Construction and Practical Research on Teaching Pathways for Problem Posing in Junior High School Mathematics Based on Polya’s "How to Solve It" Philosophy

Zeyu Wei; Yiyan Liu

doi:10.54097/nkz7zw78

Authors

Zeyu Wei
Yiyan Liu

DOI:

https://doi.org/10.54097/nkz7zw78

Keywords:

Polya, Problem Posing, Junior High School Mathematics, Teaching Pathway, Core Competencies.

Abstract

With the 2022 Compulsory Education Mathematics Curriculum Standards elevating "problem posing" as a core competency, fostering this skill has become crucial. However, junior high mathematics teaching often prioritizes problem solving over problem posing, limiting students' creative thinking. Based on Polya’s heuristic ideas in How to Solve It, this study constructs a systematic teaching pathway for problem posing. By analyzing key elements in Polya’s philosophy—such as analogy, rephrasing, decomposition, and specialization—and integrating the “What-If-Not” strategy, a four-stage teaching model is developed: overall questioning, systematic inquiry, deep exploration, and practical innovation. Using the “similar triangles” unit as a case study, the paper details instructional design and examines the use of AI tools in selecting student-generated problems. This approach offers an innovative, operable framework to enhance question-posing ability, supporting the shift toward student-centered mathematics teaching focused on core competencies.

References

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