基于波利亚解题理论的解题教学研究——以一道空间立体几何习题为例

Research on Problem-Solving Teaching Based on Polya’s Problem-Solving Theory—Taking a Spatial Solid Geometry Exercise as an Example

摘要: 文章以乔治·波利亚解题理论为核心框架，以一道空间立体几何习题为例，探索其在高中空间立体几何解题教学中的理论指导与实践应用价值。波利亚四阶段解题理论为数学问题解决提供了结构化路径，也为一线教师进行问题解决教学提供有力的理论支撑。在波利亚解题理论引领下，运用所提教学策略开展解题教学，有助于提升学生的解题能力，思维灵活性与创新性，提高教师的教学效率与质量。

Abstract: The article centers around George Polya’s problem-solving theory as its core framework, using a spatial solid geometry exercise as an example to explore its theoretical guidance and practical application value in the teaching of spatial solid geometry problem-solving in high school. Polya’s four-stage problem-solving theory provides a structured approach for solving mathematical problems and offers robust theoretical support for frontline teachers in problem-solving instruction. Guided by Polya’s problem-solving theory, employing the proposed teaching strategies in problem-solving instruction can enhance students’ problem-solving abilities, flexibility, and innovativeness of thinking, and improve teachers’ teaching efficiency and quality.