Folding back in students’ construction of mathematical generalizations within a dynamic geometry environment

Xiangquan Yao, Azita Manouchehri

Research output: Contribution to journalArticle

Abstract

In this work, we studied the cognitively recursive process of generalizing relying on data collected from a 2-week constructivist teaching experiment where a group of middle school students were working together to explore and generalize properties of geometric transformations in a dynamic geometry environment. In doing so, we focused on the role of reflection and outcomes of reflective work of learners on their progress towards construction of mathematical generalizations. Relying on the construct of folding back in the Pirie–Kieren theory, we present categories and subcategories that describe sources, forms, and outcomes of students’ reflections in the course of construction and refinement of mathematical generalizations. We then discuss the roles of teacher intervention and technology in motivating and supporting students’ folding back actions. The results of the study not only elaborate on the construct of folding back in the Pirie–Kieren theory but also provide a useful analytical tool to examine learners’ reflective practices.

Original languageEnglish (US)
JournalMathematics Education Research Journal
DOIs
StateAccepted/In press - 2020

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Education

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