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Noticing struggle during collaborative problem-solving in the middle-school mathematics classroom

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Abstract

Productive struggle is crucial to students’ mathematics learning. However, it has proven difficult for teachers to sustain struggle when it is productive or make it so when it is not. Studies show that teachers may offer students support when their struggles are productive or even refrain from offering support when students’ struggles are unproductive. This suggests that it is challenging to notice struggle, or more specifically, to attend to and interpret evidence of struggle in determining whether and how to respond. Little research, however, has examined teachers’ noticing of struggle, leaving teacher educators with limited guidance as they strive to prepare teachers to notice and respond to struggle in ways that will ensure students have sustained opportunities to struggle productively. We examined ten middle-school teachers’ noticing of struggle, conceived broadly, while observing students solve challenging problems collaboratively. Teachers attended most to students’ struggles to make sense of the mathematics, less often attending to their struggles to communicate their thinking or overcome challenging group dynamics. Teachers were also guided by three narratives about teaching and learning when interpreting the struggles they attended to, which specified that struggle is productive if students are working well together, making progress, or focused on understanding the mathematics. Teachers typically assessed students’ struggles as productive, especially when attending to students’ struggles to communicate their thinking, yet rarely differentiated their assessments for individual students in a group. We discuss implications for teacher educators striving to prepare teachers to notice and respond to struggle in the classroom.

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Notes

  1. Quotes were lightly edited for readability. For instance, phrases that were repeated and words like “um” and “like” were removed. However, we sought to maintain meaning throughout in making these edits.

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Acknowledgements

This work was supported by the National Science Foundation under Grant No 1417261, as well as a fellowship from the National Academy of Education/Spencer Foundation. Any opinions, findings, and conclusions or recommendations expressed herein are those of the authors and do not necessarily reflect the views of the funding agencies. All study participants consented to participate in this study by reading then signing a consent form that we shared with them. The authors would like to thank the teachers who so generously offered their time to take part in this study in-the-midst of the COVID-19 pandemic.

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  1. Department of Teacher Education and Learning Sciences, North Carolina State University, 208 Poe Hall, 2310 Stinson Drive, Raleigh, NC, 27695, USA

    Michael Jarry-Shore

  2. San Diego, CA, USA

    Alexander Richardson

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Correspondence to Michael Jarry-Shore.

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Appendices

Appendix 1

Video descriptions

Video

Task name and description

Summary

Video A

A race: Determine where two runners would be on a course after 60 min: (a) Amy, who ran 8 min/mile and (b) Rebecca, who ran 12 min/mile

- Students 1 and 2 previously solved the problem using different strategies

- These two students spend most of the video trying to explain and understand their respective strategies

- Student 3 frequently poses questions, yet their questions are often ignored

- Student 4 struggles to participate and is denied access to Student 1’s written strategy

- Video ends with Students 1 and 2 appearing to understand one another’s strategies

Video B

Simple interest: What is the percent interest associated with $15 interest charged weekly on a loan of $825?

- Four students spend about 1 min figuring out what problem is asking

- Student 1 divides 825/15, while Student 2 identifies a formula in their notes for finding percentage change: original/new

- Student 1 divides 15 by 16.5, the answer to the previous question: what is 2% interest of $825?

- Throughout, students assess the reasonableness of their answers

- Student 1 begins a trial and error strategy using a calculator

- Student 3 asks of each strategy if it yields the correct answer

- Video ends with students turning their attention to a groupmate trying to solve 1.5/16.5

Video C

Picture problems: Find the weights of a small, medium, and large chicken whose combined weights are portrayed on scales (e.g., one small and one large chicken weigh 8.5 kg)

- Students 1 and 2 spend significant time trying to explain and understand their respective strategies

- Student 3 tries to engage the group in discussion of weights and if they make sense, referencing their knowledge of Kentucky Fried Chicken and use of corn starch and MSG in Chinese cooking

- Student 4 says little and turns their back to the others partway through the video

- Video ends with Student 1 about to erase their work, suggesting that they regarded their strategy as unfruitful

Video D

Washing machine: Which of three options to wash clothes might you recommend based on the costs of each: (1) using a laundromat, (2) buying a front-loading washer and dryer, or (3) buying a top-loading washer and dryer?

- Four students quickly settle on a strategy they learned previously of representing the three options with algebraic equations, then finding points of intersection between them

- Students 1, 2, and 3 seem to implement this strategy with little trouble

- Student 4 says little, occasionally asking clarification questions of the group

- Video ends with students close to finding the points of intersection for their three equations

Appendix 2

Interview Protocol

  1. 1.

    Demonstrate how to play video and add & annotate tags in Torsh Talent™ (5 min).

  2. 2.

    Share screen showing focal problem students discuss in video then provide a few minutes for teacher to solve the problem (5 min).

  3. 3.

    Explain to teacher that they will watch a video-clip that is about 5-min long.

  4. 4.

    Project/read the viewing prompt: assess students’ struggle and tag any evidence of it.

  5. 5.

    Have teacher play and tag video. Mute your audio and turn off your video (10 min).

  6. 6.

    Once the video is over, ask the teacher to (10 min):

    1. a.

      Share their assessment of students’ struggle and their confidence in it.

      1. i.

        If teacher unsure how to assess the struggle, ask them if they would assess the struggle to be productive.

    2. b.

      Discuss tags that informed or supported their assessment of students’ struggle.

      1. i.

        Probes: (a) Which tag was that?, (b) Can you say more?, (c) I noticed you wrote, (d) And that informed your assessment how?, and (e) Any other tags?

  7. 7.

    Repeat steps 2–6 with second video (25 min).

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Jarry-Shore, M., Richardson, A. Noticing struggle during collaborative problem-solving in the middle-school mathematics classroom. J Math Teacher Educ (2024). https://doi.org/10.1007/s10857-024-09638-2

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