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“This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking

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Abstract

This mixed methods study investigates the ways in which secondary mathematics prospective teachers acquire skills needed to attend to, interpret, and respond to students’ mathematical thinking and the ways in which their perceived strengths and weaknesses influence their skills when this type of formalized training is not part of their program. These skills (attending, interpreting, and responding) are defined as teachers’ professional noticing of students’ thinking. Results indicate that seniors respond to students’ thinking in significantly different ways from juniors and sophomores. Converging the data highlighted inconsistencies in how participants’ were making sense of students’ mathematical thinking, as well as in participants’ self-identified strengths and weaknesses.

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Acknowledgments

We would like to thank the reviewers of this manuscript for their thoughtful and intentional comments. Comments of such high caliber helped us make significant revisions and strengthened the manuscript.

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Authors and Affiliations

  1. Indiana University, 201 N. Rose Street, 3254, Bloomington, IN, 47405, USA

    Amber Simpson

  2. Clemson University, 101 Tillman Hall, Clemson, SC, 29634-0705, USA

    Leigh Haltiwanger

Authors
  1. Amber Simpson
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  2. Leigh Haltiwanger
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Corresponding author

Correspondence to Amber Simpson.

Electronic supplementary material

Appendix: Interview protocol

Appendix: Interview protocol

  1. 1.

    Give participant copy of student work sample (similar to Fig. 2).

    1. (a)

      Please describe in detail what you think the student did in response to this problem.

    2. (b)

      Please explain what you learned about the student’s understanding. (If does not discuss misunderstanding, ask what does the student misunderstand.)

    3. (c)

      Pretend that you are the teacher of this student. What problem or problems might you pose next and why? (Have sheet of paper available.)

      If new problem not posed, ask what problem you might pose that would illustrate this. How might this help the student think about this concept differently?

  2. 2.

    What might be some reasons you did or did not work out this problem ahead of time before analyzing the student work?

  3. 3.

    What have you learned about this student from examining his or her work?

  4. 4.

    Where would you rank yourself on a scale from 1-5 (1 being low and 5 being high), in terms of your confidence in analyzing students’ mathematical thinking? Why?

  5. 5.

    What do you see as your weaknesses as related to analyzing student work?

  6. 6.

    What do you see as your strengths as related to analyzing student work?

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Simpson, A., Haltiwanger, L. “This is the First Time I’ve Done This”: Exploring secondary prospective mathematics teachers’ noticing of students’ mathematical thinking. J Math Teacher Educ 20, 335–355 (2017). https://doi.org/10.1007/s10857-016-9352-0

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  • DOI: https://doi.org/10.1007/s10857-016-9352-0

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