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Prospective middle school mathematics teachers’ reflective thinking skills: descriptions of their students’ thinking and interpretations of their teaching

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Abstract

In this study, we examined prospective middle school mathematics teachers’ reflective thinking skills to understand how they learned from their own teaching practice when engaging in a modified lesson study experience. Our goal was to identify variations among prospective teachers’ descriptions of students’ thinking and frequency of their interpretations about how teaching affected their students’ learning. Thirty-three participants responded to open-ended questionnaires or interviews that elicited reflections on their own teaching practice. Prospective teachers used two forms of nuance when describing their students’ thinking: (1) identifying students’ specific mathematical understandings rather than general claims and (2) differentiating between individual students’ thinking rather than characterizing students as a collective group. Participants who described their students’ thinking with nuance were more likely to interpret their teaching by posing multiple hypotheses with regard to how their instruction affected their students’ learning. Implications for supporting continued growth in reflective thinking skills are discussed in relation to these results.

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Acknowledgments

Preparation of this article was supported by the National Science Foundation, Grant 0083429 to the Mid-Atlantic Center for Teaching and Learning Mathematics. The opinions expressed in the article are those of the authors and not necessarily those of the Foundation. Previous versions of this study were presented at the 2007 annual meeting of the American Educational Research Association in Chicago, Illinois, USA, and the 2008 research pre-session of the annual meeting of the National Council of Teachers of Mathematics in Salt Lake City, Utah, USA. The authors would like to thank those who assisted with this study: Betsy Read taught the additional section of the middle school mathematics curriculum and methods course. Nicola Edwards-Omolewa, Delayne Johnson, and Christine Phelps assisted with data collection. James Beyers and Rachel Francis served as consultants during early phases of data analysis. We also appreciate feedback from Jim Hiebert on an earlier draft of this manuscript.

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Authors and Affiliations

  1. University of Delaware, Newark, DE, USA

    Amanda Jansen

  2. Towson University, Towson, MD, USA

    Sandy M. Spitzer

Authors
  1. Amanda Jansen
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  2. Sandy M. Spitzer
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Corresponding author

Correspondence to Amanda Jansen.

Appendix

Appendix

Questionnaire/interview items

  1. 1.

    Consider your first lesson that you taught in your field placement about division of fractions. Did the lesson go well or not? Explain.

  2. 2.

    What did you hope students would learn from this lesson?

  3. 3.

    More specifically, do you think the students learned what you hoped they would learn? How do you know? Why do you think they did or did not learn this?

  4. 4.

    If you could have changed anything about your experiences teaching this lesson in order to improve students’ learning, what would you have changed? Which of these changes would be most beneficial to promote students’ learning? Why?

  5. 5.

    How would you evaluate your teaching during this lesson?

    1. (a)

      Very effective

    2. (b)

      Somewhat effective

    3. (c)

      Neither effective or ineffective

    4. (d)

      Somewhat ineffective

    5. (e)

      Very ineffective

    Explain your reasons for this choice.

  1. 6.

    For this question, think about the design of the lesson itself rather than your teaching: Overall, to what degree would you say this lesson was an effective lesson?

    1. (a)

      Very effective

    2. (b)

      Somewhat effective

    3. (c)

      Neither effective or ineffective

    4. (d)

      Somewhat ineffective

    5. (e)

      Very ineffective

    Explain your reasons for this choice.

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Jansen, A., Spitzer, S.M. Prospective middle school mathematics teachers’ reflective thinking skills: descriptions of their students’ thinking and interpretations of their teaching. J Math Teacher Educ 12, 133–151 (2009). https://doi.org/10.1007/s10857-009-9099-y

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  • DOI: https://doi.org/10.1007/s10857-009-9099-y

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