Abstract In this study, we investigated the development of algebraic reasoning in 65 fifth-grade students who never had algebra instruction before. In the six-lesson teaching sequence on solving linear equations, a hanging mobile, a physical balance model, played the central role. We expected students’ perceptual-motor experiences with this hanging mobile to be beneficial for the development of their reasoning related to linear equation solving. To investigate how students’ reasoning developed, we analysed videos of classroom interactions, students’ written work during the lessons and students’ responses to lesson-specific assessment tasks. Our results reveal that students showed progress in their level of algebraic reasoning and in their writing down of strategies. While working with the hanging mobile, students applied algebraic strategies such as restructuring, isolation and substitution. They later used these algebraic strategies for solving linear equations in new contexts. This suggests that the experiences students gained in the embodied learning environment provided a basis for algebraic reasoning, which appeared to support them when solving systems of symbolically presented linear equations.

中文翻译：

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使用悬挂式手机作为学习支持工具在小学发展代数推理/使用天平作为支持工具在小学教育中发展代数推理

摘要在这项研究中，我们调查了65位从未接受过代数教学的5年级学生的代数推理发展。在解决线性方程组的六课教学序列中，悬挂的移动器，物理平衡模型发挥了核心作用。我们希望学生在这种悬挂式手机上的感知运动体验将有助于他们发展与线性方程式求解有关的推理。为了调查学生的推理方式是如何发展的，我们分析了课堂互动的视频，课程中学生的书面作品以及学生对课程特定评估任务的反应。我们的结果表明，学生在代数推理水平和策略写下方面表现出进步。在使用悬挂式手机时，学生运用了代数策略，例如重组，孤立和替代。他们后来使用这些代数策略在新情况下求解线性方程。学生获得的经验表明，所体现的学习环境为代数推理提供了基础，当求解符号表示的线性方程组时，似乎可以为他们提供支持。