Schooling and the Development of Transitive Inference

Copvrighl 1993 bv the American Psychological Association. Inc. 0O12-I649/93/S3.0O

Developmental Psychology 1993. Vol. 29. No. 4. 753-759

Schooling and the Development of Transitive Inference Lavee Artman and Sorel Cahan Because it is impossible to experiment with school attendance, the effect of formal education as opposed to chronological age on the development of transitive inference has never been investigated empirically. A recent quasi-experimental paradigm, which allows for disentangling the net effects of age and schooling, can help overcome this difficulty. The paradigm is applied to the estimation of the independent effects of age and schooling in Grades 5 and 6 on raw scores obtained in a 3-term series test. Results point to schooling as a major factor underlying the increase of scores as a function of age.

the development of intellectual abilities. Indeed, the learning Transitivity is a property of certain binary relations. If a tranprocesses involved in many school activities are thought to afsitive relation R exists between elements a and b in Set aRb and between elements b and c in Set bRc, this implies that it will also fect the formation of the cognitive strategies needed for successexist between elements a and c (Set aRc), for every a, b, and c in ful performance on general ability tests (Glaser, 1984). Second, the set. Transitive inferences depend, therefore, on integrating there is structural similarity between cognitive tasks and comrelational premise information: The premises aRb and bRc mon school assignments: (a) Both are self-contained; (b) there is must be integrated to produce the inference aRc. typically one "correct" answer; (c) the content of the problems The importance of transitivity to elementary thinking and are often of limited, academic interest; and (d) they are solved conceptual development is partly due to its being basic to the for their own sake. Moreover, both require children to cope concept of serial order. Transitivity of an asymmetric binary with hypothetical thinking, in which the specific object of disrelation is the denning property of an ordered set. The concept course is a spoken or written text rather than an object in the of an ordered set is, in turn, basic to all quantification above the world (Cole & Cole, 1989; Galotti, 1989; Luria, 1976; Scribner, level of a nominal scale. Therefore, any limitations that apply to 1977). Third, schooling may have an indirect effect on cognitive children's comprehension of transitivity have implications for development. The higher a child's grade level, the greater the virtually all their quantitative thinking (Halford, 1984). cognitive demands and expectations and the richer the test-takIt has been commonly found that the ability to integrate relaing experience (Cahan & Cohen, 1989). Finally, empirical evitional premise information, and thus to produce transitive inferdence points to a considerable effect of schooling on the develences, increases with age (Acredolo & Horobin, 1987; Glick & opment of cognitive skills (Ceci, 1991). Wapner, 1968; Sternberg, 1980a, 1980b). Recent developmental In addition to its effects on cognitive skills in general, the literature on transitive inference has focused on two key issues: schooling experience is also likely to have a unique positive the age at which the ability to make transitive inferences first influence on the child's ability to make transitive inferences. appears (for reviews, see Breslow, 1981; Thayer & Collyer, 1978) The school experience offers many opportunities to compare and how children of different ages actually make transitive inobjects on various unidimensional scales, such as physical or ferences (e.g., Sternberg, 1980a, 1980b). However, little attention psychological traits, all of which are characterized by the transihas been devoted to the causal model underlying this developtivity of the order relation (e.g., Ruble & Frey, 1987). For exammental process. For example, with respect to logical reasoning, ple, in history class, one has to determine which event or personScribner (1977) asserted that "we know very little about the ality preceded another; in geography, altitudes are represented social conditions which give rise to the logical genre, how culby different colors; in geometry, measurement operations are tures define the occasions for its use, through what experiences performed; in mathematics, one learns the numerical scale. All individuals acquire its schemes" (p. 499). of these activities contribute significantly to the development of There are grounds to assume that schooling provides relevant relational reasoning, which in turn promotes transitive inferexperiences in this regard. First, school is explicitly aimed at ence. Comparative processes of this sort may be made not only through academic tasks, but also as part of the social process of comparisons between classmates. A setting like the school, Lavee Artman and Sorel Cahan, School of Education, Hebrew Uniwhich provides its students with continual feedback regarding versity of Jerusalem, Israel. their relative position in the class, can encourage children to This study was supported by a grant from the National Council of develop transitive reasoning. The very existence of a schooling Jewish Women USA Research Institute for Innovation in Education, Hebrew University of Jerusalem. We acknowledge the helpful comeffect on development in this domain is to be expected, then, ments of anonymous reviewers on an earlier version of this article. We on both empirical and theoretical grounds. are also grateful for the editorial assistance of Helene Hogri. Correspondence concerning this article should be addressed to Sorel Cahan, School of Education, Hebrew University of Jerusalem, Mount Scopus, Jerusalem, Israel 91905.

