Designing pedagogical experience to serve as groundwork on which to build an understanding of abstract concepts is a challenging mission for educators. Much research has found that embodied activities could facilitate conceptual metaphor for students to understand such concepts. This study has captured the trajectory of reasoning occurred during the embodied-based experience designed for the infinity concept. The participants, 42 secondary students who had never been exposed to the formal concept of infinity, passed through a designed series of making-sense tasks, so called the Embodied-Based Activity of Infinite Sets Comparison (EBIC). The EBIC intervention was conducted in 2 phases; (i) careful observation of 2 voluntary students, and (ii) integration for 40-classroom practice. The first phase was to examine the students’ conceptual development through their utterances, actions and inscriptions. Open-ended questions were used to capture the students’ insights and reasoning in the second phase. The qualitative data was collected and mined to associate pairability and Cantor’s metaphor. The finding showed the reasoning trajectory of some participants and the shift from improper reasoning to 1-1 correspondence pairing of countably infinite sets. This mathematical thinking shift was a consequence of conceptual embodiment, outlining the analysis of the embodied-based experience to develop abstract reasoning.

中文翻译：

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通过无限集比较中基于具身的经验捕捉概念发展

设计教学经验作为建立对抽象概念的理解的基础，对教育工作者来说是一项具有挑战性的任务。许多研究发现，具身活动可以促进概念隐喻，让学生理解这些概念。这项研究捕捉到了在为无限概念设计的基于具身体验的过程中发生的推理轨迹。参与者是 42 名从未接触过正式概念的中学生，他们通过了一系列设计好的有意义的任务，即所谓的无限集比较（EBIC）基于实体的活动。EBIC 干预分两个阶段进行；(i) 仔细观察 2 名志愿学生，以及 (ii) 整合 40 个课堂练习。第一阶段是通过学生的言语、行为和铭文来检查他们的概念发展。开放式问题用于捕捉学生在第二阶段的见解和推理。收集和挖掘定性数据以关联配对性和康托尔的隐喻。该发现显示了一些参与者的推理轨迹以及从不当推理到可数无限集的 1-1 对应配对的转变。这种数学思维转变是概念体现的结果，概述了对基于体现的经验的分析以发展抽象推理。收集和挖掘定性数据以关联配对性和康托尔的隐喻。该发现显示了一些参与者的推理轨迹以及从不当推理到可数无限集的 1-1 对应配对的转变。这种数学思维转变是概念体现的结果，概述了对基于体现的经验的分析以发展抽象推理。收集和挖掘定性数据以关联配对性和康托尔的隐喻。该发现显示了一些参与者的推理轨迹以及从不当推理到可数无限集的 1-1 对应配对的转变。这种数学思维转变是概念体现的结果，概述了对基于体现的经验的分析以发展抽象推理。