The Influence Of The Mathematical Activity Experience On The Understanding Of Function Concept

In this thesis, the author deals with the question "What is the experience of mathematical activities" based on his gathering of and reflection upon related literatures home and abroad, and designs the mathematical activity class. The author establishs the pre- and post-experiment questionnaires according to the four stages in understanding the concept of function, i. e. action, process, object and schemas. He chooses 44 students from a key high school in Shanghai as subjects in his research.This research explores the influence of mathematical activity experience on the understanding of concept from the perspective of the concept of function. This research mainly deals with the following questions:To what extent do senior high students in Grade One understand the concept of function before learning function in senior high schools? To what extent do they understand the concept of function after mathematical activities? Do mathematical activities influence students' understanding of the concept of function? What factors play a role in this kind of influence?The thesis comes to the conclusion as follows by empirical research:High-school students in Grade One in Shanghai are at the action stage on average before formal study of function. After taking part in mathematical activities, though their average understanding of function remains at the action stage, the number of students at the process and post-process stages is greatly increased and students at the pre-function level decreases to about half of before, the experience of mathematical activities accelerates students'understanding of the concept of function, but this kind of acceleration can be influenced by the extent of students' participation in mathematical activities and their basic understanding of function, and the influence is positive. The research result doesn't show a remarkable effect of gender on this kind of acceleration.This thesis consists of six parts:Part One introduces the background of posing the research question, the research significance, and states the research question.Part Two summaries researches on the experience of mathematical activities and the comprehension of the concept of function in China and foreign countries. Then it elaborates the meaning of the experience of mathematical activities and defines the stages in understanding the concept of function in this thesis.Part Three illustrates the research design and process, including the choice of subjects, the layout of experimental classes, and the design of testing questionnaires.Part Four elaborates the carrying out and analysis of mathematical activity classes, including the design, carrying out and achievements of mathematical activity classes.Part Five is about the implementation and analysis of questionnaires, which is the core of this thesis. It introduces the implementation of tests and the coding of questionnaires. More importantly, it answers main research questions by analyzing and discussing statistics from tests.Part Six draws the main research conclusions on the basis of the analysis of the testing results and the implementation of mathematical activity classes. It also gives thoughts and suggestions on how to carry out mathematical activity classes and to use the experience of mathematical activities in teaching the concept of function.