Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion

Abstract

Using student mathematical thinking during instruction is valued by the mathematics education community, yet practices surrounding such use remain difficult for teachers to enact well, particularly in the moment during whole-class instruction. Teachers’ orientations—their beliefs, values, and preferences—influence their actions, so one important aspect of understanding teachers’ use of student thinking as a resource is understanding their related orientations. To that end, the purpose of this study is to characterize teachers’ orientations toward using student mathematical thinking as a resource during whole-class instruction. We analyzed a collection of 173 thinking-as-a-resource orientations inferred from scenario-based interviews conducted with 13 teachers. The potential of each orientation to support the development of the practice of productively using student mathematical thinking was classified by considering each orientation’s relationship to three frameworks related to recognizing and leveraging high-potential instances of student mathematical thinking. After discussing orientations with different levels of potential, we consider the cases of two teachers to illustrate how a particular collection of thinking-as-a-resource orientations could support or hinder a teacher’s development of the practice of building on student thinking. The work contributes to the field’s understanding of why particular orientations might have more or less potential to support teachers’ development of particular teaching practices. It could also be used as a model for analyzing different collections of orientations and could support mathematics teacher educators by allowing them to better tailor their work to meet teachers’ specific needs.

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Notes

  1. 1.

    Because of the logical connection we are making between potential to support or hinder teaching practices and potential to support or hinder the development of such practices, from here on we use “potential to support the practice” and “potential to support the development of the practice” interchangeably.

  2. 2.

    We acknowledge that no single instrument would provide sufficient data to infer a teacher’s entire set of orientations. We also acknowledge that observation data and reflection data both have affordances and constraints when inferring orientations.

  3. 3.

    Although the MOST Criteria and Building Subpractices are undergirded by the Core Principles, we did not feel that the alignment analysis over counted alignments because the Core Principles alignment captured core ideas or beliefs underlying the productive use of student thinking, while the MOST Criteria and Building Subpractice alignment captured discrete skills or practices in which teachers would engage when enacting building; in other words, the MOST Criteria and Building Subpractices represent things teachers might do.

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Acknowledgements

This work was funded in part by the National Science Foundation (NSF) under Grant Nos. 1220141, 1220357, and 1220148. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the NSF. The authors would like to thank Elizabeth Fraser and Annick Rougee for their contributions to work that informed this paper.

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Correspondence to Shari L. Stockero.

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Appendices

Appendix 1

See Table 2.

Table 2 Scenario Interview instances, with MOST classifications

Appendix 2

See Table 3.

Table 3 Alignment of high and hindering thinking-as-a-resource orientations to the building-related constructs

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Stockero, S.L., Leatham, K.R., Ochieng, M.A. et al. Teachers’ orientations toward using student mathematical thinking as a resource during whole-class discussion. J Math Teacher Educ 23, 237–267 (2020). https://doi.org/10.1007/s10857-018-09421-0

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Keywords

  • Teacher orientations
  • Teacher beliefs
  • Student mathematical thinking
  • Using student thinking
  • Building on student thinking