Other theoretical considerations, however, suggest that this effect will be lower, both absolutely and relatively, than that on other types of cognitive performance. For instance, the intelli753

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LAVEE ARTMAN AND SOREL CAHAN

gence development approach claims that schooling will only affect the development of crystallized abilities, whereas it is "incidental" childhood learning, independent of schooling, that influences the development of fluid ability. Such an approach would attribute increased scores on tests of fluid ability wholly to the age factor (Cattel, 1963; Horn, 1978). Because transitive inference tasks are conceptualized as representative of fluid ability tests (Sternberg, 1985), schooling would not be expected to have a noticeable effect on the development of transitive reasoning. Furthermore, neo-Piagetian approaches, which point to the prime importance of working memory functions (e.g., mental manipulations of the information in assumptions) in successful performance on transitive tasks, also lead us to expect a negligible schooling effect. Such approaches view working memory development as an exclusive function of biological maturation and hence expect them to be unresponsive to external interventions, like schooling (Case, 1986; Chapman, 1987; Halford, 1982; Pascual-Leone, 1970; Shayer, 1987). The issue of interest, then, is not whether schooling affects the development of transitive reasoning (it can be safely assumed that it does), but rather the extent of that effect. This raises three related questions: What is the absolute size of the schooling effect? What is its size in comparison to the effect of chronological age and related psychophysiological maturation? What is the contribution of age and schooling to transitive reasoning in comparison to their effects on other cognitive tasks? Despite the considerable theoretical significance of the relative contributions of schooling and maturation to the development of transitive reasoning, no research has been specifically devoted to its empirical investigation, to the best of our knowledge. This is mainly due to the impossibility of experimenting with school attendance, which explains the paucity and inconclusiveness of empirical research into the effect of schooling on the development of logical skills (Ceci, 1991; Madaus, Airasian, & Kellaghan, 1980; Rogoff 1981). This problem can be circumvented by the use of the betweengrades paradigm (Cahan & Davis, 1987), which allows for a post hoc estimation of the net effect of 1 year of schooling on developmental abilities at any particular grade level. The present study uses this paradigm to estimate the unique effect of schooling, as opposed to maturation and out-of-school experience (represented by chronological age), on the development of transitive inference.

Method Subjects The sample, which is identical to that used in other research on schooling versus age effects (Cahan & Cohen, 1989), included all fourth, fifth, and sixth graders in Jerusalem's Hebrew-language state elementary schools (about 4,000 in each grade). Ninety percent of the students (10,785) attended school on the day of test administration and took the transitive syllogism test: 3,425 fourth graders, 3,782 fifth graders, and 3,578 sixth graders.

