Investigation On The Understanding Of Sine Theorem

Mathematical comprehension is the essential understanding of mathematical knowledge(concepts,laws).Mathematics teaching with "mathematical comprehension" as the value orientation can promote the development of students' core qualities of mathematics.In the implementation proposals of the "Standard for Mathematics Curriculum for Full-time General senior high School(2017 Edition)",the teaching requirements of "understanding concepts,grasping essence,and clarifying arithmetic" are proposed in the implementation recommendations.As one of the important theorems that reveal the relationship between the side and angles of triangles,the sine theorem is rich in connotation,the geometric derivation methods are brilliant,and the solution of triangles is convenient,flexible,and interesting to promote.This article uses the "sine theorem" as a carrier,through quantitative and qualitative analysis to study the status quo of the understanding of the mathematics theorem for senior two students in a middle school in Yangzhou.In this study,the "memory level,explanatory level and exploratory level" proposed by Xu Yanhui was used as the theoretical framework,and the "test paper for understanding the sine theorem" was carefully designed,and a test survey was conducted on 227 senior two students in a middle school in Yangzhou.Use Excel software and Spss statistical software for statistical analysis to obtain the current level of understanding of the sine theorem of senior students.Based on in-depth interviews and situation analysis of the sine theorem by senior students,several suggestions for optimizing mathematical teaching and deep understanding of mathematical theorems are put forward.Regarding the current situation of the understanding of the sine theorem of the senior two students,the test results were analyzed using independent-sample T test and Spearman's correlation coefficient for ranked date,and the following conclusions were drawn:(1)The tested students' understanding of the sine theorem basically reached the level of memory,42.7%of the students have reached the level of explanatory understanding,and 8.4%of the students have reached the level of exploratory understanding.(2)There are gender differences in the tested students' understanding of the sine theorem,and the differences are obvious.The average understanding achieved by boys is higher than that of girls(3)There is a difference in the understanding of the sine theorem between science students and liberal arts students,and the difference is extremely significant.The average level of understanding achieved by science students is higher than that of liberal arts students.The level of understanding achieved by science students is relatively scattered.The level of understanding achieved by liberal arts students is relatively concentrated,and they are basically focused on interpretive understanding.(4)The students 'understanding of the sine theorem is affected by the students' existing knowledge base and experience,that is,the students 'understanding level of the sine theorem is related to the students' existing cognitive level.Based on the above four conclusions,the author puts forward four suggestions from the aspects of teaching and mathematical understanding to promote students' understanding of mathematical theorems:emphasis on logical reasoning and strengthen the teaching of theorem proof;carry out mathematical modeling and deepen the guidance of theorem application;learn to think and explore the key theorems;clarify the knowledge structure and correlate related content.