An Empirical Study On The Understanding Of Triangle Related Theorems By Junior Middle School Students

"Mathematical understanding",after "problem solving",has become a hot topic in modern mathematics education.Mathematical theorems are the basic content of middle school mathematics textbooks and the skeleton of mathematical knowledge,throughout the whole learning process,the understanding of mathematical theorems directly affects the individual's understanding and application of mathematical knowledge.Triangle is the most basic content of geometry,which is very important to the development of students' geometry learning and mathematical reasoning ability.In order to deeply understand junior high school students' understanding of geometric theorems,this paper divides their understanding into three levels: instrumental understanding,relational understanding and innovative understanding.Taking some junior high school students in hefei as samples,this paper studies junior high school students' understanding of triangula-related theorems.According to the investigation principle of "seeking truth from facts" and the available investigation conditions,the methods adopted include literature research,test question investigation,questionnaire investigation and interview.Based on the analysis of literature,this paper provides the theoretical basis for the paper.The survey method of test questions is to test the junior middle school students in different grades and collect the real data of junior middle school students' understanding of the theorem according to the teaching requirements of the second part of the third learning section of the mathematics curriculum standard of compulsory education(2011 Edition),"figure and geometry" And interview method is mainly from the perspective of teachers,in-depth exploration of the actual teaching situation of teachers,in order to understand the situation of students' understanding of the theorem to master more information.Through the analysis of spss25.0 statistical tools,the preliminary conclusions are as follows: 1.The overall quality of instrumental understanding of junior high school students in Hefei is high,and there is no significant difference in different grades.At the same time,although some students understand the theorem,they can't use accurate words and symbolic language to explain it;2.Some aspects of relational understanding are insufficient,and structural understanding has certain deviation Third,through the design of two topics that are conducive to the examination of innovative understanding,it is found that in relatively unfamiliar situations,some senior students show higher knowledgetransfer ability,but for deductive reasoning,the derivation form is relatively stable,The level of innovative understanding needs to be improved.Through the questionnaire survey and interview with teachers in front line,we can get the following conclusions: most junior middle school mathematics teachers think that it is important to understand triangle related theorem,which can help students learn geometry knowledge and realize knowledge transfer;but some teachers do not realize the importance of understanding.In view of the above conclusions,it can be seen that the current junior high school students' understanding of the theorem needs to be improved.In order to promote junior high school students' understanding of geometry theorem,the following suggestions are proposed: first,stimulate interest and let them like geometry learning from their heart;second,consolidate the foundation and ensure that everyone can pass the instrumental understanding;third,put relational understanding into practice in theorem proving and gradient practice;Fourth,build knowledge network and cultivate students' innovative understanding awareness;fifth,create democratic atmosphere and let them learn Never be afraid of mistakes.