The Differences On Senior Middle School Student Understanding Of The Concept Of Function From APOS Theory

Understanding of mathematical concepts is the central topic of today’s international mathematics education sector and the hot spot of mathematics educators. Function is an important foundation of modern mathematics and the core knowledge of high school mathematics course, that make the learning of the concept of function become an important part of the School Mathematics Teaching. Learning and understanding of the concept of function is the turning point for students to understand the variation of the objective world. Different educational backgrounds of different regions make the students produce some differences in understanding the function. The four stages of APOS theory can reflect students’ learning and understanding of mathematical concepts, thus we can find the learning obstacles and the difference of the students in different regions, then we can improve the learning styles and teaching methods to promote the students’ understanding of the concept of function in different parts.This paper is an investigation of the Senior high school students from Beijing and Shandong which are the representative areas, after the survey knowing that:(1) To characterize the thinking characteristics and specific performance of the student at every stage of APOS theory in different parts;(2) To find the significant difference of two areas’students in understanding the concept of function;(3) Preliminarily design learning programs of the students and the teaching plans of the teachers in studying the concept of function in different parts.Applying APOS theory to examine the differences of the students from different parts in understanding the concept of function is feasible. The survey results show that: Students in Shandong is better during the operational phase and the process stage, and students in Beijing is much better than students in Shandong in the object stage and the schema stage, especially the schema stage. According to the survey results and the literature, initially giving the advice and guidance of the two regions in teaching function.