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.

在这项工作中，我们根据从为期 2 周的建构主义教学实验中收集的数据研究了泛化的认知递归过程，在该实验中，一群中学生正在共同努力探索和泛化动态几何环境中几何变换的属性。在此过程中，我们专注于反思的作用和反思工作的学习者在构建数学概括方面取得的进展。依靠回折的构造在 Pirie-Kieren 理论中，我们提出了描述学生在构建和完善数学概括过程中反思的来源、形式和结果的类别和子类别。然后，我们讨论了教师干预和技术在激励和支持学生折叠行为中的作用。该研究的结果不仅详细说明了 Pirie-Kieren 理论中的折叠结构，而且还提供了一个有用的分析工具来检查学习者的反思实践。