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Expert and preservice secondary teachers’ competencies for noticing student thinking about modelling

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Abstract

This study examined how expert and novice (preservice) teachers solved mathematical modelling tasks as well as how they noticed written artifacts of student thinking that were in response to the mathematical modelling tasks. Some teachers in both groups were aware of the openness and underdetermination of the modelling tasks and that these characteristics implied that underlying assumptions needed to be made in order to solve the tasks. Indeed, nearly all of the expert teachers addressed the need to make assumptions for the Seashell Task. When examining student work, both expert and preservice teachers interpreted positive aspects in the students’ solutions and provided feedback to students. However, almost all of the expert teachers responded by asking questions, whereas around a third of preservice teachers directly corrected students’ mistakes and another third pointed out mistakes without correcting them. This study provides a new angle to study teachers’ mathematical competencies, the assessment of modelling competencies, and considerations for the development of teachers’ modelling competencies.

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Notes

  1. In this study, we use the term “preservice” rather than “novice” because other studies have identified novice teachers as student teachers and first-year teachers (e.g., Berliner, 1994). Hence, “preservice” is a more accurate descriptor for our novice teacher group.

  2. See Tables 2 and 3 below for examples of response characteristics that were coded.

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Acknowledgements

We are grateful for Denise Griffiths’s assistance with data collection, Tammy Garber’s assistance with data coding, and Victoria Robison’s assistance with copyediting.

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Authors and Affiliations

  1. University of Delaware, 437 Ewing Hall, Newark, DE, 19716, USA

    Jinfa Cai, Raymond LaRochelle & Stephen Hwang

  2. University of Hamburg, Hamburg, Germany

    Gabriele Kaiser

  3. Australian Catholic University, Brisbane, Australia

    Gabriele Kaiser

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  1. Jinfa Cai
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  2. Raymond LaRochelle
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Correspondence to Jinfa Cai.

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Cai, J., LaRochelle, R., Hwang, S. et al. Expert and preservice secondary teachers’ competencies for noticing student thinking about modelling. Educ Stud Math 109, 431–453 (2022). https://doi.org/10.1007/s10649-021-10071-y

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