Fostering pre-service teachers’ attention to mathematical objects: The realization tree mediator as a teaching representation

IF 2.1 2区教育学 Q1 EDUCATION & EDUCATIONAL RESEARCH

Journal of Mathematics Teacher Education Pub Date : 2024-02-26 DOI:10.1007/s10857-024-09622-w

Merav Weingarden, Einat Heyd-Metzuyanim

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Abstract

Using teaching representations is one of the common means for preparing pre-service mathematics teachers (PSTs) to learn how to teach mathematics meaningfully. However, turning PSTs’ attention to the mathematical objects that students engage with during the lesson is a challenging pursuit. This paper suggests using the Realization Tree Mediator (RTM) as a visual teaching representation for PST learning to implement cognitively demanding tasks in their classrooms. The RTM depicts the mathematical object at the core of a task and its different realizations while illustrating imaginary classroom discussions in which different realizations and the links between them are produced. By analyzing PSTs’ conversations around RTM images, we show how contrasting pairs of RTMs can be used for eliciting conversations about various aspects of cognitively demanding instruction. We discuss the affordances of the RTM as a teaching representation and how it can assist in making the mathematical content and meanings visible, public, and communicable among teachers and teacher educators.

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培养职前教师对数学对象的关注：作为教学表征的实现树中介器

使用教学表象是培养职前数学教师学习如何有意义地教授数学的常用方法之一。然而，要把職前數學教師的注意力轉移到學生在課堂上接觸的數學物件上，是一項極具挑戰性的工作。本文建议使用 "实现树中介"（Realization Tree Mediator，简称 RTM）作为可视化教学表征，帮助在职数学教师学习如何在课堂上完成认知要求较高的任务。RTM 描述了任务核心的数学对象及其不同的实现方式，同时说明了产生不同实现方式及其之间联系的想象课堂讨论。通过分析 PST 围绕 RTM 图像进行的对话，我们展示了如何利用对比鲜明的 RTM 对来激发关于认知要求较高的教学的各个方面的对话。我们讨论了 RTM 作为教学表征的能力，以及它如何帮助教师和教师教育者将数学内容和意义变得可见、公开和可交流。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Mathematics Teacher Education EDUCATION & EDUCATIONAL RESEARCH-

CiteScore

5.40

自引率

9.50%

发文量

期刊介绍： The Journal of Mathematics Teacher Education (JMTE) is devoted to research into the education of mathematics teachers and development of teaching that promotes students'' successful learning of mathematics. JMTE focuses on all stages of professional development of mathematics teachers and teacher-educators and serves as a forum for considering institutional, societal and cultural influences that impact on teachers'' learning, and ultimately that of their students. Critical analyses of particular programmes, development initiatives, technology, assessment, teaching diverse populations and policy matters, as these topics relate to the main focuses of the journal, are welcome. All papers are rigorously refereed. Papers may be submitted to one of three sections of JMTE as follows: Research papers: these papers should reflect the main focuses of the journal identified above and should be of more than local or national interest. Mathematics Teacher Education Around the World: these papers focus on programmes and issues of national significance that could be of wider interest or influence. Reader Commentary: these are short contributions; for example, offering a response to a paper published in JMTE or developing a theoretical idea. Authors should state clearly the section to which they are submitting a paper. As general guidance, papers should not normally exceed the following word lengths: (1) 10,000 words; (2) 5,000 words; (3) 3,000 words. Maximum word lengths exclude references, figures, appendices, etc. Critiques of reports or books that relate to the main focuses of JMTE appear as appropriate.