Advanced Mathematics and deductive reasoning skills: evidence for the theory of formal discipline

Introduction: Since the time of Plato, philosophers and educational policy-makers alike have assumed that the study of mathematics improves one’s logical reasoning skills. Today, this argument, known as the ‘Theory of Formal Discipline’ (TFD), is used in policy debates to prioritise mathematics in school curricula. However, there is no strong research evidence that justifies it, and some suggestive evidence that it is incorrect. Method: Participants completed Evans, Clibbens and Rood’s (1995) Conditional Inference Task at the beginning and end of one year of post-compulsory study of either mathematics or English literature. Raven’s Matrices and the Cognitive Reflection Test provided measures of potential domain-general mechanisms for reasoning improvement (Stanovich, 2009). Results: The mathematics students improved in conditional reasoning to a greater extent than the English literature students, despite having received no explicit tuition in conditional logic. Intriguingly, the improvement came about via increased rejection of invalid inferences but not increased acceptance of valid inferences. Our data further indicate that the mechanism of improvement is specifically related to mathematical study as opposed to a domain-general cognitive change. Discussion: In line with the TFD, advanced mathematical study was related to improved conditional reasoning skills. This is surprising given previous research findings that not even training in formal logic brought about improved conditional reasoning performance (Cheng et al, 1986). Furthermore, it seems that the mechanism of improvement is domain-specific rather than domain-general. Conclusion: Our results are consistent with the claims made by Plato, and many others since, that studying advanced mathematics is associated with improved logical reasoning skills.