基于认知分析的数学问题深度教学——以一道函数试题的认知分析与深度教学为例

In depth teaching of mathematical problems based on cognitive analysis: an example of cognitive analysis and in depth mathematics teaching in solving a function problem

摘要: 数学问题是数学深度教学的"心脏".数学深度教学是以数学问题的认知分析为基础、指向学生深度学习和数学核心素养生成的教学.数学问题的认知分析包括数学问题的价值分析、问题解决的认知障碍分析以及学生已有数学认知经验分析等.以一个函数综合试题为研究载体,对其作了认知分析,并从深度理解、多元表征、知识迁移、发现创新等角度提出数学问题的深度教学建议.

Abstract: Mathematical problems are the "heart" of in-depth teaching of mathematics. Teaching mathematics with depth is based on the cognitive analysis of mathematical problems and directed to the deep learning of students and the generation of core competences in mathematics. The cognitive analysis of mathematical problems includes the analysis of the value of mathematical problems, the analysis of cognitive barriers to problem solving, the analysis of students' existing mathematical cognitive experience and so on. Taking a function synthesis problem as the research carrier, a cognitive analysis was made, and the depth teaching suggestions of mathematical problems were put forward from the perspectives of deep understanding, multiple representations, knowledge transfer, discovery and innovation.