Student Sense-Making in Post-Secondary Introductory Proof Courses: An Argument for and Outline of a Methodological Approach

TL;DR

This paper advocates a methodological approach to studying how post-secondary students interpret and construct mathematical proofs, aiming to understand their discourse and reasoning patterns to improve proof education.

Contribution

It introduces a novel research framework for analyzing student discourse in proof tasks, including models of student activity and comparisons with instructor expectations.

Findings

Identified key words and phrases that evoke student proof activity

Developed models of student proof-related behavior

Compared student descriptions with instructor expectations

Abstract

While proof is a central component of postsecondary mathematical study, proof construction has historically posed significant difficulties for students who intend to earn mathematics degrees at the undergraduate level. This work is comprised of detailed literature reviews, an argument for a methodological approach, and a descriptive research plan to study how university students use their mathematical discourse to interpret proof tasks and ultimately engage in constructing proofs in response to these tasks. The theoretical outcomes of using the approach outlined therein are: (a) theorized models of undergraduate students' patterned mathematical activity in response to proof tasks; (b) identified words, phrases, or problem features that evoke this patterned activity; and (c) identified similarities and differences in students' descriptions of their uses for mathematical concepts vs. how instructors expect students to think about and use mathematical concepts.