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

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.