Problem-Solving On Mathematics History And Researching On Teaching Strategy In The HPM

Teaching thought of Problem-Solving that began in America in 1980s was received universal recognition of mathematics education domain in the world. Moreover the deep research was launched in the domain of mathematic education philosophy, mathematics learning psychology as well as mathematics methodology. Its educational idea was introduced into mathematics curriculum in many countries. Speaking of mathematic education, "Problem-Solving" is to implement the thought of applying mathematics to solve the questions in teaching creatively that study will be an active procedure of thought, or the teaching of "Problem-Solving" is a discovery process, inquisition process and innovation process. From the history of mathematics angle, the pross of problems and "Problem-Solving" is accompanied by mathematics discovery, invention and creation.Therefore, to modern "Problem-Solving", historical "Problem-Solving" is drainless power and fountainhead. The aim of this thesis is to discuss uniting the history of mathematics and mathematics education, it is instructed by epistemology theory, through thorough inspecting the historical "problem" and "problem-solving"s origin and finding classical cases about "Problem-Solving" in the process of discoverying mathematics history , inquirying about mathematics invention and the creation trail, Thus teaching strategy about uniting the historical "Problem-Solving" and modern "Problem-Solving" with the help of modern science thought, psychology and correlation theories. Therefore, this article has been mainly done the following work:1. First, the epistemology as starting point, through presenting mathematics advancement in certain classical mathematic problem and significant mathematical theory , the production and discovery to mathematics of historical problem is inspected and analysised, the influential role of mathematics problem which forming mathematics concept and impetus mathematical theory development is exposited. Simultaneously historical "problem-solving" regarded as the mathematics education powerful promotion is discussed by the historical development fact in our country history mathematics and mathematics education depending on each other mutually, and advancing together hand in hand . 2. Searching the realistic case of "Problem-Solving" and the process of mathematical theory solution in history, realistic mathematics discovery is reappeared and the clue and the method of mathematics discovery is demonstrated, then the thought factor and the question discovery way are analyzed from the actual teaching of "Problem-Solving" which lay the methodology foundation for realizing the union of the historical "Problem-Solving" and modern "Problem-Solving".3. Using scientific thought theory, the characteristic of mathematics creative thought is pointed out through discussing the classification of mathematics thought. Then uniting the process of the historical "Problem-Solving "and the mathematician utilizing the creative thought, carriying on the case analysis of mathematics discovery, mathematics creative thought is reappeared in the pross of discoverying mathematic conclusion, solution, and advancing mathematics progress. Thus the simulation of solution and situation are supplied to raise the students' innovative idea in the modern mathematics teaching.4. To begin with the importance of scientific method, tracking down the source of the classical mathematical method, the production of mathematics thinking method is carried on a reproducibility analysis with the case form in the process of the historical "Problem-Solving", understanding the essence of methodology from the orginal condition in learning mathematics ,and clearing the clue which mathematics thinking method forms, thus the way of advancing mathematics research work and reforming mathematic teaching are opened.5. The article using the migration principle of modern psychology, the similar principle of thought science and so on correlation theories, and uniting humanities education idea that modern mathematics education emphasized, synthesisly analysed mathematics creative method which mathematician facing the primitive question during the historical "Problem-Solving". The teaching strategy of problem-solving is proposed in the HPM according to students' cognition rule, mathematics learning characteristic and the fact of modern mathematics teaching.In brief, this article has studied the teaching significance and the function of problem-solving with the historical viewpoint. The united way of mathematics history and mathematics education has given in view of the historical "Problem-Solving" seepaging to modern mathematics teaching.