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Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization

Journal of Mathematics Teacher Education volume 23, pages 35–67 (2020)Cite this article

Abstract

Justifying and generalizing are essential forms of mathematical reasoning, yet, teachers struggle both to produce and identify justifications and generalizations. In comparing elementary school teachers’ self-reported levels of noticing justifying and generalizing in their own classrooms and the levels researchers observed in two consecutive lessons in those classrooms, we found significant discrepancies. In applying a framework we developed to characterize the teachers’ noticing in terms of mathematical content and reasoning form, we found that teachers rarely attended to justifying and generalizing in a manner consistent with the mathematics education community’s view and that their lenses for noticing these activities may account for discrepancies between the teachers’ reports and the researchers’ observations. We conclude by reflecting on the complexity of asking teachers to attend to justifying and generalizing and how these results may affect teacher professional development.

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Acknowledgements

The research study and preparation of this manuscript was supported by a grant from the National Science Foundation (NSF) (DRL-1223074).

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Authors and Affiliations

  1. Mathematics Department, Texas State University, 601 University Dr, San Marcos, TX, 78666, USA

    Kathleen Melhuish & Layla Guyot

  2. Fariborz Maseeh Department of Mathematics + Statistics, Portland State University, 724 SW Harrison Street, Portland, OR, 97201, USA

    Eva Thanheiser

Authors
  1. Kathleen Melhuish
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  2. Eva Thanheiser
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  3. Layla Guyot
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Corresponding author

Correspondence to Kathleen Melhuish.

Appendix A: sample coded transcript

Appendix A: sample coded transcript

See Table 8.

Table 8 A sample coded conversation excerpt
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Melhuish, K., Thanheiser, E. & Guyot, L. Elementary school teachers’ noticing of essential mathematical reasoning forms: justification and generalization. J Math Teacher Educ 23, 35–67 (2020). https://doi.org/10.1007/s10857-018-9408-4

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  • DOI: https://doi.org/10.1007/s10857-018-9408-4

Keywords

  • Justifying
  • Generalizing
  • Noticing
  • Professional development