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Characterizing Learners’ Growth of Geometric Understanding in Dynamic Geometry Environments: a Perspective of the Pirie–Kieren Theory

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Abstract

The emergence of interactive mathematics software in the early 1990shas invited mathematics education researchers to consider ways that dynamic geometry environments (DGEs) might influence K–16 learners’ growth of geometric understanding. This article examines the applicability of the Pirie–Kieren theory to trace this growth. Data for this article came from a series of task-based interviews that aimed at examining the relationship between The Geometer’s Sketchpad(GSP) usage and the development of geometric knowledge about compositions of geometric transformations. Data analysis showed that the Pirie–Kierentheory provides a useful tool to characterize, at the micro-level, a learner’s process of gaining a particular geometric understanding of a composition of geometric transformations in this DGE. By supporting the participants to transform geometric objects into their desired form, and to become acquainted with their properties or structures, tools in this DGE facilitated not only their transition between different levels of understanding, but also the to-and-fro movements within each specific level of understanding. The presence of a DGE challenges mathematics education researchers to reconsider the Primitive Knowing level of the Pirie–Kieren theory, and to attend to the difference between a visual image brought to mind by a GSP diagram and a mental image developed from manipulating the diagram.

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  1. Department of Curriculum and Instruction, Pennsylvania State University, 266 Chambers Building 274 Curtin Road, University Park, PA, 16802, USA

    Xiangquan Yao

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  1. Xiangquan Yao
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Correspondence to Xiangquan Yao.

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Yao, X. Characterizing Learners’ Growth of Geometric Understanding in Dynamic Geometry Environments: a Perspective of the Pirie–Kieren Theory. Digit Exp Math Educ 6, 293–319 (2020). https://doi.org/10.1007/s40751-020-00069-1

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