The role of productive struggle in teaching and learning middle school mathematics
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Students’ struggle with learning mathematics is often cast in a negative light. Mathematics educators and researchers, however, suggest that struggling to make sense of mathematics is a necessary component of learning mathematics with understanding. In order to investigate the possible connection between struggle and learning, this study examined students’ productive struggle as students worked on tasks of higher cognitive demand in middle school mathematics classrooms. Students’ productive struggle refers to students’ “effort to make sense of mathematics, to figure something out that is not immediately apparent” (Hiebert & Grouws, 2007, p. 287) as opposed to students’ effort made in despair or frustration. As an exploratory case study using embedded multiple cases, the study examined 186 episodes of student‐teacher interactions in order to identify the kinds and nature of student struggles that occurred in a naturalistic classroom setting as students engaged in mathematical tasks focused on proportional reasoning. The study identified the kinds of teacher responses used in the interaction with the students and the types of resolutions that occurred. The participants were 327 6th and 7th grade students and their six mathematics teachers from three middle schools located in mid‐size Texas cities. Findings from the study identified four basic types of student struggles: get started, carry out a process, give a mathematical explanation, and express misconception and errors. Four kinds of teacher responses to these struggles were identified as situated along a continuum: telling, directed guidance, probing guidance, and affordance. The outcomes of the student‐teacher interactions that resolved the students’ struggles were categorized as: productive, productive at a lower level, or unproductive. These categories were based on how the interactions maintained the cognitive level of the implemented task, addressed the externalized student struggle, and built on student thinking. Findings provide evidence that there are aspects of student‐teacher interactions that appear to be productive for student learning of mathematics. The struggle‐response framework developed in the study can be used to further examine the phenomenon of student struggle from initiation, interaction, to its resolution, and measure learning outcomes of students who experience struggle to make sense of mathematics.