Design Thinking: An innovative approach to enhancing the learning of basic mathematical function

The teaching of fundamental mathematical functions benefits significantly from innovative, student-centered strategies that bridge abstract concepts with real-world relevance. This study explores how Design Thinking (DT) a structured, iterative problem-solving approach—can be effectively adapted to enhance the teaching and learning of basic mathematical functions in high school. Grounded in the six-phase DT model (Empathize, Define, Ideate, Prototype, Test and Evaluate), the intervention engaged students in authentic, function-based challenges drawn from everyday contexts (e.g., modeling elevator motion with absolute value functions, bacterial growth with exponential functions, or turbine vibration with rational functions). In the Empathize phase, students identified real-life scenarios where mathematical functions apply; in Define, they framed specific problems and researched relevant function types; during Ideate, teams brainstormed mathematical models and solution pathways; in Prototype, they constructed physical or conceptual representations (e.g., homemade thermometers, toy cars, yogurt fermentation setups); Test, they validated their mathematical models and refining their work when inconsistencies appeared and in Evaluate, they refined their mathematical models, received feedback, and refined their understanding.基础数学函数的教学，若采用将抽象概念与现实应用场景相结合的创新型以学生为中心的教学策略，可获得显著成效。本研究探讨了如何将设计思维（Design Thinking，DT）——一种结构化的迭代式问题解决方法——有效适配，以优化高中阶段基础数学函数的教与学活动。本次教学干预以六阶段设计思维模型（共情（Empathize）、问题定义（Define）、发散构思（Ideate）、原型制作（Prototype）、测试验证（Test）与评估迭代（Evaluate））为框架，引导学生参与源自日常场景的真实函数类挑战——例如用绝对值函数模拟电梯运动、用指数函数模拟细菌生长、用有理函数模拟涡轮振动。在共情（Empathize）阶段，学生们识别出数学函数可应用的真实生活场景；在问题定义（Define）阶段，他们明确具体问题并调研相关函数类型；在发散构思（Ideate）阶段，各团队头脑风暴构建数学模型与解决路径；在原型制作（Prototype）阶段，他们搭建物理或概念化的展示载体（例如自制温度计、玩具小车、酸奶发酵实验装置）；在测试验证（Test）阶段，他们验证自身的数学模型，并在发现不一致之处时优化方案；在评估迭代（Evaluate）阶段，他们进一步完善数学模型、接收反馈并深化自身理解。