Suppression of valid inferences and knowledge structures: the curious effect of producing alternative antecedents on reasoning with causal conditionals.

These studies looked at the difficulty that reasoners have in accepting conditional ("If P then Q") major premises that are not necessarily true empirically, as a basis for deductive reasoning. Preliminary results have shown that when reasoners are asked to produce possible alternate antecedents to the major premise ("If A then Q"), they paradoxically tend to deny the modus ponens (MP) inference ("If P is true, then Q is true"). Three studies further explored these results. The first study gave university students paper-and-pencil tests in which instructions to "suppose that the major premise is true" was followed by a request to determine the next number in a sequence, to retrieve information unrelated to the premises, or to retrieve a possible case of "If A then Q." Relative to a control group, reasoners asked to produce an alternative antecedent showed a significant tendency to deny the MP inference, whereas no such tendency was observed for the two other tasks used. A second study compared performance on a condition in which reasoners were asked to produce an alternative antecedent with that when they were given an explicit alternative. Premises used in this study were such that the latter alternative antecedent was also spontaneously produced by over 70% of reasoners. Results showed that the tendency to refuse the MP premise could not be accounted for by the specific nature of the alternative produced. A third study found that the tendency to refuse the MP inference after producing an alternative antecedent was affected by the number of "disabling conditions" (i.e., conditions that allow "P to be true" and "Q to be false") available for the major premise. These results are interpreted as being consistent with a model that supposes that logical reasoning requires selective inhibition of real-world knowledge.

Evidence that children and adolescents have internal models of peer interactions that are gender differentiated.

This study examined whether children's internal representations reflect gender differences that have been found in peer interactions. The dimensions examined were (1) preferences for dyadic or group situations, (2) whether children who are friends with a given target child are likely to be friends with each other, and (3) perceptions of the probability of knowing information about friends. Participants from preschool; grades 2, 6, 8, and 10; and college (N = 278) were asked questions about typical girls and boys. Results indicate that both girls and boys (1) rate typical boys as preferring group interactions more than do typical girls, a difference present as early as preschool; (2) rate typical boys as more likely than typical girls to be friends with one another if they are friends with the same target boy or girl respectively; and (3) rate typical girls as more likely than typical boys to know certain types of information about friends. These results are consistent with the existence of internal models of social interactions that are at least partially gender specific.

The development of reasoning with causal conditionals.

A total of 512 children in Grades 1 through 6 received a conditional inference task using causal conditionals (If cause P, then effect Q) and a generation of alternatives task. The inference task used premises for which there were few or many possible alternative causes. Results show a steady age-related increase in uncertainty responses to the two uncertain logical forms, affirmation of consequent (AC) and denial of antecedent (DA), and an increase in production of disabling conditions for modus ponens. More uncertainty responses were produced to AC and DA with premises with many possible alternatives. Individual differences in inference production were related to numbers of alternatives produced in the generation task. Results support the idea that both developmental and individual differences in reasoning can be at least partially explained by differential access to knowledge stored in long-term memory.

Developmental patterns in the understanding of social and physical transitivity.

Transitive inferences using both a linear dimension (A is longer than B) and a nonlinear dimension (A and B are friends) were examined. In Study 1, 6- to 9-year-old children received two problems of each kind. Performance showed similar developmental progressions but nonsignificant correlations between the two tasks. Study 2 extended these results by modifying the linear transitivity problem and adding variation in both context and type of social relation. Children 7, 9, and 11 years of age were given problems requiring judgments about friendship and about nonfriends (children who were quarreling with each other) in two different social contexts. No correlations were found between social judgments and judgments concerning length. Both type of relation and context influenced judgments about social relations. These results suggest that children possess two distinct strategies for making transitive judgments that correspond to the logical structure of the underlying relations.

Conditional reasoning, causality, and the structure of semantic memory: strength of association as a predictive factor for content effects.

Available evidence indicates that responses to conditional inferences using concrete causal premises is affected by the relative number of available alternate causes (Cummins, D.D., 1995. Memory and Cognition 23 (5), 646-658). We propose that another important factor that may influence the kinds of inferences made to causal conditionals is the relative strength of association between such causes and the consequent term. We present a study with adult participants that examines the effect of strength of association on performance on a conditional reasoning task using causal premises for which there exist one highly associated potential cause for the given consequent term. We predicted that adults would produce a greater proportion of biconditional responses to invalid forms with strongly associated premises than weakly associated ones, while valid forms would not be affected by strength of association. The results are consistent with this hypothesis.

The relation between accuracy of self-perception and cognitive development.

BACKGROUND: It is now widely recognised that student's self-perceptions of competence have an effect on their behaviours and learning. Previous studies have shown that children only gradually develop the ability to evaluate accurately their own competence. One possible explanation for this is that younger children have not reached a level of cognitive development required to perform such evaluations. AIMS: The objective of these two studies was to examine the hypothesis that children at higher levels of cognitive development should be more accurate in their self-appraisal of competence than children of the same age at lower levels of cognitive development. STUDY 1. SAMPLE: The sample included 173 elementary school children, with almost equal gender representation. Children were first examined in fourth grade (mean age = 10.0, SD = .77) and for the next two years. METHOD: Each child responded to questionnaires of self-perceptions about reading and to a standardised test of reading. Year-end grades in reading were used as a measure of performance. RESULTS: The results show that there was no significant difference between high and low children in grade 6, but that the correlation between self-perceptions and performance was significantly higher among high ability children than among low ability children both in grades 4 and 5. STUDY 2. SAMPLE: The sample included 153 elementary school children in grade 3 (mean age = 9.1, SD = .73) and 185 in grade 5 (mean age = 11.2, SD = .75), with almost equal gender representation. METHOD: Each child responded to questionnaires of self-perceptions about mathematics and to a standardised IQ test. Year-end grades in mathematics were used as a measure of performance. RESULTS: The correlation between self-perception and performance was significantly higher among high IQ children than among low IQ children in grade 3. However, in grade 5, high and low IQ children were similarly accurate in their self-perceptions. CONCLUSIONS: These results suggest that the development of accurate self-perceptions is not strictly a matter of age or school level but is also related to cognitive development.

