Action Research Of Pythagorean Theorem In Junior High School Mathematics Based On HPM Perspective

The Pythagorean theorem,as the first principle of the ages,has always had an unshakable position in the history of mathematics.The discovery and proof of the theorem contain rich mathematical thoughts and methods throughout the whole junior middle school mathematics learning.The best teaching mode of the Pythagorean theorem is to integrate with the history of mathematics.Therefore,this paper adopts the methods of questionnaire survey and action research to carry out the research on the teaching practice of Pythagorean theorem in junior high school from the perspective of HPM,aiming to solve the teaching difficulties in the mathematics thought and method contained in the process of students’ rediscovery and understanding of the Pythagorean theorem,and to explore the educational value of integrating the history of mathematics into mathematics teaching in the reconstruction of students’ knowledge understanding and emotional attitude.Firstly,based on the history of mathematics,the present situation of the six textbooks of the human education edition is investigated.This paper discusses the principles of selecting mathematical historical materials and the methods of introducing mathematical historical materials,and selects mathematical theorems,classic titles,mathematicians and works related to the history of mathematics in textbooks.This paper mainly conducted two rounds of action research in the mode of "mathematics + history" on the Pythagorean theorem.The first round of action was to explore the Pythagorean theorem.Before the action,the current knowledge level of eighth grade students in junior middle school was investigated and the teaching design was modified according to the students’ mastery of knowledge.Students then experience reasonable reasoning such as observation and analogy and naturally experience the "rediscovery" of the Pythagorean theorem.The second round of action is to prove the Pythagorean theorem,mainly comparing four proofs,namely the geometric transformation method of Zhao Shuang’s string graph,Pythagorean proof,the deductive method of Euclid’s Elements of Geometry,and the algebraic method of Gaffi’s proof,to experience the mathematical ideas and methods in them,such as the combination of number and form,transformation,equal product transformation,area method,etc.The two rounds of action research are based on the cyclic process of action research: action plan,HPM teaching design case,HPM homework design,classroom observation,and after-class teaching reflection.Through the analysis of student questionnaire,homework feedback and teacher interview data,the following conclusions are drawn :1.The "rediscovery" of Pythagorean theorem from the perspective of HPM is conducive to the reconstruction of students’ knowledge understanding.2.Most students agree that the integration of mathematics history into mathematics teaching has a positive effect on emotional attitude.In terms of emotional attitude,the main factors are the fun that can stimulate mathematics learning,and the stories of mathematicians are inspiring.3.In the aspect of mathematics learning,the integration of mathematics history into teaching helps students to master mathematics thoughts and methods.Suggestions for teachers: 1.Improve teachers’ professional knowledge of mathematics history.2.Innovating the presentation of mathematics history into teaching;3.Develop HPM teaching cases suitable for the integration of mathematics history into teaching as far as possible.