信息加工视域下高中数学重难点突破——以“函数的单调性”为例

Breaking through the Key and Difficult Points of High School Mathematics from the Perspective of Information Processing—A Case Study of “The Monotonicity of Functions”

摘要: 函数的单调性是高中函数板块的核心内容，既是教学重难点，也是高考高频考点，对学生逻辑推理、数形结合等数学思维培养具有关键作用。基于信息加工学习理论，从信息接收、编码、存储、提取的认知过程出发，针对学生学习单调性概念时存在的认知误区、思维断层等问题，优化课堂教学环节与教学设计。构建指向重难点的教学路径，引导学生完成概念的深度建构，契合新高考命题导向下的素养育人要求，为高中数学高效课堂教学提供实践参考。

Abstract: Function monotonicity constitutes the core content of the high school function curriculum, serving as both a key teaching challenge and a frequent examination focus on the National College Entrance Examination (Gaokao). It plays a pivotal role in cultivating students’ mathematical thinking skills, including logical reasoning and the integration of numerical and graphical approaches. Grounded in information processing learning theory and examining the cognitive process encompassing information reception, encoding, storage, and retrieval, this study addresses common misconceptions and conceptual gaps students encounter when learning about monotonicity by optimizing classroom instruction and instructional design. A teaching pathway focused on critical concepts is developed to guide students toward deep conceptual understanding, aligning with the competency-oriented educational objectives of the new Gaokao framework and providing practical guidance for effective high school mathematics instruction.