A functional perspective on student thinking about the grammar of multiply quantified statements

Abstract

Fluency with formal mathematical language is necessary for students in advanced mathematics. Yet, the language has been documented as being particularly challenging for students, motivating the need for more empirical studies that investigate the language and undergraduate students’ understanding of it. This study makes progress on this goal for the case of multiply quantified statements. By using Halliday’s Systemic Functional Grammar, I identified meanings that students had for quantified variables, connected these meanings to the grammar of the statements, and explained how such meanings impacted the full statement. I argue for the utility of Systemic Functional Grammar when investigating formal mathematical language and students’ thinking about it.