Research On The Evaluation Of Junior High School Students' Academic Achievement In Theorems In Plane Geometry ——A Case Study Of The Learning Of The Vertical Path Theorem

The vertical diameter theorem is an important theorem of mathematical plane geometry in junior middle school.Literature survey shows that there has been little research on the evaluation of academic achievement.Therefore,it is important that we can develop evaluation tools to improve the evaluation system of academic achievement based on the existing research experience,and further provide suggestions for subsequent related research.Firstly,we developed an evaluation framework,according to the hierarchical structure of junior three students' cognitive level,and research results of international large-scale academic achievement evaluation projects,combined with the cognitive characteristics of vertical path theorem and its inference.The evaluation framework consists of three primary dimensions including understanding,connection and application,and a couple of secondary dimension for each primary one.Second,we set up test questions and associated scientific scoring standards based on the evaluation framework.Finally,124 students from a junior middle school in Y City were selected for evaluation to answer the following three research questions:(1)how do junior three students understand,connect and apply the vertical diameter theorem?(2)What are the learning obstacles and causes of junior three students' learning vertical diameter theorem?(3)How to improve the teaching strategy in view of the problems in the process of learning the vertical diameter theorem?Our analysis disclosed the following four conclusions:(1)by analyzing the overall situation of students' learning vertical diameter theorem and its inference,it was found that most students have arrived at a middle level,and only a few students performed very well,and a very few students failed to meet the passing standard.(2)In the dimension of understanding,students' expression was characterized by incomplete expression in written language and graphic language,lack of preciseness and conciseness in symbolic language,and other obstacles;from the viewpoint of derivation,there are some obstacles,such as confusion between theorem derivation and symbolic expression,unclear causality,unclear conditions and verification;from the viewpoint of mathematical thought and method,it is difficult for students to understand mathematical thought and method,nonstandard language description and not combined with the reality of life and learning.(3)In the connection dimension,students had the obstacles of how to construct concept mapping with required number of nodes and clear context expression.(4)In the application dimension,students had a high level of mathematical calculation and geometric proof in mathematical application,but the performance of ruler and gauge drawing was poor,which is mainly because students paied attention to the presentation of drawing results but ignored the language description of drawing steps,resulting in obstacles such as blank description and inaccurate description.The learning obstacles in practical application are mainly reflected in the fact that students and teachers ignored the transformation and interpretation of practical problems and paied great attention to the solution of problems.In view of the learning obstacles of students in the vertical diameter theorem and its inference,the main reasons caused these obstacles are as follows:(1)Affected by daily learning experience,students have formed a thought that the vertical diameter theorem only includes the part of bisecting strings,and are lack of symbolic consciousness,which results in poor expression of sign language.(2)Students are confused with the essential meaning of expression and derivation,and have weak logical reasoning ability,and ignore the practical value of mathematics textbooks.(3)The main causes of connection barriers lie in students' lack of knowledge reserve,unclear related concepts and lack of attention to the connection between knowledge.(4)Teachers do not pay sufficient attention to the teaching of ruler and gauge drawing.Students simply imitate mechanically and therefore cannot fully understand the principle of each step of ruler and gauge drawing.Based on the above learning disabilities and the associated causes,this thesis raise the following suggestions:(1)pay considerable attention to the theorem expression of three mathematical languages,to the derivation teaching of theorems,and to the teaching value of teaching materials;(2)show the consciousness of infiltrating mathematical ideas and methods;(3)demonstrate the teaching value of concept map;(4)pay attention to the application of rule drawing of theorems.