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Reflective analysis as a tool for task redesign: The case of prospective elementary teachers solving and posing fraction comparison problems

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Abstract

Mathematical task design has been a central focus of the mathematics education research community over the last few years. In this study, six university teacher educators from six different US institutions formed a community of practice to explore key aspects of task design (planning, implementing, reflecting, and modifying) in the context of comparing fractions using reasoning and sense-making. By presenting results of their implementation of two tasks with 63 prospective elementary teachers across three institutions and their reflective analysis of the implementation, the authors highlight the importance of collecting and analyzing data and reflecting on this analysis to inform the redesign of tasks. The authors also found that considering different types of tasks (problem solving vs. problem posing) helps illuminate different aspects of prospective elementary teachers' understanding, which can inform task redesign. Finally the authors contribute to the knowledge base on reasoning strategies for comparing fractions and prospective elementary teachers’ knowledge of these strategies.

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Notes

  1. In one of the classrooms, PTs received a second worksheet (in a different color) and were asked to use that one for taking notes during the whole class discussion. Both copies of the worksheet were collected at the end of the discussion.

  2. Since we developed the codes with this data set, we did not do an inter-rater reliability check. However, we independently double coded all data and through subsequent discussion came to resolution on all cases for which we initially disagreed.

  3. When comparing fractions that are both greater or less than a benchmark value, a person must: (a) identify the benchmark value, (b) determine the distances between each of the fractions and the benchmark value, (c) compare these distances (typically by using SNP or SSP), and then (d) use that knowledge to determine which of the original fractions is larger. Thus, we consider this BV strategy to be a combination of strategies, which will receive its own label later in the paper.

  4. Sixty-three PTs participated in the study, and 58 engaged in Task 2.

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Author information

Authors and Affiliations

  1. Portland State University, Portland, OR, USA

    Eva Thanheiser

  2. Widener University, Chester, PA, USA

    Dana Olanoff

  3. Kennesaw State University, Kennesaw, GA, USA

    Amy Hillen

  4. Boston University, Boston, MA, USA

    Ziv Feldman

  5. Illinois State University, Normal, IL, USA

    Jennifer M. Tobias

  6. Western Washington University, Bellingham, WA, USA

    Rachael M. Welder

Authors
  1. Eva Thanheiser
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  2. Dana Olanoff
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  3. Amy Hillen
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  4. Ziv Feldman
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  5. Jennifer M. Tobias
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  6. Rachael M. Welder
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Corresponding author

Correspondence to Eva Thanheiser.

Appendix

Appendix

See Table 12.

Table 12 Fraction comparison strategies, abbreviated codes, descriptions, and example problem
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Thanheiser, E., Olanoff, D., Hillen, A. et al. Reflective analysis as a tool for task redesign: The case of prospective elementary teachers solving and posing fraction comparison problems. J Math Teacher Educ 19, 123–148 (2016). https://doi.org/10.1007/s10857-015-9334-7

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