A Study Of Teaching Junior-middle-school Function Based On APOS Theory

Being one of the most significant basic concepts in junior-middle-school mathematics, the function is the mathematical model depicting laws of changes in the objective world and the basic knowledge for students to further their learning in mathematics. In practical teaching, we have no clear picture as to how many different levels in terms of understanding the concept of the function the students achieve and how many students can reach a certain level. Without a profound comprehension of the status quo of students'understanding, their different levels of understanding and limitations, we can in no way adopt correct teaching strategies, which should be based on our familiarity with students'current levels. This thesis aims at using the APOS (Action, Process, Object, Scheme) theory to analyze the constructional process of the function. Through a careful analysis, this thesis tries to investigate what kind of level junior-middle-school students have achieved in terms of understanding the concept of the function and the reasons why the students have achieved a certain level of understanding and then to put forward several suggestions concerning the teaching of the function.The APOS theory is a theory of learning, aiming at studying the learning process of some mathematical concepts. The theory points out the learning of concepts requires the following four phases of psychological construction──action, process, object and scheme. Nowadays, the APOS theory has been applied extensively in many fields in mathematical teaching.The thesis is composed of six sections. The first section points out the importance of the function in mathematical education and practical teaching and puts forth several questions. The second section introduces the main contents and related studies of the APOS theory and related studies of the function by way of a literature review. The third section presents the designed format and process of the research and investigation, including subjects of the research, the format of the questionnaire, the implementation of the testing and the collecting of data. The fourth section analyzes students'understanding of the concept of the function from the four phases of the APOS theory respectively and briefly analyzes the reasons triggering the results and offers corresponding suggested teaching methods. The cases in practical teaching would be analyzed in the fifth section. And the final section presents conclusions of the research and some reflections concerning the topic.