Correspondence Relationship Generalization of Junior High School Students in Solving Mathematics Problems

Generalization is a fundamental component of mathematical thinking, allowing students to recognize and articulate patterns beyond specific instances. This study investigates the process and reflection of generalization among junior high school students when solving problems involving correspondence relationships. Generalization is conceptualized as a dynamic process consisting of three core actions: relating, searching, and extending. Reflection of generalization is identified through students' written and oral explanations. Employing a qualitative approach, this research involved 26 eighth-grade students who engaged in problem-solving activities using think-aloud protocols and semi-structured interviews. Based on their approaches to generalization, students were categorized into three groups: (1) global formal correspondence relationship generalization, where students extended patterns using the nth term of an arithmetic sequence; (2) inductive formal generalization, where rules were derived through repeated pattern recognition; and (3) partial formal generalization, where generalizations were made based on selective pattern components. The novelty of this research lies in its detailed analysis of students' cognitive strategies during generalization, a topic that remains underexplored at the middle school level. Given the urgency to enhance mathematical reasoning in early education, these findings offer valuable insights into how students form general rules and relationships, informing instructional practices aimed at nurturing generalization skills. This study contributes to the growing body of research on mathematical cognition by highlighting the diverse ways students engage with and reflect on mathematical patterns.