Design Research On Teaching Of Gou Gu Theorem Which Based On HPM

Currently,HPM has become a main research category of mathematics education,and HPM related design has also been a hot topic for history and pedagogy of mathematics(HPM)research.Many cases have been developed successfully.This research mainly discussed the instructional design of Gou gu theorem from the perceptive of HPM,and the Gou gu theorem is selected as a carrier,Furthermore,design and research methods of HPM field are combined to develop instructional design from the perspective of integrating mathematics history into pedagogy of mathematics.To understand the position of mathematics history in Gou gu theorem learning,questionnaire and interview survey are implement to teachers and students respectively during the study process.On the basis of practical research,following informat ion is acquired through data sorting out and analys is,Teachers and students in junior high schools lack the knowledge of mathematics history relat ively.Though teachers on the front and students agree the teaching method of integrating mathematics history in teaching,it is rarely applied in actual course teaching.The reasons may have two.On one aspect,it is restricted by exam-oriented education.More teachers are willing to input more time on practices,i.e.“focusing on applicat ion and lightening explorat ion”.On the other aspect,competency level of teachers and unbalanced distribution of educational resources are not conducive for teachers to develop HPM teaching cases,and the students are in a confliction between the fun of knowledge explorat ion and pressure of exam results.Aim ing at the dilemma of introducing mathematics history in course teaching of mathematics,this study takes researches on instructional design of Gou gu theorem on the basis of status surveys.Firstly,instructional design of Gou gu theorem shall comply with students' cognitive characteristics.Secondly,instructional concept and scheme of integrating mathemat ics history and Gou gu theorem are proposed from the theoretical proof of instructional design of the Gou gu theorem,principles of instructional design of the Gou gu theorem,and the strategies and methods of instructional design of the Gou gu theorem.The study discovers that HPM still needs attentions from all aspects.It shall strengthen mathematics knowledge of teachers on the front,deepen HPM teaching cases development,and change the way of educational evaluat ion,so as to introduce mathematics history contents in mathematics teaching course as soon as possible and play its educational value effectively.