Preliminary Study On Understanding Level Of Function Concept From High School Students Aspect

Mathematical understanding has become another main issue in the international mathematics education, being focus in the mathematics education research and practice after"problem Solving". Function concept is an important foundation of modern mathematics, its concept and the way of thinking being the main one in the high school mathematics teaching. Learning Function concept helps students understand the relationship from specific real-world to the abstract. However, due to the complexity of the concept of function and the diversity of function representation, the task of teaching function makes very difficulty.This paper has done the following research through the questionnaires of High School students and the interviews of expert teachers: (1) the division of the understanding level of function concept; (2) Describing the students thinking and specific performance characteristics at each level; (3) Designing the teaching of mathematics teaching goals and teaching tasks.In this paper, SOLO classification standards and APOS theories have been used to divide four levels about conceptual understanding from the "surface" (that means) and "layer" (level) in two dimensions .Survey results show that the majority of students is in the first and second level, few students achieve a higher third and fourth levels. According to the survey results and literature research, asking the expert teachers, this paper describes the students thinking and specific performance characteristics at each level. the corresponding four teaching phases are designed: experience phase, the formation of the concept phase, the object integration phase and schema stage formed. Finally we give teaching objectives, teaching tasks, and specific examples in every stage.