基于PBL教学模式的问题链设计与素养生成路径研究——以“等比数列的前n项和公式”为例

Research on Problem Chain Design and Literacy Generation Path Based on PBL Teaching Model—Taking “The Formula for the Sum of the First n Terms of a Geometric Sequence” as an Example

摘要: 在核心素养导向的新课改背景下，问题链设计成为实现PBL教学模式有效实施的关键策略。文章聚焦PBL教学模式与高中数学教学的深度融合，以学生已有认知结构为起点，深入分析学情与教学内容的内在关联，系统设计了以“等比数列前n项和公式”这一典型内容为研究载体的“文化浸润–问题驱动–思维外显–应用反思”四位一体的教学实施方案。在教学实践中，通过问题驱动策略激发学生主观能动性，注重数学思维过程的可视化呈现与逻辑结构的系统梳理。有效促进了学生对等比数列前n项和公式的深度理解与灵活应用，更在解决真实问题的过程中，显著提升了学生的数学抽象能力、逻辑推理水平与数学建模素养。

Abstract: Under the backdrop of the new curriculum reform oriented towards core competencies, problem chain design serves as a pivotal strategy for the effective implementation of Problem-Based Learning (PBL). This paper focuses on the deep integration of PBL in high school mathematics. Taking the “Sum of the First n Terms of a Geometric Sequence” as a research vehicle and anchoring instruction in students’ existing cognitive structures, this study systematically constructs a four-dimensional instructional framework: “Cultural Immersion, Problem-driven, Thinking Externalization, and Application Reflection.” In practice, the study employs problem chains to stimulate student initiative and emphasizes the visualization of mathematical thinking and the systematic organization of logical structures. The results demonstrate that this approach not only promotes a deep understanding and flexible application of the formula but also significantly enhances students’ core competencies in mathematical abstraction, logical reasoning, and mathematical modeling through the resolution of authentic problems.