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Using representations, decomposition, and approximations of practices to support prospective elementary mathematics teachers’ practice of organizing discussions

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Abstract

This paper examines a series of instructional activities that provide prospective elementary teachers with an opportunity to engage in one of the more difficult practices to learn within mathematics teaching—organizing a mathematical discussion. Within a mathematics methods course, representations and decomposition of practice built from the Five Practices framework (Smith and Stein in Five practices for orchestrating productive mathematics discussions. Corwin Press, Thousand Oaks, CA, 2011) were implemented and studied to examine how prospective elementary teachers set goals, selected and sequenced available student work, and planned questions within a mathematical discussion. We examined prospective elementary teachers’ strengths and weaknesses in these facets through an approximation of practice set in a lesson context familiar to the prospective elementary teachers. Our results demonstrated that although prospective elementary teachers set varying goals for a discussion, their pedagogical choices in planning their discussion tended to be consistent with the goals they have set. These results support the focused development of prospective elementary teachers’ goal setting as an implication for mathematics teacher educators.

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Notes

  1. In using the term Standards-based curriculum, we are referring to the curriculum materials funded by the National Science Foundation and aligned with the NCTM Standards.

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Acknowledgments

This work was supported, in part, by the National Science Foundation under NSF Grant No. 0643497; Corey Drake, PI. Any opinions, findings, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation.

Author information

Authors and Affiliations

  1. Eugene T. Moore School of Education, Clemson University, 407A Tillman Hall, Clemson, SC, 29634-0975, USA

    Andrew M. Tyminski

  2. Department of Mathematical Sciences, Clemson University, O-221 Martin Hall, Clemson, SC, 29634-0975, USA

    Andrew M. Tyminski

  3. Clemson University, Clemson, SC, USA

    V. Serbay Zambak

  4. Michigan State University, East Lansing, MI, USA

    Corey Drake

  5. Drake University, Des Moines, IA, USA

    Tonia J. Land

Authors
  1. Andrew M. Tyminski
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  2. V. Serbay Zambak
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  3. Corey Drake
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  4. Tonia J. Land
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Corresponding author

Correspondence to Andrew M. Tyminski.

Appendices

Appendix 1: NOTD presentation

In your groups, you will facilitate a NOTD task to your colleagues. Each NOTD task should build on a previous NOTD. In other words, choose a concept that was addressed in a previous NOTD and expand on it in your NOTD. Before you present your NOTD, answer questions 1–5 to help you plan. On your assigned day, you will facilitate NOTD. After NOTD, respond to questions 6–9. All responses are due a week after you present. One response from each group will suffice. Make sure to list all group members on the document.

Before NOTD

  1. 1.

    What is your NOTD and rationale for that particular number?

  2. 2.

    What are your parameters (e.g., only addition sentences) and rationale?

  3. 3.

    What is your goal for NOTD?

  4. 4.

    Generate a list of expressions you anticipate will be given by your colleagues. (Note: While your colleagues are actually generating the expressions, you may want to cherry-pick the responses you want shared during the discussion by marking them with a star on their paper.)

  5. 5.

    Generate a list of questions to ask your colleagues after they provide their expressions. (Note: If none of your anticipated expressions are generated, you may have to come up with new questions.)

After NOTD

  1. 6.

    Did your anticipated expressions match the ones that were given? Explain.

  2. 7.

    What questions was your group able to ask?

  3. 8.

    What is a question that you wished your group asked but didn’t. Why?

  4. 9.

    Do you feel that you met the learning goal? Explain.

Appendix 2

Students’ strategies for 349 + 175

figure a

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Tyminski, A.M., Zambak, V.S., Drake, C. et al. Using representations, decomposition, and approximations of practices to support prospective elementary mathematics teachers’ practice of organizing discussions. J Math Teacher Educ 17, 463–487 (2014). https://doi.org/10.1007/s10857-013-9261-4

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