History Of Mathematics And Mathematics Education Integration

The Integration between Pedagogy and the History of Mathematics is an important project on Mathematical Instruction. The integration has deeply historical root. Since 19th, it develops rapidly because of the advocation of mathematicians, mathematical instructors and historians. Until 1970's, the foundation of HPM is of itself. The foundation and development of HPM make the integration between pedagogy and the history of mathematics observed by the International, and cause a series of important result. The historical-genetic principle is the historical root of this integration, that the students recognition of these concepts resembles that of mathematicians in the history. The psychology base of the integration is that the history of mathematics can participate mathematical activity through affecting both cognitive and non-cognitive factor.The integration between the history of mathematics and curriculum has been an important field of HPM. Embodying mathematical culture value is taken as an basic notion of the new curriculum criterion, and the anthology of history of mathematics is made as a special issue. During introduce modern mathematical notions, thoughts, methods, the curriculum reform of that middle school should also pay attention to the link with history. Firstly, the new curriculum should embody the important effect of ancient notions, thoughts, methods; secondly, the new curriculum embody mathematical culture valve through the history. That the history comes into curriculum should do not simply plant, must think the meaning way suitation of the integration. Futhermore, the use of history material must appropriate, do not affect the basic teaching.The famous problem of the history of mathematics is also an important issue. Mathematical famous problem has different sorts according to different standard. The education value of the problem includes: inspire study interest; afford humanism background; promote students' thought ability. Finally, the research afford problem solving on the basis of HPM, analyse the basis, tragedy and a case of gou-gu theorem, and this will help modern problem solving.