The Development Of Pre-Service Teachers' Conception Of Mathematics-From The Perspective Of History Of Mathematics

In recent decades,the research focus of mathematics teaching has changed a lot.Traditional study focus is about students' and teachers' behaviors,and now has been shifted to thier knowledge and conceptions of mathematics.Many studies have shown that,conception of mathematics that individual holds has an effect on his/her mathematics teaching or learning.The main objective of this study is to figure out the meaning of pre-service teachers' conceptions of mathematics,and search after a corresponding path to develop thier conception of mathematics.In this study,pre-service teachers mean master students majoring in mathematics education.Theoretical research and empirical research are combined in this study.In the theoretical research section,the concept of "pre-service teachers' mathematical world" is put forward and the meaning of pre-service teachers' conceptions of mathematics is iedentified,based which the study provides a framework for exploring conceptions of mathematics of pre-service teachers.And in the empirical research section,this study has detected an approach to developing pre-service teachers' conceptions of mathematics by the way of design-based research with the course history of mathematics according to the previous framework.In this study,the goal of the design-based research is to enrich the pre-service teachers' mathematical world and to develope their conceptions of mathematics,and the design objects are overall position of the course history of mathematics,the course rationales and the contents.The design-based research has two cycles,each of which includes the following four stages:the preparation stage,the design stage,the implementation stage,and the evaluation stage.And finally this study has put forward an approach to developing pre-service teachers' conceptions of mathematics and the corresponding mechanism.The main conclusions of the study are as following:(1)The course history of mathematics can enrich the preservice teachers'mathematical world and promote the development of mathematics teachers'conceptions of mathematics,if this course provides with reflection and discussion about the objective and subjective knowledge from elementary mathematics to university mathematics combining with the richness of history of mathematics and the profoundity of mathematicians.(2)The internal mechanism of how the course history of mathematics promotes the development of mathematics teachers' conceptions of mathematics is:on the basis of riching the pre-service teachers' subjective and objective knowledge about mathematics,the course enhances their understanding of mathematics,and so have promoted the development of pre-service teachers' conceptions of mathematics.The major contributions of the study are as following:(1)The author puts forward the constuction of "pre-service teachers'mathematical world",the meaning of pre-service teachers' conceptions of mathematics and a framework for exploring conceptions of mathematics of pre-service teachers.(2)The author puts forward an approach to developing pre-service teachers'conceptions of mathematics by using mathematics history,including overall position of the course history of mathematics,the course rationales and the contents.(3)The author puts forward the mechanism of how the course history of mathematics promotes the development of pre-service teachers' conceptions of mathematics.