初等与中等教育中的几何变换与对称：1990 年至今的主题、媒介与理论框架综述

摘要

初等与中等教育需要更多地关注几何变换与对称，也需要更多研究来支撑几何变换的教与学。为了识别未来研究与教学的方向，本文尝试系统梳理已有研究的版图，并指出当前的关键着力点与未来的机会所在。为此，本系统综述考察了 1990 年以来关于二维几何变换与对称之教与学的62 篇同行评议论文。综述以“系统综述与元分析优先报告条目”（PRISMA）方案为指引，围绕四个方面展开：（a）学生如何学习变换；（b）变换教学是如何被概念化的；（c）媒介如何被用以支持变换的学习；（d）研究采用了哪些理论框架，这些框架又如何随时间变迁。讨论与结论部分指出了该领域未来若干关键的生长点，以更好地支持教师的教与学生对对称与变换的学习。

Abstract

There is need for increased focus on geometric transformations and symmetry in primary and secondary education, as well as increased research to support learning and teaching of geometric transformations. To identify directions for future research and teaching, we set out to map the research that has already been conducted and to identify key areas of focus and opportunity going forward. Toward these goals, this systematic review examines 62 peer-reviewed articles on teaching and learning about 2D geometric transformations and symmetry since 1990. To guide our review, we use the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) protocol. The review explores the research in terms of: (a) how students learn about transformations, (b) how teaching about transformations has been conceptualized, (c) how media have been leveraged to support learning about transformations, and (d) which theoretical frames have been leveraged and how have those frames shifted over time. Discussion and conclusions consider key areas of growth for the field going forward to better support teachers and students learning about symmetry and transformations.