0012-1649/90/S00.75. Conditional Reasoning, Representation, and Level of Abstraction. Henry Markovits and Robert Vachon. Universite du Quebec a Montreal.
Developmental Psychology 1990, Vol. 26, No. 6, 942-951
Copyright 1990 by the American Psychological Association, Inc. 0012-1649/90/S00.75
Conditional Reasoning, Representation, and Level of Abstraction Henry Markovits and Robert Vachon Universite du Quebec a Montreal Montreal, Quebec, Canada This study examined the idea that (a) reasoning involves construction of mental representations (models) of premises and that (b) there is a developmental progression in the ability of subjects to reason with models containing concrete and abstract elements. Experiment 1 found that for 13- and 16-year-old subjects, reasoning with abstract content was more difficult than with concrete content. Younger subjects appeared to rely more on concrete representations that used real-world knowledge than on more general abstract representations. Experiment 2 explored order effects in the presentation of concrete and abstract problems. Abstract followed by concrete problems led to reduced concrete-problem performance for high school students but did not affect performance for university students. These results support the hypotheses and suggest that development of formal reasoning abilities goes through 2 levels.
The Piagetian analysis of deductive reasoning can be taken to imply the development of a capacity to make cognitive judgments that are relatively independent of the immediate material content of deductive reasoning problems. Piaget (1983/1987b) characterized formal thought as a period in which reality is "subordinated to systems of necessary connections" (p. 5). This definition implies that a formal reasoner should be capable of producing deductive arguments that reflect the logical relationships between given premises and that are relatively free of contextual variability that does not affect these relationships. However, research into human reasoning has consistently found that content significantly influences the way that people derive conclusions (Johnson-Laird, Legrenzi, & Legrenzi, 1972; Markovits, 1986; Markovits & Vachon, 1989; O'Brien, Costa, & Overton, 1986; Overton, Ward, Black, Noveck, & O'Brien, 1987). Such results have led to the abandonment of the notion of cross-domain generality (Piaget, 1972) and to the search for processes that can explicitly integrate contextual influences within the scope of the formal operational model (Byrnes, 1988a; Overton, 1990; Piaget, 1981/1987a). These results have also led to attempts to incorporate meaning systems into models of deductive logic (Piaget & Garcia, 1986; Pieraut-Le Bonniec, 1980). Nonetheless, it can be argued that the nature of development as conceived by Piagetian theory involves processes such as reflective abstraction (Piaget, 1987)
Portions of this article were presented at the annual meeting of the Jean Piaget Society, Philadelphia, June 1, 1988. Preparation of this article was supported by grants from the Quebec Ministry of Education (Fonds Pour la Formation de Chercheurs et 1* Aide a la Recherche) and the Natural Sciences and Engineering Research Council of Canada to Henry Markovits. We would like to thank the teachers and students of the College des Eudistes and the Ecole Secondaire St-Leonard for their assistance. We would also like to thank the anonymous reviewers for their very useful comments and criticisms. Correspondence concerning this article should be addressed to Henry Markovits, Departement de Psychologie, University du Qu6bec, C.P. 8888, Succ "A," Montreal, Quebec, Canada H3C 3P8. 942
that should converge toward a logic that is progressively less context dependent (Borel, 1987). One of the major challenges for this approach to reasoning is to specify processes that can integrate contextual variability into the description of formal deductive thinking while maintaining the idea that cognitive development tends toward capacities that are more impervious to such variability. A series of studies (Byrnes & Overton, 1986; Markovits, Schleifer, & Fortier, 1989; Markovits & Vachon, 1989; O'Brien & Overton, 1980,1982; Overton et al, 1987) indicated that the ability to reason consistently on a variety of conditional reasoning tasks does not appear until early adolescence and that any content effects must be superimposed on this basic competence. Overton's competence-moderator-performance model (Overton, 1985; Overton & Newman, 1982) specifically incorporates this idea by suggesting that an underlying level of formal competence must be attained before other factors, such as content, can operate to facilitate prepositional reasoning. In the present study, we attempted to extend this model by suggesting a specific mechanism by which content effects in conditional reasoning may be understood and to propose a developmental sequence that tends toward a reasoning process that is relatively insensitive to content variation. One approach to understanding the way in which content might affect reasoning involves the amalgamation of two distinct notions that are drawn from very different paradigms. Johnson-Laird (1983) recently introduced the idea that one of the basic processes underlying reasoning may involve the construction by the subject of a "mental model." This requires the generation of an internal representation of the premises. The characteristics of such a model determine to a large extent the conclusions at which people may arrive. In the context of conditional reasoning tasks that require subjects to reason from a given conditional relation of the form "If P then Q," one critical aspect of any representation of the premises appears to involve the incorporation of relations of the form "If A then Q" (where A is any term that is different from P) into the model (JohnsonLaird, 1983; Markovits, 1984,1985,1988; Rumain, Connell, & Braine, 1983) or into an alternate model of the premises.
