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Anticipating students’ reasoning and planning prompts in structured problem-solving lessons

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Abstract

Structured problem-solving lessons are used to explore mathematical concepts such as pattern and relationships in early algebra, and regularly used in Japanese Lesson Study research lessons. However, enactment of structured problem-solving lessons which involves detailed planning, anticipation of student solutions and orchestration of whole-class discussion of solutions is an ongoing challenge for many teachers. Moreover, primary teachers have limited experience in teaching early algebra or mathematical reasoning actions such as generalising. In this study, the critical factors of enacting the structured problem-solving lessons used in Japanese Lesson Study to elicit and develop primary students’ capacity to generalise are explored. Teachers from three primary schools participated in two Japanese Lesson Study teams for this study. The lesson plans and video recordings of teaching and post-lesson discussion of the two research lessons along with students’ responses and learning are compared to identify critical factors. The anticipation of students’ reasoning together with preparation of supporting and challenging prompts was critical for scaffolding students’ capacity to grasp and communicate generality.

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Notes

  1. Pseudonyms are used throughout for the names of the Lesson Study teams and students.

  2. The teacher did not comment on the accuracy of this equation.

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Acknowledgements

The project team gratefully acknowledges the contributions of participating teachers, coaches, students, and schools and Max Stephens, who provided the “outside expert commentary” in the post-lesson discussions of the research lessons discussed in this article.

Funding

The Implementing structured problem-solving mathematics lessons through Lesson Study project was funded by the research centre at authors’ university.

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Authors and Affiliations

  1. Monash University, Clayton, Australia

    Colleen Vale

  2. Deakin University, Burwood, Australia

    Wanty Widjaja, Brian Doig & Susie Groves

Authors
  1. Colleen Vale
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  2. Wanty Widjaja
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  3. Brian Doig
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  4. Susie Groves
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Correspondence to Colleen Vale.

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Vale, C., Widjaja, W., Doig, B. et al. Anticipating students’ reasoning and planning prompts in structured problem-solving lessons. Math Ed Res J 31, 1–25 (2019). https://doi.org/10.1007/s13394-018-0239-5

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  • DOI: https://doi.org/10.1007/s13394-018-0239-5

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