks in an order that conforms to the gestalts in the test design. In the synthetic strategy, then, the placement order is dependent upon the pattern in the design, whereas in the analytic strategy, the order is independent of that pattern.

There is another behavior index that differentiates these two strategies: the number of times the subject refers to the test design. In the synthetic strategy, subjects were found to refer little to the design, doing so essentially between two gestalts, whereas in the analytic strategy, subjects rely often on the design, and in the most extreme cases may even look at it after placing each block.

1.3. Developmental changes in strategies

The purpose of the present study was to contribute to the analysis of developmental changes in the performance of a block design task by examining subjects aged 12, 17, and adults. We shall focus on strategy changes.

To our knowledge, except for the Jones and Torgesen (1981) study on children and the Royer et al. (1984) study on aging adults, few researchers have taken an interest in developmental patterns on the Kohs task, other than the empirical performance changes noted in standardization of intelligence scales where the block design task is a subtest (normative data). In a recent study, Akshoomoff and Stiles (1996) analyzed 4.5- to 8-year-old children's performance and errors on patterns that differed in perceptual cohesiveness, a structural variable defined by Royer and Weitzel (1977), Royer et al. (1984), and Schorr et al. (1982). The authors found differences both as a function of age and as a function of the structural variable.

Jones and Torgesen (1981) studied developmental changes in the solving behaviors of children aged 6, 8, 10, and 16 on Kohs blocks and on the Wechsler version of it (1974). They analyzed behavior on the basis of two indices, a persistence index and block placement order. Their first hypothesis was that persistence index would get better with age. Their second hypothesis was that older subjects would place the blocks in a systematic order no matter what design they were working on. Both hypotheses were invalidated, since there was no age difference on either measure. This lack of progress can be explained in several ways. First of all, since the authors were trying to measure how persistent subjects were in not leaving any mistakes in the final solution, the persistence score was calculated by discarding protocols in which all sequences were correct. They also removed all subjects who were unable to finish within 2 min. Lastly, testing was stopped after two consecutive failures. One can therefore assume that most of the variability was eliminated. Finally and more fundamentally, the lack of developmental changes on the indices may be partly due to the characteristics of the designs used, which contained only four blocks and had few gestalts (the perceptual cohesiveness of the patterns was not even mentioned until the last sentence of the article). The absence of change may also be due to the behavior indices themselves. We shall return to this topic later.

1.4. What designs should be presented to subjects?

We deliberately did not give the subjects designs that were in the earlier versions of Kohs blocks. Two criteria seemed essential: (1) the designs had to be complex enough from the information processing standpoint to still be problems for the subjects, and (2) they had to be based on a cognitive theory rather than on empirical grounds, as in traditional intelligence tests.

The question of what designs to have subjects reproduce is particularly important here, since we are attempting to analyze the development of this task at relatively advanced ages compared to the Jones and Torgesen and Akshoomoff and Stiles studies. First of all, as several authors have now shown, the designs have to be sufficiently complex, i.e. they must look to the subject like a gestalt that is difficult to break down. If the inside edges of the design are conspicuous (Royer & Weitzel, 1977; Royer et al., 1984; Schorr …