When time is an implicit variable: An investigation of students’ ways of understanding graphing tasks

Cody L. Patterson, Rebecca H Mcgraw

Research output: Contribution to journalArticle

1 Scopus citations

Abstract

In this study, we investigate students’ ways of understanding graphing tasks involving quantitative relationships in which time functions as an implicit variable. Through task-based interviews of students ages 14–16 in a summer mathematics program, we observe a variety of ways of understanding, including thematic or visual association, pointwise thinking, and reasoning parametrically about changes in the two variables to be graphed. We argue that, rather than comprising a hierarchy, these ways of understanding complement one another in helping students discover an invariant relationship between two dynamically varying quantities, and develop a graph of the relationship that captures this invariance. From these ways of understanding, we conjecture several mathematical meanings for graphing that may account for students’ behavior when graphing quantitative relationships.

Original languageEnglish (US)
Pages (from-to)295-323
Number of pages29
JournalMathematical Thinking and Learning
Volume20
Issue number4
DOIs
StatePublished - Oct 2 2018

ASJC Scopus subject areas

  • Mathematics(all)
  • Education
  • Developmental and Educational Psychology

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