REASONING, REPRESENTATION, AND ABSTRACTION It would be useful at this point to give an example of how such a process might work (for this, we have adapted JohnsonLaird's, 1983, description of syllogistic inference, pp. 94-125). Let us suppose that the following problem (which is an example of the affirmation of the consequent) is presented: "If it rains, then the street outside will be wet. The street outside is wet." The first step in the reasoning process would involve the creation of a model of the major premise. There are two possible ways of doing this; these are presented schematically as Models 1 and 2: Model 1
It rains -
- street wet
Model 2
It rains -
- street wet
Street cleaned -
- street wet
Model 2 contains an alternative of the form "If A then Q" (if the street is cleaned, then the street will be wet). The second step involves adding the information contained in the second premise to the model of the major premise (i.e. The street is wet) while attempting to take into account the different ways that this might be done. If we use the convention that underlining a term indicates that it is to be considered true, then Model 1 generates the following representation: It rains -
- street is wet.
There is only one possible conclusion from this (i.e., It has rained), which is obtained by reading backward through the causal relation. This response corresponds to a biconditional interpretation of the if-then relation (i.e, the model implies that the street is wet if and only if it has rained). However, Model 2 leads to three possible representations: It rains Street cleaned It rains Street cleaned It rains Street cleaned -
- street wet street wet - street wet street wet - street wet - street wet
These three representations lead to three possible conclusions: (a) It has rained; (b) the street has been cleaned; or (c) it has rained and the street has been cleaned. Thus, subjects starting from Model 2 have the possibility of reaching the (logically correct) answer (i.e, that it is not certain that it has rained) if they are able to generate at least the first two of the three possible representations. It must be noted that a similar analysis would be made for problems involving the negation of the antecedent ("If P then Q, P is false), for which the logically correct answer is also that there is no certain conclusion (both the affirmation of the consequent and the negation of the antecedent are indeterminate forms). Explicitly incorporating a representational component of the kind suggested by Johnson-Laird (1983; see also Overton, 1990; Russell, 1987) provides an elegant explanation for content effects because varying the specific "If P then Q" relation would conceivably affect the probability that a subject would generate
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a model that includes an "If A then Q" relation. Many different mechanisms could have such effects, from "invited inferences" (Geis & Zwicky, 1971) to various pragmatic schemas (Cheng & Holyoak, 1985) and contextual effects (Byrne, 1989). This approach thus supposes that correctly reasoning with a given "If P then Q" relation requires that subjects generate a model (or models) that includes an "If A then Q" relation. The second part of our analysis attempted to examine the problem of how and why people generate such additional relations in the context of problems in which these are not explicitly present. To do this, we used the Piagetian analysis of the role and developmental pattern of "the possible" (Piaget, 1981/1987a). According to this analysis, there is a developmental progression in the extent to which children and adolescents can extrapolate from a given situation to possible outcomes or configurations. Generally speaking, younger children appear to be more constrained by the specific parameters of a given situation and tend to generate possibilities that are determined either by direct analogy with what is visible or by anticipating possible outcomes that are directly attainable. The two final forms interest us particularly: The third level is characterized by the generation of specific examples, which are inferred with respect to the characteristics of the problem and represent a subset of many other possibilities. The fourth level is determined by the realization that possibilities may exist despite the subjects' inability to specify their exact form. Our general approach assumed that someone who is presented with an "If P then Q" proposition must spontaneously generate an alternate relation of the form "If A then Q" to correctly resolve the problems requiring uncertainty responses (indeterminate forms). Without perceptual support, neither direct analogy nor anticipating possible outcomes would permit this, implying that younger children should tend to produce biconditional responses to these problems, which is what is generally observed. However, the third-level strategy should enable production of alternate possibilities if the "If P then