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Learning to Notice Student Thinking About the Equal Sign: K-8 Preservice Teachers’ Experiences in a Teacher Preparation Program

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Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks

Part of the book series: Research in Mathematics Education ((RME))

Abstract

In this chapter, we present our work and research related to preservice teacher (PST) noticing, describing how we provide PSTs with opportunities to notice student thinking about the equal sign and equality. We designed an instructional intervention in an integrated mathematics content and pedagogy course (with a field experience) to support PSTs in (1) learning about key mathematical ideas related to the equal sign and equality, and (2) rehearsing teacher noticing skills. Our PSTs rehearsed and reflected on their noticing skills by conducting two one-on-one clinical interviews with elementary students and participating in debriefing interviews with course instructors. Using this context, we examined (1) the extent to which PSTs attended to and further explored student understanding of the equal sign and equality, and (2) what PSTs perceived they learned about aspects of their teacher professional noticing skills and student thinking about the equal sign and equality. Our results indicate that the PSTs predominantly noticed the strategies students used to solve a task without focusing on student thinking about the equal sign and equality. In addition, our PSTs perceived that they strengthened either their own knowledge or student knowledge of the equal sign and equality while conducting their diagnostic clinical interviews.

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Author information

Authors and Affiliations

  1. Marquette University, Milwaukee, WI, USA

    Leigh A. van den Kieboom, Marta T. Magiera & John C. Moyer

Authors
  1. Leigh A. van den Kieboom
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  2. Marta T. Magiera
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  3. John C. Moyer
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Corresponding author

Correspondence to Leigh A. van den Kieboom .

Editor information

Editors and Affiliations

  1. Morehead State University, Morehead, Kentucky, USA

    Edna O. Schack

  2. University of Kentucky, Lexington, Kentucky, USA

    Molly H. Fisher

  3. STEM Education, University of Kentucky, Lexington, Kentucky, USA

    Jennifer A. Wilhelm

Appendix 1: Diagnostic Clinical Interview Protocol

Appendix 1: Diagnostic Clinical Interview Protocol

Task #1

Gr. 3/Gr. 8:

The arrow points to a symbol.

What is the name of that symbol?

What does that symbol mean?

Can it mean anything else?

5 + 3 = 8

↑

Task #2

Gr. 3:

What number goes in the box?

5 + 4 = ☐ + 6

Gr. 8:

What value of a makes the number sentence true?

55 + 54 = a + 56

Task #3

Gr. 3:

Fill in the box with a number that makes the sentence true:

13–7 = ☐ − 6

Gr. 8:

What value of a makes the number sentence true?

130–70 = a − 60

Task #4

Gr. 3:

Fill in the box with a number that makes the sentence true:

☐ + 4 = 5 + 7

Gr. 8:

What value of a makes the number sentence true:

a + 34 = 35 + 37

Task #5

Gr. 3:

Fill in the box with a number that makes the sentence true:

☐ = 7 + 6

Gr. 8:

What value of a makes the number sentence true?

a = 700 + 600

Task #6

Gr. 3:

What value would make the number sentence true:

☐ = 25 − 12

Gr. 8:

What value of a makes the number sentence true?

a = 2500–1200

Task #7

Gr. 3:

What value would make the number sentence true:

8 + ☐ = 12

Gr. 8:

What value of a makes the number sentence true?

8 + a = 12

Task #8

Gr. 3:

What value would make the number sentence true:

12 + 9 = 10 + 8 + ☐

Gr. 8:

What value of a makes the number sentence true?

120 + 90 = 100 + 80 + a

Task #9

Gr. 3/Gr. 8: Write your own number in each box to make the number sentence true:

☐ + ☐ = ☐ + ☐

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van den Kieboom, L.A., Magiera, M.T., Moyer, J.C. (2017). Learning to Notice Student Thinking About the Equal Sign: K-8 Preservice Teachers’ Experiences in a Teacher Preparation Program. In: Schack, E., Fisher, M., Wilhelm, J. (eds) Teacher Noticing: Bridging and Broadening Perspectives, Contexts, and Frameworks. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-319-46753-5_9

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  • DOI: https://doi.org/10.1007/978-3-319-46753-5_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-46752-8

  • Online ISBN: 978-3-319-46753-5

  • eBook Packages: EducationEducation (R0)

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