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Making sense of student mathematical thinking: the role of teacher mathematical thinking

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Abstract

In mathematical whole-class discussions, teachers can build on various student ideas and develop these ideas toward mathematical goals. This requires teachers to make sense of their students’ mathematical thinking, which evidently involves mathematical thinking on the teacher’s part. Teacher sense-making of student mathematical thinking has been studied and conceptualized as an aspect of teacher noticing and has also been conceptualized as a mathematical activity. We combine these perspectives to explore the role of teacher mathematical thinking in making sense of student mathematical thinking. In this study, we investigated that role using video-based teacher discussions in a teacher researcher collaboration in which five Dutch high school mathematics teachers and one researcher developed discourse based lessons in cycles of design, enactment, and evaluation. In video-based discussions, they collaboratively reflected on whole-class discussions from the teachers’ own lessons. We analyzed these discussions to explore the mathematical thinking that teachers articulated during sense-making of students’ mathematical thinking and how teachers’ mathematical thinking affected their sense-making. We found five categories concerning the role of teacher mathematical thinking in their sense-making: flexibility, preoccupation, incomprehension, exemplification, and projection. These categories show how both the content and the process of teacher mathematical thinking can support or impede their sense-making. In addition, we found that the teachers often did not articulate explicit mathematical thinking. Our findings suggest that sense-making of students’ mathematical thinking requires teachers to (re-)engage in reflective thinking with regard to the mathematical content as well as the process of their own mathematical thinking.

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Notes

  1. We use “they” and “their” as gender-neutral singular pronouns.

  2. For a more elaborate description of the design, goals, and outcomes of the project, see Kooloos et al. (2020).

  3. See Appendix Table 2 for three examples of problems from the teachers’ lessons.

  4. To distinguish descriptions of classroom situations and classroom discourse from the situations and discussions in the group meetings, descriptions of classroom episodes and classroom discourse are in italics.

  5. See Appendix Table 2 for the problem that the students were given.

  6. General teacher responses that were highly regarded during the video-based discussions were (1) request the student to give further explanation in front of the class and (2) ask the class or a specific student for a reaction or a reformulation.

  7. To clarify: In the Dutch textbooks these teachers use students are presented with many exercises involving circles and tangent lines in which they use the procedure of setting up a quadratic formula and the fact that the “discriminant equals zero” if the line is tangent to the circle. Making these exercises does not always require understanding of why the method works.

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Acknowledgements

We owe many thanks to the cooperating teachers. Cooperating with them in this project, we have learned a good deal from them, as well as from their students.

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Authors and Affiliations

  1. Radboud Teachers Academy, Radboud University Nijmegen, Erasmusplein 1, 6525 HT, Nijmegen, the Netherlands

    Chris Kooloos, Helma Oolbekkink-Marchand & Saskia van Boven

  2. HAN University of Applied Sciences, Nijmegen, the Netherlands

    Helma Oolbekkink-Marchand

  3. Mathematical Institute, University of Bonn, Bonn, Germany

    Rainer Kaenders

  4. Department of Mathematics, Radboud University Nijmegen, Nijmegen, the Netherlands

    Gert Heckman

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  1. Chris Kooloos
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  2. Helma Oolbekkink-Marchand
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  3. Saskia van Boven
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Correspondence to Chris Kooloos.

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Appendix 

Appendix 

1.1 The problems

Table 2 The problems
Full size table

1.1.1 Categories of sense-making

Our classification of teacher sense-making was based upon the categorization of Sherin and van Es (2009) and adapted according to our data analysis. Whereas Sherin and van Es (2009) coded “idea units” and “segments in which a particular idea was discussed,” we coded individual contributions by teachers, resulting in a more detailed variation of sense-making. In addition to the stance that teachers take with regard to student thinking, we found that their sense-making focused on different aspects of students’ articulated thinking: namely, the formulation; the meaning of the utterance; the intention (what the student actually meant); or the reasoning that underpins a statement.

Table 3 Teacher sense-making of student mathematical thinking
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Kooloos, C., Oolbekkink-Marchand, H., van Boven, S. et al. Making sense of student mathematical thinking: the role of teacher mathematical thinking. Educ Stud Math 110, 503–524 (2022). https://doi.org/10.1007/s10649-021-10124-2

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