Study On Teaching And Learning Of Congruent Triangles Based On History Of Mathematics

Geometry is an important field in mathematics teaching.Congruent form is one of the basic theorems of geometry,the important knowledge of plane geometry,the hot and difficult point of junior high school mathematics teaching,and the foundation of learning approximation and solid geometry.Through extensive investigation,it is shown that the difficulty coefficient of congruent triangle is reflected in two aspects :first,the geometric proof,the transformation of written language into mathematical language;The second is the application of congruent triangles.This study is based on the HPM(History and Pedagogy of Mathematics)angle of view.We design instructional designs,refer to Chinese and western of congruent triangles content,analysis of the historical materials,history of similarity,the analysis of students' learning cognitive impairment,and the theoretical framework of HPM instructional design.We conduct teaching practice under the guidance of the tri-pyramid model of teaching practice in the HPM domain.In this study,four eighth grade classes were selected as the research in a middle school in Hefei,two of which were taken as experimental classes and the other two as control classes.The research questions are:1.Whether the teaching of HPM with congruent triangles can help students overcome the original cognitive barriers.2.Whether the teaching of HPM with congruent triangle has a positive influence on students' emotional values.3.What is the influence of HPM integration into congruent triangle teaching on teachers' teaching of congruent triangle knowledge.Into congruent triangles to the history of mathematics in the teaching design,test,congruent triangles knowledge teaching student feedback questionnaire,student and teacher interviews as a research tool,we conducted quantitative and qualitative analysis on the data.We investigate the effects of integrating the teaching of congruent triangles into the history of mathematics on students' learning of congruent triangle judgment on teachers' teaching of congruent triangle knowledge.Conclusion of this study:1.Students emotional attitude is positive about the history of mathematics into teaching.In the process of problem solving,students have significantly improved their ability to solve practical application problems and measurement problems of congruent triangles,which helps students overcome the obstacles of description and drawing process,mathematical language and symbolic language conversion,and understand the nature of congruent triangle application.2.After teachers participate in HPM teaching practice,their educational beliefs change slightly,and their knowledge and access to the history of mathematics are also improved.