The Test A pencil-and-paper transitive syllogism test, comprising 22 threeterm series problems, was specifically created for this study (see the Appendix for their content and for success rates per item and grade). The sampled items were a subgroup of the Cartesian product of three dichotomous dimensions: (a) affirmative versus negative formulation of the premises; (b) determination of the conclusion (determinate vs. indeterminate); and (c) marked versus unmarked adjectives. The items were formulated on the basis of three relational content categories (fat-thin, strong-weak, and quick-slow) and referred to common children's names. All of the names per item were of the same gender. An example of a typical three-term series problem is as follows: John is stronger than Bill. Bill is stronger than Sam. Who is the strongest? 1. John 2. Bill 3. Sam 4. Can't tell. Procedure The test was administered on a classroom basis at the end of the school year as part of a 15-test battery (see Cahan & Cohen, 1989). The duration of the test, which was the fifth in the series, was 4 min. Two testers (university students who had received special instruction) were present in each classroom. Before proceeding with the transitive syllogism test, the children were given two practice tasks and were encouraged to ask questions. Design and Methodological Considerations Belween-grades paradigm. We used a between-grades regression discontinuity approach (Cahan & Cohen, 1989; Cahan & Davis, 1987) to carry out post hoc estimations of schooling versus age effects on success in transitive reasoning. This approach involves administering the same test to at least two adjacent grade levels. It relies on the following assumptions: (a) the "allocation" of children to birth dates is random, and (b) grade level is solely a function of chronological age; that is, admission to school is based on chronological age only according to some arbitrary cutoff point, and progression through grades is automatic (i.e., there are no dropouts and children are neither kept back nor skipped). On the basis of these assumptions, the net effect of chronological age and schooling are estimated by means of a regression discontinuity design (Cook & Campbell, 1979), in which test scores are regressed on chronological age within grades. In this design, the effect of age is reflected in the slope of the within-grade regression of test scores on chronological age, and the effect of schooling is reflected in the discontinuity between these regressions (see Figure 1). Specifically, the estimated effect of a 1 -year difference in chronological age in a given grade equals the difference between the oldest and youngest students in that grade in mean predicted scores (see dotted arrows in Figure 1), and the estimated effect of 1 year of schooling equals the differences in mean predicted scores between the youngest children in that grade and the oldest children in the lower adjacent grade (X — 1). Truth of the model's assumptions. As mentioned earlier, the between-grades model makes two assumptions: that children in a given class are randomly allocated to birth dates and that admission to school is based solely on chronological age, and grade progression is automatic. Certain reservations about the truth of these assumptions, which have been raised before (Cahan & Cohen, 1989; Cahan & Davis, 1987), should be reiterated. The truth of thefirstassumption cannot be empirically tested. However, because we tested students in only three adjacent grades within a

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TRANSITIVE SYLLOGISM

AGE EFFECT NO

d So

YES

v

A GRADEX-1|

GRADE X

LU

a

1

i"

c

GRADE X

GRADE X - 1

u

CO AGE

AGE

Figure 1. The independent effects of age (dotted arrows) and schooling (solid arrows) in the betweengrades regression discontinuity design: four hypothetical examples. (From "Age Versus Schooling Effects on Intelligence Development" by S. Cahan and N. Cohen, 1989, Child Development, 60, p. 1241, Figure 1. Copyright 1989 by the Society for Research in Child Development. Reprinted by permission.)

relatively homogeneous population, this assumption seems reasonable with respect to between-grades variability. As far as within-grade randomization is concerned, exceptions to this assumption can affect the estimation of age and schooling effects only if they are monotonically related to birth date, which is very unlikely. The second assumption of the model is only partially true. Although grade retention and grade skipping are seldom practiced in the Israeli elementary school system, admission to school is sometimes delayed and sometimes accelerated (Cahan & Cohen, 1989). About 5% to 10% of the children in any given grade are "overage" or "underage" (see Table 1), that is, children whose age should place them in a higher or lower grade. To allow for the use of the regression discontinuity model, we excluded such "misplaced" children from the data analysis. This is only a partial solution to the problem, because grade misplacement is nonrandom. The misplaced children are a selective population: Overage children (delayed admission) are likely to be less intel-

lectually developed than other children in their age group, whereas underage children (accelerated admission) are apt to be more highly developed. This means that the children who remain in the "appropriate" grade are also selective (in the opposite direction). Had the percentage of grade misplacement been random across months of birth, it would not affect the estimation of the age and schooling effects. However, misplacement is nonrandom: The relative frequency of grade misplacement is much higher (about 25%) close to the cutoff point of admission (among children born in November and December) than in other months (2%-8%; see Cahan & Cohen, 1989). This means that children remaining in the appropriate grade and born in November or December are a particularly selective population. The selective nature of this subgroup is likely to affect within-grade regressions and consequently to distort the estimates of age and schooling effects. Moreover, because these children are at the extreme of the age range within each grade (youngest children), their impact on the

Table 1 Sample by Grade and Age Status (N)

Table 2 Linearity of the Within-Grade Regressions of Test Scores on Chronological Age Grade

Age status

4

5

6

Underage Normal age Jan.-Oct.a Nov.-Dec. Overage

151 3,107 2,773 334 167

61 3,486 3,089 397 235

52 3,411 2,862 549 115

3,425

3,782

3,578

Total a

Data analysi;> was carried out only for these children.

Grade Source Linearity (df= 1) F P Deviation from linearity (df= 8) F P

4

5

6

10.5 .01

3.9 .05

0.01 .90

2.2

0.90

0.90

.50

.50

.03

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LAVEE ARTMAN AND SOREL CAHAN 50

40-

Grade 6 Grade 5 w