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Instructional Supports for Mathematical Problem Solving and Learning: Visual Representations and Teacher Gesture

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Mathematical Teaching and Learning

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Abstract

Teachers’ efforts to guide students’ attention are potentially important for students’ learning. In this chapter, we consider two types of external supports that teachers frequently use to guide students’ attention: diagrams and gestures. We argue that teachers use diagrams and gestures to schematize specific features of mathematical problems or tasks, such as important elements and structural relations. In turn, teachers’ schematizing increases the likelihood that students encode those features. If the schematized features are relevant to the problem or task at hand, students’ appropriate encoding of those features will support their performance and learning. We present a selective review of research (including our own) on the roles of diagrams and teacher gestures in helping students encode key features and discern structure in instructional material.

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Acknowledgements and Funding Sources

The geometry lesson excerpt was drawn from a dataset collected with support from the National Science Foundation under award DRL 0816406. We thank Mitchell Nathan and Matthew Wolfgram for fruitful discussions of this excerpt. The research on students’ encoding of linear equations described herein was supported by the Institute of Education Sciences, U.S. Department of Education (award R305A130016). We thank Amelia Yeo, Susan Wagner Cook, Voicu Popescu, Mitchell Nathan, Andrea Donovan, and Meng-Lin Wu for their contributions to that line of work. The studies of diagrams and algebra problem solving described herein were supported by the Institute of Education Sciences, U.S. Department of Education through a training grant award to the University of Wisconsin–Madison (award R305B150003). We thank Helen Huang and Vanesa Meneses for their assistance with that work. The opinions expressed are those of the authors and do not represent the views of the National Science Foundation or the U.S. Department of Education.

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Authors and Affiliations

  1. University of Wisconsin-Madison, Madison, WI, USA

    Martha W. Alibali & Anna N. Bartel

  2. National Institute of Education, Singapore, Singapore

    Amelia Yeo

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  1. Martha W. Alibali
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  2. Anna N. Bartel
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  3. Amelia Yeo
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Correspondence to Martha W. Alibali .

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Editors and Affiliations

  1. Department of Psychology, Campion College at the University of Regina, Regina, SK, Canada

    Katherine M. Robinson

  2. Faculty of Education, University of Western Ontario, London, ON, Canada

    Donna Kotsopoulos

  3. Department of Educational & Counselling Psychology, McGill University, Montreal, QC, Canada

    Adam K. Dubé

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Alibali, M.W., Bartel, A.N., Yeo, A. (2023). Instructional Supports for Mathematical Problem Solving and Learning: Visual Representations and Teacher Gesture. In: Robinson, K.M., Kotsopoulos, D., Dubé, A.K. (eds) Mathematical Teaching and Learning. Springer, Cham. https://doi.org/10.1007/978-3-031-31848-1_2

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  • DOI: https://doi.org/10.1007/978-3-031-31848-1_2

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  • Online ISBN: 978-3-031-31848-1

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