Research On The Evaluation Of Vector Concept Understanding

Mathematical understanding has always been a hot issue in the field of mathematical education.Based on the theory of "instrumental understanding and relational understanding" by Skemp,this study aims to explore how students understand mathematical concepts?This paper focuses on the evaluation of high school students' understanding of vector concept.The concept of vector plays an important role in senior high school mathematics.Its concept is abstract and has considerable research value.Based on the research of lesh and Lando,this study enriches the mathematical concept understanding evaluation model(as shown in the table below)by combining the research ideas of seven basic mathematical abilities and many other scholars in the 2018 International Assessment Project(PISA).The first level dimensions are perception,representation,connection and application;the second level dimensions are discrimination and interpretation,example and statement definition,analytical form,symbol and figure,concept map,mathematical application and practical application.Taking senior three students of two ordinary middle schools in Y City as the research object,two classes are selected respectively,and test papers are distributed to all students.The test papers are compiled according to the above concept understanding evaluation model.Through data analysis and comparison,it is found that senior high school students have the following problems in understanding vector concept:1.In the concept perception dimension,most students can initially judge which concepts in life and physics are vectors,can give good examples of vectors,and can correctly understand the concept of vectors,but there are still a few students lack of flexibility in the application of related concepts,the examples lack of innovation.2.Most of the students can correctly represent symbols and images according to the requirements of the topic,but they need to be strengthened.3.Students show obvious limitations in concept application,showing a certain"instrumental understanding".4.The students present the fixed thinking situation in concept connection,and the concept map is not completeThrough the analysis of the test results,it is found that students' understanding of the concept of vector and the causes are as follows1.Affected by the students' cognitive level,some students can't understand the algebraic meaning of vectors well2.some students can not realize the convenience of solving the problem of the geometric meaning of vector clearly because of the thinking set3.Due to the instrumental understanding of the concept of vector,students lack flexibility in the application of the whole meaning of vector.Finally,in view of the above conclusions,from several stages of concept teaching,this paper puts forward some humble opinions:concept introduction focuses on the process,concept introduction is not abrupt,concept deepening builds the system,and concept application is variable.