Discovering and addressing errors during mathematics problem-solving—A productive struggle?

• Students who observe their errors engage in productive or unproductive struggle.
• If the students return to explore and analyze, their struggles is likely to be productive.
• During productive struggles, students will correct and reconstruct prior knowledge.
• During productive struggles, students will construct new knowledge.
• If they do not go back to explore and analyze, their struggles will be unproductive.

The present study investigates students’ struggles when encountering errors in problem-solving. The focus is students’ problem-solving activities that lead to productive struggle and what the students might gain therefrom. Twenty-four students between the ages of 16 and 17 worked in pairs to solve a linear function problem using GeoGebra, a dynamic software application. Data in the form of recorded conversations, computer activities and post-interviews were analyzed using Hiebert and Grouws’ (2007. Second handbook of research on mathematics teaching and learning (Vol. 1). 404) concept of productive struggles and Schoenfeld's (1985. Mathematical problem solving: ERIC) framework for problem-solving. The study showed that all students made errors concerning incorrect prior knowledge and erroneously constructed new knowledge. All participants engaged in superficial, unproductive struggles moving between a couple of Schoenfeld's episodes. However, a majority of the students managed to transform their efforts into productive struggle. They engaged in several of Schoenfeld's episodes and succeeded in reconstructing useful prior knowledge and constructing correct new knowledge—i.e., solving the problem.