Advanced mathematical study and the development of conditional reasoning skills

Area of Science:

• Cognitive Psychology
• Educational Policy
• Philosophy of Mathematics

Background:

• The long-held belief, originating with Plato, posits that mathematics study enhances general thinking skills, termed the Theory of Formal Discipline.
• This theory is frequently invoked in educational policy to justify prioritizing mathematics curricula.
• Empirical evidence supporting the Theory of Formal Discipline remains limited.

Purpose of the Study:

• To empirically test the Theory of Formal Discipline by examining the development of conditional reasoning.
• To compare reasoning development in students of post-compulsory mathematics versus English literature.

Main Methods:

• Longitudinal tracking of conditional reasoning behavior development.
• Comparative analysis between students in post-compulsory mathematics and English literature courses.
• Assessment of reasoning towards material conditional versus defective conditional understanding.

Main Results:

• Mathematics students showed greater development in conditional reasoning compared to English literature students.
• This development occurred without explicit instruction in conditional logic.
• The reasoning improvement leaned towards a 'defective conditional' understanding, not the normative 'material conditional'.

Conclusions:

• While advanced mathematics study may be linked to logical reasoning development, as Plato suggested, the nature of this development is nuanced.
• The findings challenge simplistic interpretations of the Theory of Formal Discipline.
• Further research is needed to understand the complex cognitive shifts associated with advanced mathematical study.