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

In mathematical teaching, geometry is an active field, which provides us withan interesting and challenging course from primary school to university. Similar shapes arecore knowledge of plane geometry, which is not only a turning point of identical to similartransformation from high school students, but also the most popular and difficult parts inexamination of the middle school. HPM can promote student learning and MKT of teacher,by dating back to the history of similar triangles, the author finds out some impacts that thehistory of mathematics bring about learning of students about concept、theorem andapplication of similar triangles and the teachers’ knowledge of similar triangles for teaching.The research object was two classes of the eighth grade, a ninth grade students and a teacher,one of the eighth grade classes regarded as an experimental class, and the remaining deemedto be the control classes. The research means included the instructional design of similartriangles to integrate the history of mathematics, and the test paper of similar concept, as wellas the students feedback questionnaire of in-and-out complementary principle integrating toteaching of similar triangles, which investigated the impact on students of the history ofmathematics integrating to similar triangles; Teacher about knowledge of similar triangles forteaching was investigated through the form of record and interviews.The following conclusions can be found in the study:1. the influence on learning of students about concept、theorem and application of similartriangles:(1) The intuitive judgment and proportional calculations the concept of similar concepts hadno distinct effect, but in-depth understanding of students had a significant role. It helpedstudents in promoting a clear understanding of "similar" and essence of structure of the "sameshape”.(2) In judging theorem and application of similar triangles. In-out complementary principle can inspire curiosity and motivation of students to solve problem about prepare theorem andsimilar proportion, and can take the initiative to study and think about these issues. In short,students existed significant differences on emotion and behavior, in cognitive aspect affectedonly for superior students, but the majority of students had no significant effect.2the influence on teachers’ knowledge of similar triangles for the teaching:(1) From the content knowledge perspective. Through understanding relevant historicalmaterials of similar triangles, the teachers "unpacked" consciously textbook from condensedand static similar triangles knowledge to processing and dynamic knowledge, which increasedknowledge of ’decompressed’ function.(2) From the teaching perspective. To help teachers understand arrangement and presentationin the textbook; Teachers can promote to understand students’ problems, as well as tounderstand students’ mistakes; To enrich teachers’ experience on similar triangles, such as theintroduction of historical origins of similar concept, or direct or indirect references to theancient similar problem, or the use of in-and-out complementary principle for similarproblems.