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Article
The Function of Graphs and Gestures in Algorithmitization
The Journal of Mathematical Behavior (2007)
  • Karen A. Marrongelle, Portland State University
Abstract
The purpose of this paper is to present evidence supporting the conjecture that graphs and gestures may function in different capacities depending on whether they are used to develop an algorithm or whether they extend or apply a previously developed algorithm in a new context. I illustrate these ideas using an example from undergraduate differential equations in which students move through a sequence of Realistic Mathematics Education (RME)-inspired instructional materials to create the Euler method algorithm for approximating solutions to differential equations. The function of graphs and gestures in the creation and subsequent use of the Euler method algorithm is explored. If students’ primary goal was algorithmatizing ‘from scratch’, they used imagery of graphing and gesturing as a tool for reasoning. However if students’ primary goal was to make predictions in a new context, they used their previously developed Euler algorithm to reason and used graphs and gestures to clarify their ideas.
Keywords
  • Mathematics -- Study and teaching (Higher),
  • Differential equations -- Study and teaching (Higher),
  • Discourse analysis
Publication Date
2007
DOI
10.1016/j.jmathb.2007.09.005
Publisher Statement
Copyright © 2007 Elsevier Inc. All rights reserved.
Citation Information
Marrongelle, K. (2007). The function of graphs and gestures in algorithmitization. The Journal of Mathematical Behavior.26, 211-229.