Analysis of a Structural Thinking Task Solved by Pre-Service Mathematics Teachers

Structural thinking is widely recognized as an important aspect of mathematical thinking, yet the role of structuring representations in supporting generalization has received relatively little attention. This study examined how pre-service mathematics teachers construct mathematical structure when solving a pattern generalization task. Written solutions produced by 62 pre-service mathematics teachers at different stages of their teacher education program were analyzed using qualitative thematic analysis informed by theoretical perspectives on emergent and mathematical structure. Six distinct solution strategies were identified, differing primarily in the structuring representations participants used to reorganize the mathematical situation. The findings indicate that participants differed not only in their solution procedures but also in the mathematical relationships highlighted by their representations. These differences were reflected in the general rules participants formulated and in the mathematical reasoning they used to support their conclusions. The study highlights the importance of structuring representations as a component of structural thinking and suggests that developing pre-service teachers’ ability to construct and interpret mathematically productive representations may support the transition from recognizing local relationships to formulating general mathematical relationships and supporting them through mathematical reasoning.