A Systematic Review of Productive Struggle Definitions and an Investigation of Prospective Teachers' Mathematical Struggle During a Whole-Class Discussion of a High-Leverage Contribution

Date of Award

5-2026

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Laura R. Van Zoest, Ph.D.

Second Advisor

Jane-Jane Lo, Ph.D.

Third Advisor

Theresa J. Grant, Ph.D.

Fourth Advisor

Mariana Levin, Ph.D.

Keywords

Mathematically productive struggle, mathematics learning, perseverance, productive struggle, struggle, whole-class discussion

Abstract

Struggle is an integral part of the learning process. Despite the widespread use of the term “productive struggle” in mathematics education research, there remains limited consensus on how it is defined and operationalized. This three-paper dissertation addresses this gap through two complementary studies: (a) a systematic review of definitions of productive struggle in mathematics learning research and (b) an empirical investigation of what mathematically productive struggle looks like during prospective elementary teachers’ (PTs) whole-class discussion of a high-leverage PT contribution.

The first paper reports the systematic review examining how productive struggle has been defined in research on mathematics learning. I used the findings from the review of 39 publications to propose a Framework for Defining Productive Struggle to support researchers’ and practitioners’ efforts to articulate and operationalize productive struggle in their work.

The second and third papers arose from the empirical study centered on the PTs’ discussion of a high-leverage PT contribution about comparing two fractions. In the second paper, I used the proposed Framework to define mathematically productive struggle and to identify evidence of mathematical struggle (n = 55) and evidence of mathematical progress (n = 36) for the 26 PTs who participated in the study. These data informed the analysis and description of variations in mathematically productive struggle, supporting further refinement of the Framework. The data also provided concrete and nuanced images of what mathematically productive struggle can look like in the context of a whole-class discussion. As an initial attempt to illuminate this complex phenomenon in mathematics learning, this paper provides a foundation for identifying and describing productive struggle across diverse learning contexts.

The third paper used the PTs’ evidence of mathematical struggle and evidence of mathe-matical progress to identify their struggle experiences—No Struggle, Mathematically Productive Struggle, or Mathematically Unproductive Struggle. I used the PTs’ mathematical justifications before and after the whole-class discussion to describe the PTs’ types of understanding and the changes in their mathematical understanding. The majority of the PTs’ mathematical justifications after they engaged in the whole-class discussion demonstrated growth in their understanding, regardless of whether they struggled themselves or their initial understanding. The findings highlight the benefits of optimizing opportunities for mathematically productive struggle.

Together, the three papers lay a foundation for continued investigation of productive struggle as a complex learning phenomenon within and beyond mathematics learning contexts.

Comments

Fifth Advisor: Hiroko K. Warshauer, Ph.D.

Access Setting

Dissertation-Abstract Only

Restricted to Campus until

5-1-2036

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