Mathematical task design has been a central focus of the mathematics educa￾tion 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 insti￾tutions 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 ele￾mentary teachers’ knowledge of these strategies.

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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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