高中生平面向量认知水平的调查研究

发布时间：2018-04-13 10:10

本文选题：高中生 + 平面向量　；参考：《西南大学》2015年硕士论文

【摘要】：向量是近代数学最基本的概念之一。它作为沟通代数、几何等内容的桥梁及其广泛的应用性受到数学课程改革的关注,不少发达国家在20世纪中期就已在中学数学中增加了向量内容。我国新一轮数学课程改革中也将向量作为高中数学的重要内容,《普通高中数学课程标准(实验)》在必修4中设置的平面向量内容,同“大纲”版相比有了较大调整。在此背景下,笔者研究学生平面向量的认知现状,以期能对向量内容的教材编写和教师的教学提供一定的改进依据。本研究采用文献分析法和问卷调查法对高中生平面向量的认知水平及学习中存在的问题进行研究。笔者以《普通高中数学课程标准(实验)》为依据,在收集文献、分析教材、请教一线教师等基础上编制测试卷。测试对象是重庆市的366名高中学生(高二184人,高三182人)。根据学生的作答情况做了以下工作：1.以SOLO理论为依据对学生回答进行分析统计,得到高中生平面向量的认知水平现状：(1)平面向量概念的认知水平：总体上47.3%的学生处于水平R-3,高二(46.2%)、高三(48.4%)；22.7%的学生达到水平E-4,高二(22.3%)、高三(23.1%)。不同学校学生平面向量概念的认知水平有一定差距,但差距不明显。(2)平面向量运算的认知水平几何运算认知水平：总体上52.7%的学生处于水平R-3,高二(51.1%)、高三(54.4%);19.7%的学生达到水平E-4,高二(18.5%)、高三(20.9%)。坐标运算认知水平较好：总体上58.5%的学生处于水平R-3,高二(57.1%)、高三(59.9%)；28.4%的学生达到水平E-4,高二(26.6%)、高三(30.2%)。代数运算认知水平较差：总体上46.7%的学生处于水平R-3,高二(45.1%)、高三(48.4%)：17.5%的学生达到水平E-4,高二(16.3%)、高三(18.7%)。在三种运算的E-4水平上,重点中学学生要明显好于普通中学学生。(3)平面向量应用认知水平较差：总体上42.6%的学生处于水平R-3,高二(39.2%)、高三(46.2%);仅12.6%学生,高二(11.4%)、高三(13.7%)达到E-4水平。在应用的R-3、E-4水平上,重点中学学生要明显好于普通中学学生。综上所述：学生平面向量运算的认知水平依次高于平面向量概念、平面向量应用的认知水平,其中平面向量应用的认知水平明显低于其他水平。平面向量的三种运算中坐标运算认知水平最高,随后依次为几何运算、代数运算。学生对于向量知识的掌握倾向于“重坐标,轻代数；重运算,轻应用”。高三年级平面向量应用的认知水平明显高于高二年级,在运算认知水平上略高于高二年级,而在平面向量概念的认知上,高三年级和高二年级相差不大。2.找出了学生在平面向量学习中出现的主要问题,分析原因并提出了相应的教学建议。
[Abstract]:Vector is one of the most basic concepts in modern mathematics.As a bridge of communication algebra, geometry and so on, it is concerned by the mathematics curriculum reform. Many developed countries have added vector content in middle school mathematics in the middle of the 20th century.In the new round of mathematics curriculum reform in our country, vector is also regarded as an important part of senior high school mathematics. The content of plane vector which is set up in compulsory course 4 in "ordinary Senior School Mathematics Curriculum Standard (experiment)" has been greatly adjusted compared with "outline" version.In this context, the author studies the cognitive status of students' plane vector, in order to provide some improvement basis for the compilation of vector content textbook and teachers' teaching.In this study, literature analysis and questionnaire were used to study the cognitive level and learning problems of plane vector in senior high school students.Based on the Mathematics Curriculum Standard (experiment) of General Senior Middle School, the author compiled the test paper on the basis of collecting literature, analyzing teaching materials and consulting front-line teachers.The subjects were 366 senior high school students in Chongqing (184 in Grade 2 and 182 in Grade 3).According to the student's answer, I did the following work: 1.Based on the SOLO theory, the students' answers are analyzed and counted.There is a certain gap in the cognitive level of the concept of plane vector among students in different schools.The cognitive level of coordinate operation is good: 58.5% of the students are at the level of R-3, 57.1% of the students are at the level of R-3, 59.9% of the students have reached the level of E-4, 26.6% of the students have reached the level of E-4, and 30.2% of the students are in grade three.On the whole, 46.7% of the students were at the level of R-3, 45.1% of the senior students were at the level of R-3, and 48.4% of the students had reached the level of E-4, 16.3% of the students and 18.7% of the students.At the level of R-3 E-4, key middle school students are obviously better than ordinary middle school students.To sum up: the cognitive level of the students' plane vector operation is higher than that of the plane vector concept in turn, and the cognitive level of the plane vector application is obviously lower than that of the other level.Among the three operations of plane vector, coordinate operation has the highest cognitive level, followed by geometric operation and algebraic operation.Students' knowledge of vectors tends to be "heavy coordinates, light algebra, heavy operation, less application."The cognitive level of plane vector application in grade 3 is obviously higher than that in grade two and slightly higher than that in grade two in operation, but in the concept of plane vector, the difference between grade 3 and grade 2 is not significant.This paper finds out the main problems of students in plane vector learning, analyzes the reasons and puts forward corresponding teaching suggestions.
【学位授予单位】：西南大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G633.6

【参考文献】