Examining the development of syllogism (categorical reasoning) and its relationship with mathematics

Abstract

Studies have shown significant relationships between mathematical ability and logical reasoning abilities, such as transitive reasoning. These findings provided insights into how mathematics is processed. Nonetheless, little research has been done on the relationship between Syllogism (categorial reasoning) and mathematics. Therefore, the present study explored the development of Syllogism in three grades, namely grades 6, 8, and 10 (N = 520) and investigated its relationship with mathematics. A Syllogism test, as well as a mathematics achievement test covering three domains in mathematics (i.e. Measurement, Algebra, Geometry), were developed, with both showing good internal consistencies (α = .733 for Syllogism, α = .818 for mathematics). A transitive reasoning test, as well as other basic cognitive and mathematical skills (i.e., fluid intelligence, working memory, and arithmetic fluency), were also assessed as covariates. The accuracy of the Syllogism performance showed support for a rank order of the individual mood. The analysis on grade differences revealed no grade-related changes in both Syllogism and transitive reasoning. Regression analysis illustrated that both Syllogism and transitive reasoning accounted for unique variance in mathematics competence. The relationship between the two logical reasoning skills and mathematics achievement appeared to be consistent across grades, as indicated by an absence of moderation effects between logical reasoning skills and grades. Further examination indicated that only unbelievable items of Syllogism were significantly related to mathematical performance. The present results showed the unique relationships between different reasoning abilities and mathematics, and underlay the need for the development of reasoning in mathematics education.