“一题多解”在高中数学教学中的高阶思维培养路径——以一道三角函数题为例

The Path of Cultivating Higher-Order Thinking through “Multiple Solutions to One Problem” in High School Mathematics Teaching—A Case Study of a Trigonometric Function

摘要: 新课标背景下，数学教学以培育学生数学核心素养为核心目标，而高阶思维能力是数学核心素养的关键构成，主要涵盖分析、综合、评价与创造四大思维维度。本文以数学试题探究为载体，依托一题多解教学模式，引导学生从多元视角、不同解题路径剖析同一数学问题，通过对比、评析各类解题思路的优劣与适用场景，进一步衍生新问题、探究新解法，创造性地完成问题求解。该教学路径可为中小学数学课堂培养学生高阶思维能力提供实践参考，助力学生梳理知识脉络、搭建系统化知识框架，构建完整的数学知识体系。

Abstract: Under the background of the new curriculum standards, mathematics teaching aims to cultivate students’ core competencies in mathematics, with higher-order thinking ability being a key component, which mainly covers four cognitive dimensions: analysis, synthesis, evaluation, and creativity. Taking mathematical problem exploration as a carrier and relying on the “multiple solutions to one problem” teaching model, this paper guides students to analyze the same mathematical problem from multiple perspectives and different solution paths. By comparing and evaluating the advantages, disadvantages, and applicable scenarios of various solution approaches, students are encouraged to further generate new problems, explore new solutions, and solve problems creatively. This teaching approach can provide practical references for cultivating students’ higher-order thinking ability in primary and secondary mathematics classrooms, help students sort out their knowledge context, build a systematic knowledge framework, and construct a complete mathematical knowledge system.