The Mathematical Theory And Practice Of Instructional Design Based On Problem Solving

“Problem solving” although has come up with more than 20 years, but today it is still the important gripper education reform in many countries. Experts, scholars from multi-angle research problem solving: as the center of the mathematics education, as the teaching goal, as a teaching mode, as a mechanism of psychological activity, as a way of training students’ innovative ability, etc., but it is unable to agree.In the spirit of the new curriculum reform, under the advocacy of quality-oriented education has been gradually attracting attention of all parties. To cultivate students ability to innovate, is one of the important goals, and solving mathematical problems is one of the ways to cultivate students’ innovative ability.The first chapter focuses on the research content and meaning of mathematical problems, research status, research methods and ideas. Special stress that based on mathematical problem solving, can be from two dimensions of history of mathematics and mathematical psychology research, the corresponding is carrier and psychological layer. This article from two dimensions can be incorporated into the teaching design, and compared with the traditional teaching design analysis, and then optimize the teaching design.In the second chapter, the key is mathematical problems, and analysis of the emergence and development of problem solving. For its research in the psychological level prepare to premise. The analysis of the psychological theories of problem solving, such as psychological culture and history of the development of the theory and cognitive information processing theory. And interpretation of mathematical problem solving model, and we analysis the influencing factors of problem solving, including external factors and internal factors. In the evaluation of mathematical problem solving mainly introduce the pyramid evaluation model.The third chapter, this paper discusses mainly the mathematics teaching design based on problem solving, including the design of teaching process and types.Through the teaching practice,the fourth chapter compares to the traditional teaching design and innovation teaching design.The fifth chapter is the conclusion and further research prospects.