<p>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.</p>

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A framework of mathematical thinking experience: Core components, hierarchical levels, and group differences in mathematical creativity

  • Jingyi Li,
  • Yufeng Guo,
  • Juewen Zhang

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.