Research On Experiential Learning Of Mathematical Problem Solving In Senior High School

Mathematical problem solving is an important part of mathematical studies. People, be they students or researchers, have to make progresses through problem solving. The main research results on mathematical problem solving are on the cognitive construction modes, the problem solving strategies, the solution errors et al. The researches of G. Polya on the project of problem solving have been widely recognized by the mathematical society. His theory is based on the four steps of understanding the problem, devising a plan, carrying out the plan, and looking back which can be found in his book How to Solve It. But in the real case, the fourth step of looking back or checking is often overlooked. Nowadays, the teachings of problem solving are still starving in the circle of simple imitation and repeating in most of our country’s middle schools, and are especially lack in the aspects of rethinking, checking, and summarizing. In recent years, many researches are carried out on the projects of metacognition, conscious analysis, self-monitoring in problem solving and have got valuable results for practical teachings. Some researchers view problem solving experience as a special mathematical activity experience, and in combination with experiential learning theory they have got valuable results for problem solving. This thesis will focus on the problem solving issue in respect of the experiential learning theory.This thesis composes six parts.The first part is the introduction which will declare the background, the research projects, and the meaning of this study. In the meantime, an research overview on this issue will be presented in this part.The second part is the theoretical construction of the experiential learning theory. In this part, the explanation and analysis of the concept of problem solving by Prof. Zengru Luo are summarized, in order to give the basics of problem solving. The cognitive model of Prof. Ping Yu which includes understanding the problem, choosing the operator, using the operator, and results evaluation is used. These components correspond to the problem characterization, mode identification, problem spread, and monitoring in problem solving mode. I also choose Kolb’s experiential learning theory as the theoretical support for experiential learning in problem solving. The spiral mode of experiential learning in problem solving is constructed in order to give the principals. The contents of experiential Learning in problem solving are illustrated in a specific case. In the meantime, the modes of experiential learning in problem solving are classified and analyzed in which the positive influences of experiential learning for innovation and quizzing ability are stressed.The third part is the analysis of the circumstances in experiential learning from the aspects of mathematical problem and the personality of the leaner. From the former aspect, the expression of the conditions, the language as well as the hardness of the problem are relative to the effect of experiential learning. In the analysis of the leaner’s personality, I will present the relationship of the basic knowledge, the skills, the thinking methods and ability, the mathematical intuition, the mathematical metacognition ability, and the emotion to the experiential learning, respectively.The fourth part is positive research on this issue. Taking the students of the liberal arts class of Chang’an No.2middle school as research object, I performed the experiments on "Investigation of Experiential Learning on Problem Solving" and "Test of Experiential Learning on Problem Solving and Ability of Quizzing". Based on the data, I get the conclusion that experiential learning has positive effect for problem solving. The metacognition strategies and conscious analysis of experiential learning are clearly helpful to problem solving. In addition, the metacognition strategies as well as open questions is extremely useful for students to quiz.The fifth part is the specific cases of the problem solving procedure based on experiential learning. The detailed processes of experiential Learning are demonstrated in the cases of problem summary, multiple solutions for a problem, and the problem’s spread. These can promote the problem solving ability of students as well as the coaching ability of teachers.The sixth part is the research conclusion. In this part, the main results and deficiencies of the research are summarized. The unsolved questions as well as their spreads are proposed which are outlooks for further studies.