通法为主，巧解为辅：论高考数学解题教学的守正创新——以2025年数学全国卷I第16题为例

Primarily Emphasizing General Methods, Supplementing with Ingenious Solutions: On Upholding Fundamentals and Pursuing Innovation in Teaching Mathematical Problem-Solving for the Gaokao—Taking Question 16 of the 2025 Mathematics National Volume I as an Example

摘要: 以2025年新高考数学全国卷I第16题为例，探讨高中数学解题教学中的“守正”与“创新”。“守正”即夯实基础，强调对教材中通法的深刻理解与熟练运用；“创新”即发展思维，追求在通法基础上的优化和升华。通过对该题两问的多种解法进行比较分析，明确“通法”的基础性地位与“巧解”的思维价值，并提出“以通法筑牢根基，以巧解提升素养”的启示与反思，为改进高中数学解题教学提供实践参考。

Abstract: Taking Question 16 of the 2025 New Gaokao Mathematics National Volume I as an example, this paper explores the balance between “upholding fundamentals” and “pursuing innovation” in teaching mathematical problem-solving in senior secondary education. “Upholding fundamentals” refers to consolidating foundational knowledge, emphasizing a deep understanding and proficient application of general methods found in textbooks. “Pursuing innovation” involves developing students' thinking, aiming for optimization and enhancement based on general methods. Through a comparative analysis of various approaches to the two parts of the question, this study clarifies the foundational role of general methods and the cognitive value of ingenious solutions. It also proposes insights and reflections on “using general methods to build a solid foundation and ingenious solutions to enhance competencies,” providing practical references for improving the teaching of mathematical problem-solving in senior secondary schools.