Exploring the role of metonymy in mathematical understanding and reasoning: The concept of derivative as an example

Michelle Zandieh, Jessica Knapp

Research output: Contribution to journalArticle

28 Citations (Scopus)

Abstract

In this paper we examine the roles that metonymy may play in student reasoning. To organize this discussion we use the lens of a structured derivative framework. The derivative framework consists of three layers of process-object pairs, one each for ratio, limit, and function. Each of the layers can then be illustrated in any appropriate context, for example graphically as slope, verbally as rate of change, or kinesthetically as velocity. We will illustrate three main cases of metonymy using data from student reasoning with derivative-paradigmatic metonymy, individual metonymy and part-part metonymy. Metonymies may function both in powerful and problematic ways for students as they come to understand and work with a complicated concept such as the derivative. It is the goal of this paper to illuminate and clarify how metonymy may function in student reasoning in the hopes of providing insights to teachers and researchers.

Original languageEnglish (US)
Pages (from-to)1-17
Number of pages17
JournalJournal of Mathematical Behavior
Volume25
Issue number1
DOIs
StatePublished - 2006

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Reasoning
Students
Derivatives
Derivative
student
Rate of change
Lenses
Lens
Slope
Research Personnel
Concepts
teacher
Framework

Keywords

  • Calculus
  • Derivative
  • Metaphor
  • Metonymy
  • Rate
  • Slope

ASJC Scopus subject areas

  • Applied Mathematics
  • Applied Psychology
  • Education

Cite this

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