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The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks

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Abstract

This study explores the extent to which a teacher elicited students’ mathematical reasoning through the use of challenging tasks and the role her knowledge played in doing so. I characterised the teacher’s knowledge in terms of a local theory of instruction, a form of pedagogical content knowledge that involves an empirically tested set of conjectures situated within a mathematical domain. Video data were collected and analysed and used to stimulate the teacher’s reflection on her enactments of an instructional sequence. The teacher, chosen for how she consistently elicited student reasoning, showed evidence of possessing a local theory in that she articulated the ways student thinking developed over time, the processes by which that thinking developed, and the resources that facilitated the development of student thinking. Her knowledge informed how she revised and enacted challenging tasks in ways that elicited and refined student thinking around integer addition and subtraction. Furthermore, her knowledge and practices emphasised the progressive formalisation of students’ ideas as a key learning process. A key implication of this study is that teachers are able to develop robust knowledge from enacting challenging tasks, knowledge that organises how they elicit and refine student reasoning from those tasks.

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Notes

  1. The names of the teachers and students are pseudonyms.

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Acknowledgements

I would like to thank the anonymous reviewers for their substantial and helpful feedback on earlier versions of this manuscript. This research was supported in part by the U.S. National Science Foundation under grant No. DRL-0746573. The opinions expressed herein are those of the author and do not necessarily reflect the views of the National Science Foundation.

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  1. Department of Teaching and Curriculum, The University of Rochester, Dewey Hall 1-160K, Box 270425, Rochester, NY, 14627, USA

    Jeffrey Choppin

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  1. Jeffrey Choppin
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Correspondence to Jeffrey Choppin.

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Choppin, J. The role of local theories: teacher knowledge and its impact on engaging students with challenging tasks. Math Ed Res J 23, 5–25 (2011). https://doi.org/10.1007/s13394-011-0001-8

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