The development of conditional reasoning and the structure of semantic memory.

The present article examines 2 predictions concerning conditional reasoning in children derived from a revised version of Markovits's model of conditional reasoning. The first study examined the prediction that younger children (8 years of age) would have greater difficulty in responding correctly to premises where the antecedent was strongly associated with the consequent than to premises where the association was weaker; for example, "If something is a car, then it has a motor" should be more difficult than "If something is a refrigerator, then it has a motor." A total of 55 children in grades 2 and 3 (average age: 8 years) and 49 children in grades 5 and 6 (average age: 11 years) were given either 2 strongly associated problems or weakly associated counterparts. Results indicated that 8-year-olds did better on the weakly associated problems than on the strongly associated problems, but there was no difference among the 11-year-olds. The second study examined the prediction that younger children (8 years of age) would have greater difficulty in responding correctly to causal premises ("If a rock is thrown at a window, the window will break") than to corresponding ad hoc premises ("A rock is something that can be used to break a window"). A total of 53 children in grades 2 and 3 (average age: 8 years) and 49 children in grades 5 and 6 (average age: 11 years) were given either 2 causal problems or ad hoc counterparts. Results indicated that 8-year-old did better on the ad hoc problems than on the causal problems, but there was no difference among the 11-year-olds. These studies are interpreted as consistent with the idea that 1 major factor in the development of reasoning in this age level is the development of children's ability to explore their own knowledge base.

Pragmatic schemas and the selection task: to reason or not to reason.

Cheng and Holyoak (1985) have proposed that people possess classes of linguistically based schemas that have an internal structure that is determined by pragmatic considerations. They found that when permission schemas ("If you want to do P, then you must do Q") are used in the selection task, the success rate is much superior to what is usually observed. According to Cheng and Holyoak, this is due to the fact that the permission schema is defined by a set of production rules that give the same answers to problems of conditional inference as those of formal logic. In order to test this hypothesis specifically, 160 university students were given one of two tests. The first contained two sets of inferential reasoning tasks, one using a permission schema, the second using a relation of multiple causality. The second test employed the same two conditional relations, but in an appropriate context. The results indicated that subjects did better on the reasoning task with the schema of multiple causality when presented in context, but, as predicted, their performance was much worse on the inferential reasoning task with the permission schema, which generated a higher proportion of logically incorrect responses. These results suggest that contrary to what has been affirmed, permission schemas might not have a logical structure that is equivalent to conditional logic. A second experiment examined selection task performance using the same two relations in context. Performance on the permission schema was superior to that found with the relation of multiple causality. This confirmed previous results indicating that permission schemas do improve selection task performance, but also suggests that this effect is not related to understanding of conditional reasoning.

Reasoning with contrary-to-fact propositions.

In the initial study, the ability of subjects at four age levels (10, 13, 15, 18 years) (1) to accept if-then premises as a basis for reasoning and (2) to reason correctly with if-then premises was examined. Half the subjects were assessed with four reasoning problems involving factually accurate premises. The other half received factually inaccurate premises which were derived from the preceding ones by altering a single term. Both tests included an abstract problem which preceded the concrete propositions. Results indicate that the 10 year olds, and to a lesser extent the 13 year olds, did have difficulty in accepting contrary-to-fact premises as a basis for reasoning. The 15 and 18 year olds did not, but did find reasoning correctly more difficult with contrary-to-fact premises. The second study examined the ability of 5 and 7 year olds to accept contrary-to-fact premises. Subjects were given factually false premises either alone or within a fantasy context. Results indicate that the fantasy context decreases the extent to which empirical knowledge interferes with accepting contrary-to-fact premises. This result supports the notion that a representational process may be involved in accepting contrary-to-fact premises.

The belief-bias effect in the production and evaluation of logical conclusions.

In this study, we examined whether adult subjects' beliefs regarding the empirical truth of a conclusion affected their production as well as their evaluation of a logical conclusion in a reasoning task. In addition, the relation between the ability to resolve an abstract reasoning problem correctly and the effect of belief-bias was examined. The subjects were given one of four paper-and-pencil reasoning tasks, two of them using an evaluation paradigm, and two of them using a production paradigm. Each paradigm comprised either neutral problems or belief problems. The neutral problems were constructed to be as similar as possible to the belief problems, in order to control for extraneous factors. All four tasks also included an abstract reasoning problem. The results indicate a significant belief-bias effect for both the evaluation and the production tasks. Qualitative analysis indicated that the belief-bias effect was more pervasive in the production condition. In addition, the belief-bias effect was found to exist independently of the subjects' abstract reasoning ability. The results are discussed with reference to a two-stage model, in which belief is used to resolve uncertainties in inferentially produced conclusions.