Q" relation is such that it permits generation of specific examples, (i£, by use of subjects' real-world knowledge). This implies the corollary construction of a model using referents to specific, concrete elements. People who are able to function at the fourth level could be expected to generate alternate possibilities that are not necessarily well defined, and could thus do this in the context of models that do not use such referents in their construction. Thus, children and adolescents should initially perform better with conditional reasoning problems for which the specific content easily permits accessing appropriate alternate relations by use of real-world knowledge, whereas the ability to consistently resolve problems that do not permit such access should be a later development and should be associated with a corresponding representational component. In this context, it is important to specify that both of the proposed modes require the ability to reason on the basis of propositions and are thus formal operational in the Piagetian sense. The term concrete here refers to the referents of the propositions and does not imply the necessity for the kind of direct perceptual support that characterizes concrete operational thought. The purpose of this study was thus two-fold. First, we wished to examine the prediction that the spontaneous production of uncertainty responses to the indeterminate logical forms, affir-
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HENRY MARKOVITS AND ROBERT VACHON
mation of the consequent and negation of the antecedent, would be easier for conditional propositions with content for which real-world knowledge should permit generation of specific "If A then Q" relations than for problems without such content. It must be noted that studies of problems of inclusion (Bucci, 1978) and the selection task (Overton et al, 1987) have provided indirect support for this conclusion. However, there does not appear to be a systematic study of this distinction for conditional syllogisms. The second aim of the present study was to attempt to examine age differences in the relation between the generation of representations of conditional relations of varying degrees of access to appropriate possibilities and performance on reasoning problems.
Experiment 1 This initial experiment examined two specific questions. The first concerned expected performance on the indeterminate logical forms, affirmation of the consequent and negation of the antecedent. It was hypothesized that there would be poorer performance on conditional reasoning problems with content that did not easily permit generation of "If A then Q" relations by accessing real-world knowledge than on problems with content that did permit such access. Three content types were used to test this hypothesis: (a) concrete terms such that generating alternate possibilities of the form "A implies Q" was facilitated (many alternatives); (b) concrete terms such that generating alternate possibilities was considered less probable (few alternatives); and (c) terms with two elements that involved nonsense words so that real-world knowledge would not provide any specific alternates (no alternatives). The few-alternatives problems were included to provide an intermediate level between the many-alternatives and the no-alternatives contents. Few-alternatives problems were found by Bucci (1978) to be more difficult on class inclusion tasks that are similar to conditional syllogisms. It was predicted that many-alternatives problems would yield the most successful reasoning performance, followed by few-alternatives and no-alternatives problems. The second question concerned the relation between the ability to generate spontaneous representations of if-then relations that included alternate possibilities of the form "A implies Q," and reasoning performance. Short scenarios (modeled after Markovits, 1984) were included that presented subjects with an "If P then Q" relation (these relations were different from, but modeled after, those used in the reasoning problems). Subjects were informed that "Q was true" and were asked to imagine the possible reason for this. These scenarios were designed to provide a measure of the spontaneous tendency ofsubjects to generate a representation of the premises that included alternate possibilities, in a situation that did not require reasoning. Globally, it was predicted that subjects who spontaneously indicated that something other than "P" could have been the reason would perform better on the reasoning problems. More specifically, the model proposed here implies that younger adolescents would rely primarily on real-world knowledge (the Level 3 strategy) in attempting to solve conditional reasoning problems. Thus, these subjects should show consistent relations between reasoning performance and the ability to generate other possi-
bilities in the many-alternatives scenario; such relations would explicitly suggest the use of a Level 3 strategy.
