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Cases as a Vehicle for Developing Knowledge Needed for Teaching

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Book cover Transforming Mathematics Instruction

Part of the book series: Advances in Mathematics Education ((AME))

Abstract

In this chapter, we describe a practice-based curriculum for the professional education of preservice and practicing secondary mathematics teachers that (1) focuses on reasoning-and-proving, (2) has narrative cases as an integrated component, and (3) supports the development of knowledge of mathematics needed for teaching. We first provide an argument for the importance of reasoning-and-proving in the secondary curriculum and the unique role that cases can serve in providing opportunities to develop teachers’ knowledge of mathematics, students learning, and teaching practices. We then provide an overview of the practice-based curriculum and discuss the overarching questions that have guided its design and development. We conclude with a discussion of what teachers appeared to learn from their experiences with the curriculum, with a particular emphasis on what the narrative cases appear to have contributed to their learning.

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Notes

  1. 1.

    The particular iteration of the course depicted in Fig. 1 was conducted over 12 sessions, each of which is represented by a column in the figure. Across different iterations of the course, what remains constant is the sequence of activities.

  2. 2.

    While the cases are based on real events, they have been enhanced at times in order to bring out specific aspects of instruction we wish to highlight.

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Acknowledgement

The Cases of Reasoning-and-Proving in Secondary Mathematics (CORP) project was supported by the National Science Foundation under award no. DRL 0732798. The views expressed are those of the authors and do not necessarily represent the views of the supporting agency. The authors which to acknowledge the contributions of James Greeno, Amy Hillen, Gaea Leinhardt, and Michelle Switala who collaborated in conceptualizing, designing, and/or creating the materials described herein.

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Authors and Affiliations

  1. Department of Instruction and Learning, School of Education, University of Pittsburgh, 230 S. Bouquet Street, Pittsburgh, PA, 15260, USA

    Margaret S. Smith

  2. College of Education, University of New Mexico, Hokona Hall, Albuquerque, NM, 87131, USA

    Justin Boyle

  3. Department of Curriculum and Instruction, Pennsylvania State University, 259 Chambers Building, University Park, PA, 16802, USA

    Fran Arbaugh

  4. Department of Curriculum and Instruction, School of Education, University of Wisconsin-Milwaukee, Milwaukee, WI, USA

    Michael D. Steele

  5. Department of Education, University of Oxford, 15 Norham Gardens, Oxford, OX2 6PY, UK

    Gabriel Stylianides

Authors
  1. Margaret S. Smith
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  2. Justin Boyle
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  3. Fran Arbaugh
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  4. Michael D. Steele
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  5. Gabriel Stylianides
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Correspondence to Margaret S. Smith .

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Editors and Affiliations

  1. Department of Teaching, Learning and Culture, Texas A&M University, College Station, Texas, USA

    Yeping Li

  2. School of Education, University of Michigan, Ann Arbor, Michigan, USA

    Edward A. Silver

  3. Dept. of Mathematics, East China Normal University, Putuo, China

    Shiqi Li

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Smith, M.S., Boyle, J., Arbaugh, F., Steele, M.D., Stylianides, G. (2014). Cases as a Vehicle for Developing Knowledge Needed for Teaching. In: Li, Y., Silver, E., Li, S. (eds) Transforming Mathematics Instruction. Advances in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-04993-9_18

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