TY - JOUR
T1 - Folding back in students’ construction of mathematical generalizations within a dynamic geometry environment
AU - Yao, Xiangquan
AU - Manouchehri, Azita
N1 - Publisher Copyright:
© 2020, Mathematics Education Research Group of Australasia, Inc.
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
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U2 - 10.1007/s13394-020-00343-w
DO - 10.1007/s13394-020-00343-w
M3 - Article
AN - SCOPUS:85087484009
SN - 1033-2170
VL - 34
SP - 241
EP - 268
JO - Mathematics Education Research Journal
JF - Mathematics Education Research Journal
IS - 2
ER -