Mathematical Reasoning in Secondary Classrooms: Problem-Solving Instruction, Cognitive Strategy Use, and Task Complexity

Abstract

Existing scholarship on mathematical reasoning in secondary education frequently prioritizes procedural proficiency and final-answer accuracy, with comparatively limited exploration of how problem-solving instruction interacts with cognitive strategy use and task complexity to shape students’ reasoning processes. Addressing this gap, the present study examines how structured problem-solving instruction influences students’ mathematical reasoning, focusing on variations in strategy application and responses to tasks with differing cognitive demands. Employing a sequential explanatory mixed-methods design, the study was conducted in secondary classrooms involving 52 students across two grade levels in East Java, Indonesia. Quantitative data were obtained through performance-based reasoning assessments and structured questionnaires measuring cognitive strategy use, while qualitative insights were derived from semi-structured interviews with six selected participants. The findings demonstrate that problem-solving instruction enhances students’ ability to construct mathematical justifications, utilize diverse strategies, and engage in conceptual interpretation, particularly when tasks are systematically scaffolded and moderately complex. Nevertheless, disparities were observed in students’ capacity to sustain reasoning when encountering highly complex or open-ended problems, with several participants reverting to procedural reliance and exhibiting difficulty transferring strategies across unfamiliar contexts. These outcomes indicate that although problem-solving instruction strengthens analytical engagement and strategic adaptability, its effectiveness is closely influenced by task design, instructional scaffolding, and the integration of metacognitive guidance within classroom practices.