指向高阶思维培养的高中数学教学设计与实施——以“导数与函数恒成立问题”为例

Instructional Design and Implementation of Senior High School Mathematics Aimed at Higher-Order Thinking Cultivation—Taking “The Constant Establishment Problem Related to Derivatives and Functions” as an Example

摘要: 本研究以高中数学中的“导数与函数恒成立问题”为例，探讨了旨在培养学生高阶思维的教学设计与实施策略。研究针对学生在解题时常套用公式、机械模仿的现象，提出并实践了围绕“比较–概括–迁移”这一思维进阶主线的教学模式。文章详细阐述了从教学目标设定、教学过程设计(包括创设情境、暴露思路、比较辨析、提炼结构、变式迁移)、到评价设计的完整方案。文章提供了一个完整、细致且可复制的教学案例。从问题选择、环节设计、时间分配到评价要点，都给出了具体建议，对一线教师有很强的直接指导作用。

Abstract: Taking the topic of “derivatives and the constant establishment problem of functions” in high school mathematics as an example, this study explores the teaching design and implementation strategies aimed at cultivating students’ higher-order thinking. Aiming at the common phenomenon that students tend to blindly apply formulas and engage in mechanical imitation when solving problems, this study proposes and practices a teaching model centered on the main thread of progressive thinking development: “comparison-generalization-transfer”. The paper elaborates a complete solution covering the whole process: from the setting of teaching objectives, the design of teaching procedures (including situation creation, exposing thinking processes, comparative analysis, structural refinement, and variant transfer), to the design of evaluation system. This research provides a complete, detailed and replicable teaching case, and puts forward specific suggestions on problem selection, session design, time allocation and evaluation key points, which offers strong and direct guidance for front-line teachers.