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Selected Works of Alison Lynch
Article
Student thinking with examples: The criteria-affordances-purposes-strategies framework
The Journal of Mathematical Behavior (2017)
  • Amy B. Ellis, University of Georgia
  • Zekiye Ozgur, University of Wisconsin-Madison
  • Rebecca Vinsonhaler, University of Wisconsin-Madison
  • Muhammed Fatih Dogan, Adıyaman University
  • Tracy Carolan, University of Wisconsin-Madison
  • Elise Lockwood, Oregon State University
  • Alison Lynch, California State University, Monterey Bay
  • Pooneh Sabouri, New York University
  • Eric Knuth, University of Wisconsin-Madison
  • Orit Zaslavsky, New York University
Link
Abstract
A persistent challenge in supporting students’ proof activity is fostering the transition from less formal, empirical arguments to formal deductive arguments. A number of researchers have begun to investigate students’ thinking with examples, addressing how example use can support conjecture understanding, exploration, and proof. We extend this line of work in presenting the CAPS (Criteria, Affordances, Purposes, and Strategies) Framework, a framework addressing students’ choices, uses, strategies, and affordances gained with examples. Based on individual interviews with 38 participants from middle school through the undergraduate level, the CAPS Framework simultaneously addresses multiple aspects of students’ example-based exploration and provides a way to analyze how these different aspects mutually inform one another as students conjecture and prove. We present the framework, exemplify its use through vignettes of student thinking, and share findings on how students’ thinking with examples shifts across the populations of middle school, high school, and undergraduate students.
Keywords
  • Example use,
  • Conjecturing and proving,
  • Student reasoning
Disciplines
Publication Date
August, 2017
DOI
10.1016/j.jmathb.2017.06.003
Citation Information
Amy B. Ellis, Zekiye Ozgur, Rebecca Vinsonhaler, Muhammed Fatih Dogan, et al.. "Student thinking with examples: The criteria-affordances-purposes-strategies framework" The Journal of Mathematical Behavior (2017)
Available at: http://works.bepress.com/alison-lynch/3/