Analysing And Exploring Of Investigative Study Of Mathematics Based On History Of Mathematics

The Relation between History and Pedagogy of Mathematics (HPM) is the tendency of international mathematical education. It started from the 19th century. O.Terquem A.De Morgan and other mathematicians advocated the educational function of history of mathematics. American scholars had agreed on it in the 20th century. However, how to apply history of mathematics in mathematical education is still an important topic of researching.Applying history of mathematics to maths teaching and investigative study are two hotspots in the mathematics course innovation. But there are several problems: teaching of mathematics history hasn't affected the mathematical education of China essentially. Investigative study hasn't been really put into practice.Investigative study of mathematics based on history of mathematics in high school is a concrete and definite teaching model in the background above. History of mathematics is the content of investigative study. Investigative study is the teaching form of applying history of mathematics to math teaching.The characteristics of mathematics and mathematics study, the historical-genetic principle, constructivism provide the theory support for this research. And the significance of this research is the characteristics of investigative study of mathematics comparing with others: (1) Interesting. The interest of stories and characters inspire students' interest in investigating. Therefore the temporary interest of students would transform into the permanent interest in mathematics study. (2) Scientific. Investigative study of mathematics is closed to the process of mathematical discover. It follows the rules of the real research. (3) Valid. Investigative study of mathematics would be universally and can be effectively put into practice. This may have important significance in solving the problems in teaching of mathematics history and investigative study of mathematics.Further, the paper discusses the strategies of how to put it into practice. It analies and explores three aspects: how to organize teaching material, how to improve the teachers' knowledge of mathematics historyand how to design the process of teaching, among which organizing teaching material is of most important. In the paper several cases of organizing are provided.In the end, the experiment and the conclusion are introduced. The experiment result supports the view of the research in general and illustrates that the design and suggestion are feasible.