Method Subjects. A total of 168 French-speaking middle-class boys from a private high school in Montreal were examined. Of these, 98 were in the 2nd year of high school (mean age = 13 years, 4 months) and 70 were in the 5th year of high school (mean age = 16 years, 1 month). Material. Test booklets written in French and containing six items were constructed. Each of the three conditional reasoning problems were presented (one per page) in the following format: At the top of each page was written "Suppose that it is true that:" followed by a statement in the form "If P then Q." Four multiple-choice questions were then presented. These were in the following form: A) If P is true, then you can say that: a) you are certain that Q is true. b) you are certain that Q is false. c) you are not certain whether Q is true or not. The four multiple-choice questions corresponded to the logical forms "P is true" (modus ponens; MP), "P is false" (negation of the antecedent; NA), "Q is true" (affirmation of the consequent; AC), and "Q is false" (modus tollens; MT). The three representational scenarios were presented in the following form: France and Brigitte are talking about trees. France is certain that if one cuts down a tree, the tree will fall down. Last week, Brigitte saw a tree that had fallen down. Can you imagine what could have made the tree fall down? All three of the scenarios were presented on the same page. The if-then statements used for the reasoning problems were taken from one of two sets of three relations (the if-then statements used in the scenarios were always taken from the set not used for the reasoning problems). These were as follows: Setl (a) If a rock is thrown through a window, the window will break, (many alternatives) (b) If one cuts down a tree, the tree will fall down, (few alternatives) (c) If one fretres, the puyge will fall, (no alternatives) Set 2 (a) If an object is put into boiling water, the object will become hot. (many alternatives) (b) If a myopic person puts on glasses, they will see well, (few alternatives) (c) If one fruitines, then the motiyou will be stained, (no alternatives) For each of the two sets, the first item was designed to have concrete content such that it should be easy to find specific examples of the form "If A then Q" (other ways of breaking windows or heating objects). The second item had concrete referents but presented more difficulties in generating possibilities. The third item had nonsense referents that did not permit generation of specific real-world possibilities. For half of the booklets, the reasoning problems used the first set of relations and the scenarios used the second set. This was reversed for the other half of the booklets. In addition, the scenarios preceded the reasoning problems in half of the booklets and followed them in the other half. The order of the three reasoning problems and the three scenarios were systematically varied. Finally, the order of the four questions asked on each reasoning problem was also varied. Procedure. Test booklets were given to entire classes of students. No
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REASONING, REPRESENTATION, AND ABSTRACTION
Table 1 Mean Number ofCorrect Responses by Problem Type on the Four Logical Forms No alternatives
Few alternatives
Many alternatives Age
MP
MT
AC
NA
MP
MT
AC
NA
MP
MT
AC
NA
13 years 16 years
0.86 0.93
0.77 0.83
0.54 0.58
0.34 0.44
0.86 0.94
0.87 0.94
0.41 0.44
0.31 0.37
0.89 0.93
0.84 0.93
0.30 0.39
0.23 0.33
Note. MP = modus ponens; MT = modus tollens; AC = affirmation of the consequent; NA = negation of the antecedent.
time limit was imposed, and subjects were asked to respond to their own satisfaction.
Results We were initially interested in subjects' performance on the reasoning problems. Table 1 gives the mean number of correct responses for the four logical forms by problem type (many alternatives, few alternatives, and no alternatives) and age level. A 4 (logical form) X 3 (problem type) X 2 (age) analysis of variance (ANOVA) with repeated measures of logical form and problem type was performed. This analysis indicated significant main effects of problem type, F(2,163) = 5.41, p < .01, logical form, F(3,162)= 81.46, p1.2. The role of necessity in cognitive development (H. Feider, Trans.). Minneapolis: University of Minnesota Press. (Original work published 1983) Piaget, J, & Garcia, R. (1986). Vers une logique des significations [Toward a logic of meaning]. Geneva, Switzerland: Murionde. Pi6raut-Le Bonniec, G. (1980). The development of modal reasoning. San Diego, CA: Academic Press. Rumain, B, Connell, J, & Braine, M. D. S. (1983). Conversational comprehension processes areresponsibleforreasoningfallacies in children as well as adults. Developmental Psychology, 19, 471-481. Russell, J. (1987). Rule-following, mental models, and the developmental view. In M. Chapman & R. A. Dixon (Eds.), Meaning and the growth of understanding (pp. 23-48). New York: Springer-Verlag. Received April 21,1989 Revision received May 21,1990 Accepted May 24,1990 •
