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Emergent mathematical worlds from teacher knowing in whole-class discourse: using an enactivist lens on the teaching of exponential functions

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Abstract

This paper reports findings related to the pursuit of describing a lived knowing for teaching mathematics. Specifically, we used an enactivist perspective to describe the knowing exhibited by three experienced high school teachers in their instructional actions while leading whole-class instruction on the topic of the equations of exponential functions. From classroom observations, we constructed maps of the emergent mathematical worlds of ideas and collective mathematical activity. Three major categories of ideas emerged in all three teachers’ classrooms relating to the recursive multiplicative nature of exponential functions, the role of the independent variable, and the definition of exponential. Findings of this study suggest attending to teacher knowing for mathematical whole-class instruction must include describing the role of the mathematical activity in the emergence of the ascribed mathematical ideas. When teachers facilitated the collective mathematical activity as the means by which the mathematical ideas and justifications emerge, the mathematical worlds were diverse and complex, and connections among ideas were more robust in their comprehensibility.

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Notes

  1. We conceive of task broadly to include the solving of a mathematical problem, the reading and interpreting of mathematical definitions or a given text, or other activities.

  2. Student 1 and Student 2 denote two different student speakers.

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Acknowledgements

This research was supported by the National Science Foundation under Grant No. DUE1552954. The views expressed do not necessarily reflect the official positions of the Foundation (Fig.

Fig. 12
figure 12

Concept maps for a Gabe, b Evelyn, and c Abby

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12).

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Authors and Affiliations

  1. Department of Mathematics, University of Wisconsin - Eau Claire, Hibbard Humanities Hall 508, 124 Garfield Avenue, Eau Claire, WI, 54701, USA

    Melissa Troudt

  2. Department of Mathematical Sciences, University of Northern Colorado, Campus Box 122, 501 20th Street, Greely, CO, 80639, USA

    Lindsay Reiten & Jodie Novak

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  1. Melissa Troudt
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Troudt, M., Reiten, L. & Novak, J. Emergent mathematical worlds from teacher knowing in whole-class discourse: using an enactivist lens on the teaching of exponential functions. J Math Teacher Educ (2024). https://doi.org/10.1007/s10857-023-09610-6

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