Student Quantifications as Meanings for Quantified Variables in Complex Mathematical Statements

Morgan Early Sellers, Kyeong Hah Roh, Erika David Parr

Research output: Contribution to journalArticlepeer-review

Abstract

This study investigates undergraduate students’ meanings for quantified variables in mathematical statements involving multiple quantifiers. Clinical interviews with nine undergraduate students were conducted to explore students’ meanings for quantified variables. More specifically, students were asked to interpret and evaluate the Intermediate Value Theorem (IVT) and three other statements with similar logical structure to the IVT. In this paper, we provide our definitions for a quantified variable and student quantification as theoretical constructs from a constructivist viewpoint. Using these theoretical constructs, we interpret our main results, five categories of students’ meanings for quantified variables, which emerged from our qualitative analysis. We also discuss how our findings of students’ various meanings for quantified variables contribute to literature on theories of meaning and address issues in curriculum and instruction.

Original languageEnglish (US)
Article number100802
JournalJournal of Mathematical Behavior
Volume61
DOIs
StatePublished - Mar 2021

Keywords

  • Calculus
  • Intermediate Value Theorem (IVT)
  • Meaning
  • Quantifiers
  • Student Quantification

ASJC Scopus subject areas

  • Education
  • Applied Psychology
  • Applied Mathematics

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