锚定生长教学策略，建构学生CPFS结构——以余弦定理的教学为例

Anchorinng Growth Teaching Strategy and Constructing Students’ CPFS Structure—Taking the Teaching of the Cosine Theorem as an Example

摘要: 在传统教学中，学生对余弦定理的理解仅停留于表面，没有形成系统的知识网络，无法灵活应用知识解决问题；针对此教学困境，基于CPFS结构理论，结合生长教学策略，设计余弦定理的教学。通过“探索生长–深度生长–变式生长–结构化反思”四个环节的递进式教学，以勾股定理为生长点，引导学生探索余弦定理生成过程，通过几何法、坐标法、向量法多元证明搭建知识联结，借助分层变式习题强化知识应用，结构化反思梳理知识脉络，促进学生构建完善余弦定理CPFS结构，深化知识理解，提升逻辑推理等核心素养，提高知识综合运用与问题解决能力。

Abstract: In traditional teaching, students’ understanding of the cosine theorem merely stops at the surface level, failing to form a systematic knowledge network and being unable to flexibly apply the knowledge to solve problems. To address this teaching predicament, based on the CPFS structure theory and combined with the growth teaching strategy, the teaching of the cosine theorem is designed. Through the progressive teaching of “exploration growth-deep growth-variation growth-structured reflection” in four stages, using the Pythagorean theorem as the growth point, students are guided to explore the generation process of the cosine theorem. Through multiple proofs using geometric methods, coordinate methods, and vector methods to build knowledge connections, with the help of graded variation exercises to strengthen knowledge application, structured reflection to sort out the knowledge framework, students are encouraged to construct a complete CPFS structure for the cosine theorem, deepen their understanding of the knowledge, enhance core competencies such as logical reasoning, and improve the ability to apply knowledge comprehensively and solve problems.