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Teachers pose and design context-based mathematics tasks: what can be learned from product evolution?

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Abstract

This study proposes a model of several dimensions through which products of teachers’ context-based mathematics problem posing (PP) can be modified. The dimensions are Correctness, Authenticity, Task Assortment (consisting of Mathematical Diversity, Multiple Data Representations, Question–Answer Format, Precision-Approximation, and Generalization), Task Flow, and Student Involvement. A study was conducted in the context of a professional development (PD) program in which eight secondary school teachers iteratively designed 22 context-based mathematics tasks. Using the variation theory of learning as a theoretical framework and qualitative content analysis methodology, we compared different versions of the same tasks, focusing on items participants added or revised. To demonstrate the usability of the resulting semi-hierarchical model, we apply it to characterize the teachers’ final products of context-based PP. We found that most items teachers composed did not deviate from what we call the “common item form”—items that require numeric, exact, particular-case-related, and close-form answers without involving students in decision-making. Our findings may inform teacher educators and researchers on planning and implementing context-based mathematics task development by teachers in PD.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author upon reasonable request.

Notes

  1. From now on, we use the word “dimension” to refer to “dimension of possible variation”—in the sense of the variation theory of learning (Lo & Marton, 2012).

  2. The excerpts brought here are taken from all of the eight teachers recorded in the PD meetings and in personal interviews conducted during and after the PD.

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Acknowledgements

We thank Talya Sperling for her contribution to this study and Jason Cooper for his insightful comments on the first draft.

Funding

This work was partially supported by the Israeli Jules and Edmond Trump Family Foundation [grant number 340] and with the support of the Center for Research on Teachers’ Learning and Development (CRTLD) in the Seymour Fox School of Education, The Hebrew University.

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  1. School of Education, The Hebrew University, Jerusalem, Israel

    Nadav Marco & Alik Palatnik

  2. The David Yellin Academic College of Education, Jerusalem, Israel

    Nadav Marco

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Correspondence to Nadav Marco.

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Marco, N., Palatnik, A. Teachers pose and design context-based mathematics tasks: what can be learned from product evolution?. Educ Stud Math 115, 223–246 (2024). https://doi.org/10.1007/s10649-023-10271-8

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