A framework of mathematical thinking experience: Core components, hierarchical levels, and group differences in mathematical creativity
摘要
While previous research has emphasized the role of mathematical thinking experience in developing creativity, few studies have examined mathematical creativity with high-complexity tasks and analyzed the relationship between creativity and such experience. The study constructs an empirical framework of mathematical thinking experience and explores its relationship with creativity through high-complexity tasks. A four-stage design was employed: Stage 1 proposed eight hypothesized components of mathematical thinking experience by synthesizing literature on mathematicians’ thinking and analyzing 69 teachers’ perceptions of students excelling in mathematical thinking. Stage 2 developed an assessment based on these components, administered to 120 twelfth-grade students, and identified four core components through exploratory factor analysis. Stage 3 applied hierarchical clustering to categorize students into different levels of experience according to the four core components. Stage 4 compared creativity across 48 students at different experience levels using insight-allowing tasks, followed by ANOVA and Games-Howell post-hoc tests. Results revealed four core components of mathematical thinking experience: inductive reasoning, analogical reasoning, mathematical expression, and mathematical proof. Hierarchical clustering categorized students into high, medium, and low experience levels. High-experience students outperformed their peers in overall creativity, fluency, flexibility, and originality, while significant differences between medium- and low-experience students were found only in fluency and flexibility. High-experience students were more likely to propose insightful solutions and demonstrate greater originality, highlighting how mathematical thinking experience fosters both analytical and intuitive insights. This study develops a framework of mathematical thinking experience, shows that high-experience students exhibit stronger creativity, and provides a foundation for future longitudinal research.