Abstract In this paper, we examine the conceptual pedagogical value of representational gestures in the context of teaching halving to first graders. We use the concept of the ‘polysign’ as an analytical tool and introduce the notion of a ‘mathematics gesture sequence’ to assess the conceptual role gestures play in explicating mathematical concepts. In our study of four teachers each teaching a lesson on halving, they produced representational polysign gestures that provided multiple layers of information, and chained these gestures in mathematical gestural sequences to spatially represent the operation of halving. Their use of gestures and their ability to use gestures accurately to convey mathematical concepts varied. During the lesson, learners, whose teachers used few representational gestures or used gestures that were conceptually incongruent with the mathematical concept, expressed more confusion than learners whose teachers used conceptually appropriate gestures. While confusion can be a productive part of the learning process, our analysis shows that producing conceptually appropriate gestures may be important in mediating concepts and the transition from concrete and personal symbolic processes to institutional mathematical signs.

中文翻译：

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手势多符号和手势序列在数学概念教学中的作用

摘要在本文中，我们在对一年级学生进行减半教学的背景下研究了代表性手势的概念教学价值。我们使用“polysign”的概念作为分析工具，并引入“数学手势序列”的概念来评估手势在解释数学概念中所起的概念作用。在我们对四位老师的研究中，他们每人都教授一堂关于减半的课程，他们制作了提供多层信息的具有代表性的多符号手势，并将这些手势链接在数学手势序列中，以在空间上表示减半的操作。他们对手势的使用以及他们准确使用手势传达数学概念的能力各不相同。在上课期间，学生，那些老师很少使用代表性手势或使用与数学概念在概念上不一致的手势的学生比老师使用概念上合适的手势的学生表现出更多的困惑。虽然混淆可能是学习过程的一个富有成效的部分，但我们的分析表明，产生概念上适当的手势可能对调解概念以及从具体和个人符号过程到制度数学符号的过渡很重要。