Mathematical Reasoning and Communication: Analyzing Skills Development in University Students and High-Level Math Competitors

Abstract

Integrating mathematical reasoning and communication is essential for mastering and advancing mathematical learning, yet these competencies often develop along parallel tracks rather than in concert. This thesis investigates how students themselves perceive the link between reasoning and communication by studying three cohorts: first-year undergraduates in an introduction to mathematical reasoning course, upper-level mathematics majors, and high school competitors in math contests. Using surveys, semi-structured interviews, and a discussion-based “talking circle,” it examines students’ baseline communication skills, tracks their growth over a semester of formal reasoning instruction, and explores the role of proof-writing and collaborative problem solving in deepening their reasoning.

Findings reveal that, although nearly all participants recognize the importance of clear justification for their academic and professional futures, they seldom connect reasoning with communication until advanced coursework or competitive settings explicitly foreground the act of explaining and defending ideas. Introductory students gained confidence in constructing formal proofs but continued to struggle with audience-appropriate articulation; upper-level majors demonstrated precision in argumentation yet found it challenging to translate technical proofs for non-specialists; and high-school competitors excelled at adapting explanations under time pressure and in team contexts. These results underscore that standard curricula alone do not guarantee integrated skill development. Deliberate pedagogical strategies -- such as structured peer-explanation exercises, scaffolded analogical reasoning tasks, and sustained discussion opportunities -- are needed to cultivate students who are not only proficient problem solvers but also articulate mathematical communicators prepared for advanced STEM study and engaged citizenship.