Recent studies have shown that deductive reasoning skills are related to mathematical abilities. Nevertheless, so far the links between mathematical abilities and these two forms of deductive inference have not been investigated in a single study. It is also unclear whether these inference forms are related to both basic maths skills and mathematical reasoning, and whether these relationships still hold if the effects of fluid intelligence are controlled. We conducted a study with 87 adult participants. The results showed that transitive (...) reasoning skills were related to performance on a number line task, and conditional inferences were related to arithmetic skills. Additionally, both types of deductive inference were related to mathematical reasoning skills, although transitive and conditional reasoning ability were unrelated. Our results also highlighted the important role that ordering abilities play in mathematical reasoning, extending findings regarding the role of ordering abilities in basic maths skills. These results have implications for the theories of mathematical and deductive reasoning, and they could inspire the development of novel educational interventions. (shrink)

Conditional reasoning is one of the key components of logical reasoning. Studies examining the way that children and adults make conditional inferences have shown that while there are some clear developmental patterns, there is also a great deal of variation in performance due to factors such as problem content. Such variation is difficult to model without an explicit process model. In the following we propose a variant of mental model theory that can explain much of the empirical data. This model (...) suggests that the development of conditional reasoning can be explained, at least partly, by such factors as the capacity of working memory, the range of knowledge available to a reasoner and his/her ability to access this knowledge on-line. (shrink)

This study examined the idea that reasoning involves construction of mental representations of premises and that there is a developmental progression in the ability of Ss to reason with models containing concrete and abstract elements. Exp 1 found that for 13- and 16-yr-old Ss, reasoning with abstract content was more difficult than with concrete content. Younger Ss appeared to rely more on concrete representations that used real-world knowledge than on more general abstract representations. Exp 2 explored order effects in the (...) presentation of concrete and abstract problems.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. (shrink)

Mental model theory has been used to explain many differing phenomena in adult reasoning, including the extensively studied case of conditional reasoning. However, the current theory makes predictions about the development of conditional reasoning that are not consistent with data. In this article, young children's performance on conditional reasoning problems and the justifications given are analysed. A mental model account of conditional reasoning is proposed that assumes that (1) young children can reason with two models and (2) the fleshing out (...) of conditionals involves activation of information in semantic memory that uses the minor premise as a retrieval cue. (shrink)

The authors outline a theory of conditionals of the form If A then C and If A then possibly C. The 2 sorts of conditional have separate core meanings that refer to sets of possibilities. Knowledge, pragmatics, and semantics can modulate these meanings. Modulation can add information about temporal and other relations between antecedent and consequent. It can also prevent the construction of possibilities to yield 10 distinct sets of possibilities to which conditionals can refer. The mental representation of a (...) conditional normally makes explicit only the possibilities in which its antecedent is true, yielding other possibilities implicitly. Reasoners tend to focus on the explicit possibilities. The theory predicts the major phenomena of understanding and reasoning with conditionals. (shrink)

An experiment was conducted to investigate the relative contributions of syntactic form and content to conditional reasoning. The content domain chosen was that of causation. Conditional statements that described causal relationships were embedded in simple arguments whose entailments are governed by the rules -of truth-functional logic. The causal statements differed in terms of the number of alternative causes and disabling conditions that characterized the causal relationship. Subjects were required to judge whether or not each argument’s conclusion could be accepted. Judgments (...) were found to vary systematically with the number of alternative causes and disabling conditions. Conclusions of arguments based on conditionals with few alternative causes or disabling conditions were found to be more accept-able than conclusions based on those with many. (shrink)

Johnson-Laird's mental models theory claims that reasoning is a semantic process of construction and manipulation of models in working memory of limited capacity. Accordingly, both a deduction and a given interpretation of a premise would be all the harder the higher the number of models they require. The purpose of the present experiment was twofold. First, it aimed to demonstrate that the interpretation of if...then conditional sentences in children (third, sixth, and ninth graders) evolves as a function of the number (...) of models the children can produce. We proposed a theory of conditional reasoning development that hypothesises a developmental trend of three successive levels of interpretations underlain by one, two, and then three models, i.e. conjunctive, biconditional, and conditional respectively. Second, we aimed to show that these different levels correlate with working memory capacities: the higher the working memory span, the higher the number of models underlying the conditional interpretation. These two hypotheses were verified, supporting the mental models theory. The results are compared with the rival theory of mental logic. (shrink)