Study on Learning Difficulties of Function Concepts and Solutions

Abstract

Mathematical concepts are the cornerstone of mathematics, the foundation of students’ cognition, and the carrier of students’ mathematical thinking activities. Mathematical concepts are learned in stages, and students may make errors at all stages, which in turn affect the quality of subsequent learning of related mathematical content. This paper analyzes and summarizes the difficulties in each stage of learning mathematical concepts from the student's point of view, drawing on the “Action-Process-Object-Scheme” stage of learning mathematical concepts according to the APOS theory. Combined with the corresponding teaching strategies proposed by the APOS theory, we guide and help students to feel, obtain, understand and connect the concepts, and give a case study of the application of the solution strategy of “teaching the concept of function”, in order to give some insights into the effective learning and teaching of mathematical concepts.