A Case Study Of Involving Mathematical Culture To The Trigonometric Expression Of Complex Numbers

Mathematical culture is one of the hotspots in the research of mathematics education and plays a very important role in teaching.Many researchers have integrated mathematics culture into teaching of complex numbers.However,the most of cases that integrates mathematical culture into teaching of complex numbers are only related to the history of mathematics,and cases designed are only related to the concept and operations of complex numbers.In view of this situation,this paper chooses the history of mathematics,the beauty of mathematics and the related contents of mathematical thoughts in mathematical culture,and tries to integrate these mathematical cultural contents into the triangular representation curriculum of complex numbers.By consulting the literature,this study designs a case of integrating mathematical culture into the triangular representation curriculum of complex numbers,and chooses 18 students from the International Department of Senior Two of a Key School of Ning Bo to implement the designed case.Through classroom observation,pretest and posttest questionnaires and interviews to teachers,I hope to answer the following two questions:1.Through the implementation of the case,will students change their attitudes towards mathematical culture and what kind of changes will they make?2.Through the implementation of the case,we investigate which mathematical culture fragments and ways of integration in the case are more interesting to students.According to the data analysis,the following two conclusions are:1.Generally speaking,the integration of mathematical culture into the case indicates that students' attitudes have undergone a positive change.Students are more interested in mathematical culture and more agree that mathematical culture is helpful for learning.2.Students are more interested in the basic theorem of algebra in the curriculum of trigonometric representation of complex numbers,which is a historical material of mathematics.They think that the symmetrical beauty of graphics is the most aesthetic form,and they most agree that the idea of combining numbers and shapes is helpful for learning.