A Longitudinal Investigation on the Relation Between Logical Reasoning and Mathematical Competence

A relation between logic and mathematics has long been hypothesized, and is a matter of interest to mathematicians, psychologists, and educators (e.g., Piaget, 1952; Russell, 1919; Smith, 2004). Given the long-standing presumption of such a relation, it is surprising that very few studies have investigated whether logical reasoning is indeed related to mathematical competence, and even fewer have looked into why such a relation might exist. The aim of the proposed study is therefore to investigate the nature of the logic-math relation. Three hypotheses regarding the relation will be tested. The first hypothesis is that logical reasoning and mathematical problem-solving involve shared general cognitive factors, such as intelligence, working memory, and inhibition skills. The second hypothesis is that logical reasoning predicts mathematical problem-solving because the former is inherently involved in the latter. For instance, perhaps to solve more abstract mathematics problems, the reasoner needs to identify the underlying logical structure of the problem before applying the relevant logical rules. The third hypothesis is that we learn to think logically through the mathematics education we receive. If that is the case, then mathematical competence, as a proxy for mastery of the mathematics curriculum, should predict people’s future logical reasoning performance. To tease apart these different theoretical possibilities, a longitudinal study is proposed. Three-hundred-and-sixty seventh graders (i.e., 12-13-year-olds) will be recruited and assessed yearly over a three-year period. The assessments will include tests of logical reasoning skills, mathematical problem-solving, basic cognitive skills (i.e., intelligence, working memory, inhibition), as well as potential mediators of the logic-math relation (i.e., the ability to extract problem structures from word problems, number ordering, number line estimation, and fraction relations). Such a design will enable us to tease apart the different theoretical possibilities outlined above. Employing a longitudinal design targeting early adolescence, when both logical reasoning and mathematical problem-solving skills are rapidly developing, will allow a clearer picture of the developmental relation between logic and math to be obtained, and the inclusion of multiple logical reasoning measures, as well as potential confounding factors and mediators, will allow us to learn more about the specificity and nature of that relation. This knowledge will, in turn, inform the future development of educational interventions, and have implications for curriculum design (e.g., including logic instruction in the mathematics curriculum) and educational policy (e.g., increasing the resources devoted to mathematics education).

Funding Source: RGC - General Research Fund (GRF)