A Study On Luis Radford 's Mathematical Education Thought

We must regard history not only as a way from which to learn of the nature of mathematics knowledge but as a mean of transforming the teaching of the subject itself. The peculiarity of the pedagogical use of history is that it interweaves our knowledge with the conception of the past conceptual developments in the current school activities, and the goal is to promote the students’ development of mathematical thinking. History and culture, environment are inextricably linked. His research interests cover both theoretical and practical aspects of mathematics thinking, teaching, and learning. The central of his research is a sustained involvement in classroom work with teachers and students. This paper mainly studies his HPM concept and his HPM theory application in class practice. This paper is divided into two parts.The first part of the paper summarizes Radford’s main idea. The first is about the recapitulation, Radford submits Piaget and Vygotsky’s thinking. During long term study for class, he thinks development of students’ thinking is not just simply similar in history of the content, it should be similar in mechanisms. The second is that because scientists acknowledge the recapitulation law to produce the genetic method. And design a lesson. Third, Radford explains the essence of Epistemological Obstacles is the culture. The fourth introduces his class research method based on Mikhail Bakhtin’s dialogism.The second part of article is that author gets some inspiration from Radford, there are many things to learn. When teachers start the HPM research, first they need to know more original literature, and meanwhile notice the analysis to students(students’ speaking words, gesture,chart and so on), create suitable environment. Teacher need to have systematic documents. So they can really apply mathematics history to teaching, have better usage of all kinds of performance and thoughts showed by students in study, and know better about students.