Advanced Mathematical Study and the Development of Conditional Reasoning Skills

Abstract

Since the time of Plato, philosophers and educational policy-makers have assumed that the study of mathematics improves one's general ‘thinking skills’. Today, this argument, known as the ‘Theory of Formal Discipline’ is used in policy debates to prioritize mathematics in school curricula. But there is no strong research evidence which justifies it. We tested the Theory of Formal Discipline by tracking the development of conditional reasoning behavior in students studying post-compulsory mathematics compared to post-compulsory English literature. In line with the Theory of Formal Discipline, the mathematics students did develop their conditional reasoning to a greater extent than the literature students, despite them having received no explicit tuition in conditional logic. However, this development appeared to be towards the so-called defective conditional understanding, rather than the logically normative material conditional understanding. We conclude by arguing that Plato may have been correct to claim that studying advanced mathematics is associated with the development of logical reasoning skills, but that the nature of this development may be more complex than previously thought.

The development of reasoning skills during compulsory 16 to 18 mathematics education

“…However, it should be noted that the change Attridge and Inglis (2013) observed was not quite as the TFD would predict. Proponents of the TFD suggest that mathematics teaches students to reason with 'logic', implying that their reasoning should become more normative.…”

“…They argued that studying mathematics at A level (a non-compulsory qualification taken at the ages of 16-18 in England and Wales) may have been responsible for the initial difference between groups. This was supported by Attridge and Inglis (2013) who studied abstract conditional reasoning skills in mathematics and literature A level students, and found no difference between groups in reasoning behaviour at the start of post-compulsory education. While the literature students' reasoning did not change during their first year of undergraduate studies, the mathematics students' did.…”

“…While Attridge and Inglis's (2013) findings seemed to support the suggestion that studying mathematics develops at least one type of reasoning skill, the students in their sample had chosen to study mathematics at the post-compulsory level, suggesting that on the whole they enjoyed it or considered it important, and would likely have been engaged with it. If someone were compelled to study a reduced syllabus of mathematics, it is not necessarily the case that they would see the same benefits.…”

“…In Cyprus, students have the option to study mathematics as a low-or high-intensity subject from the age of 16 to 18. This provides a good opportunity to see whether the changes found in the mathematics group in Attridge and Inglis's (2013) study are also seen in groups who study a reduced mathematics syllabus, and who are studying mathematics as a requirement rather than as an option.…”

Magnitude Processing in Developmental Dyscalculia : A Heterogeneous Learning Disability with Different Cognitive Profiles

“…Previous research has established a bidirectional relationship between mathematics and logical reasoning skills. For example, Attridge and Inglis, (2013) found that education in mathematics improved logical reasoning skills, and Morsanyi, Devine, Nobes, and Szücs (2013) found that children with superior mathematical abilities excelled in logical reasoning.…”