Students To Understand, Based On The Induction And Mathematical Induction

Nowadays, high quality education is popularized all over the country. It is a common view in educational circles that the goal of mathematics education is to cultivate students' mathematical abilities and lead them to master mathematical thoughts and methods.In order to give some available and reasonable advices to enhance teaching mathematical thoughts and methods, the author set out a series of investigations to inquire students' status quo on topics such as abilities about induction, abilities to get general rule, etc.The main body of this thesis comprises five parts.The first part includes the first three chapters. This part mainly introduces the background and the significance of the thesis. The thesis gets support from two psychological theories: behaviorism psychology and cognitive psychology. The merits of CAI cover these two theories' strongpoint.In the second part, the author explains some basic concepts confronted in the study, i.e. induction, mathematical induction etc.Two parts followed are core parts of the thesis. Part three introduces the sample, tools and ideas for designing questionnaires, partly discussed the main idea for the computer program. The discussion about the pre-test result tells us to which samples can this papers' conclusion applied.The fourth part illustrates students' answer to the questionnaires. The main methods describe in this part are of quality, accompanied with SOLO (Structure of Learned Outcomes or Responses ) Taxonomy as a tool for classification.In the last part, author sums up the whole thesis and draws two main conclusions from the study. First, in a Computerized Environment, pupils grasp the inner rulers during the factorization of polynomial. Second, students have a deep understanding of the induction base of mathematical induction method, although other researchers had claimed student had a "bad" understanding about mathematical induction method. Concurrently, the author observes that students are not good at view the problems as whole, so sometime the answers to questions looks like blindly.As a conclusion, the author provides some available and rationalization proposals for teachers to cultivate students' mathematical ideas and methods ability.