A Study On The Integration Of History And Pedagogy Of Mathematics

History and Pedagogy of Mathematics, abbreviated to HPM, has been a worldwide influential movement since 1970s. Many historian and teachers of mathematics are attracted to pay much attention to this field. Unfortunately, at present, although scholars in mainland China are interested very much in HPM, few people make serious research in this topic. A systematic study on HPM is significant not only to the investigation of method on integrating history and education of mathematics, but also to the understanding of the pattern of HPM. Therefore, the history, causes, and methods of integrating history and education of mathematics are introduced in details. Based on analyzing the materials in home and abroad, a relatively comprehensive study of HPM is made. The main results we have obtained in this paper are as follows:1) It traces the development of HPM systematically, and puts forward the conception of integrating history and education of mathematics. It investigates the necessity of HPM from the research purpose of history of science and mathematics as well as the educational function of history of mathematics. Further, it explores and analyses the reasonable theoretical bases of HPM are genetic approach and constructionism.2) It probes into all the levels of causes of HPM. First, from the nature of mathematics, mathematics results from the constant development of human activities. It is a dynamic science. Second, mathematics is one part of human culture, especially as it is multicultural, leads that history of mathematics is the carrier of culture of mathematics. Third, mathematics is closely related to other sciences, and it embodies concretely in other sciences. Therefore, the study of mathematics can illustrate the multiculturalism of mathematics and make students no longer regard mathematics as a cold and pure science.3) It makes a concrete study on the mathematics teaching functions of HPM, especially that of stimulating the development of students' thinking. Based on Piaget's genetic epistemology and Vygotsky's sociocultural theory, it makes a concrete study on how to overcome the students' cognitive difficulties and how to construct students' knowledge under specific society and culture. Furthermore, with concrete examples, it explains the function of HPM under the genetic approach and sociocultural construction from the development of mathematics conception and students' mathematics thinking styles.4) It probes into the methods of integrating history and education of mathematics. It introduces the use of mathematics historical materials, including how to choose the original and second hand reference materials, and how to use them into teaching properly. It also introduces how to use mathematics historical materials directly and indirectly in class and how to use them in class activities and advances the pattern and strategy of mathematics teaching under the conception of HPM. It summarizes four research methods of HPM: questionnaire, comparability study, transference, and teachers' teaching case.5) It gives a brief outline on the studies of HPM in America and some European countries, and summaries what have been done on this study at present China. By comparison, it concludes that the study on HPM in China is not enough, either in the organization work or in the research scope. A great deal of introductory work and experimental studies on HPM continue to be needed, and the study of HPM in teachers' colleges and teachers' continuing education still should be strengthened.6) It probes into the necessary conditions of integrating history and education of mathematics, including thinking ideology and resource technology. Also, it introduces in detail that integrating history and education of mathematics can include historical snippet, student research projects based on historical text, work sheet, historical package and experience of mathematics activity etc. The common procedure of HPM practical developments is given. At last, it introduces the main content and feature of history module project developed by America.