A Study On The Design Of Teaching Concepts In High School Mathematics From HPM Perspective

Since the education reform has been carried out,mathematical culture has received increasing attention day by day,and the history of mathematics,as an important part of mathematical culture,is an important carrier to realize the cultivation of people in the subject.mathematics education from the perspective of HPM also fits in with the current concept of quality education for comprehensive development.With the implementation of the General High School Mathematics Curriculum Standards(2017 Edition),higher requirements have been put forward for teaching mathematics at the high school level to enhance the understanding and mastery of basic concepts.Teachers who want to integrate the history of mathematics into high secondary mathematics concept teaching to achieve the purpose of providing students with a deeper understanding of mathematical concepts,it is first necessary to have a scientific and standardized instructional design as a guarantee.In this paper,based on the literature of HPM research and mathematical concept teaching research,we conduct a study on the design of mathematical concept teaching from the perspective of HPM in conjunction with the problem-driven teaching model.Firstly,the literature research method is used to summarize the relevant literature on HPM research and mathematical concept research at home and abroad,to discuss theoretical discussions and educational values,and to define the relevant concepts.Second,in order to understand the application of the history of mathematics to the teaching of mathematical concepts in high school,this paper selects the concept of "logarithm",which is often neglected in teaching but has an important position in history,as an example,and uses questionnaires and teacher interviews to investigate and analyze the current situation of teaching mathematical concepts from the perspective of HPM and In this study,students’ attitudes toward the integration of the history of mathematics into their teaching were investigated through questionnaires and teacher interviews,and the current problems in teaching were summarized and analyzed in depth.Again,based on the curriculum standards as well as the content of the textbook,the author constructs a design process for teaching mathematical concepts from the HPM perspective based on the principles of science,applicability,fun and exploration,and the five ways of integrating the history of mathematics into teaching,combined with the problem-driven teaching model,which are:(1)unpacking historical materials and analyzing the elements;(2)screening historical materials and setting goals;(3)integrating historical materials and creating situations;(4)reconstructing history and constructing concepts;(5)understanding the essence and applying learning.Finally,based on the conceptual teaching design process of high school mathematics from the perspective of HPM constructed by the research,a case study of teaching design is given for "logarithm" and "logarithmic function".Based on the research and findings,three pedagogical suggestions were made:(1)focusing on the effectiveness of history integration and practicing a new concept of mathematics teaching;(2)to carry out targeted training activities to improve teachers’ mathematical history literacy;(3)to promote cooperation between HPM researchers and teachers to develop implementable HPM cases.