高二学生解析几何学习障碍及对策研究
发布时间：2018-10-17 13:38
【摘要】：解析几何是高中数学课程的重难点所在,高中生在解析几何课程的学习中存在诸多障碍。笔者采用调查问卷结合访谈的形式对某高级中学高二学生进行了调研,内容包括:学生学习解析几何课程的习惯、态度和心理状况;学生的计算能力;学生对解析几何课程中概念、公式及定理的掌握情况;对所包含的数学思想方法的运用情况。本文对某中学320名高二学生进行问卷和测试卷调查。问卷的统计数据显示有76.2%的学生表示对解析几何不感兴趣,有23%的学生认为解析几何的最大障碍是计算过程复杂繁琐,15%的学生认为公式太多记不住,14%的学生不会运用思想方法,测试卷中两个解析几何题的答题正确率分别为32%和8%。笔者仔细分析调查结果,查阅大量资料,认为学生在解析几何学习中存在以下几个问题:(1)学习目标不明确,对解析几何的学习情感淡漠;(2)学习功利化,看重分数,对解析几何的学习过分焦虑;(3)解析几何课程中融合了函数、向量、三角等知识,但学生对这些已学过的基础知识掌握较差,在知识迁移上存在障碍;(4)解析几何课程概念定义多且易混淆,学生对概念的学习停留在机械识记上,没有理解,导致在概念定义运用上存在障碍;(5)解析几何问题计算量大且涉及字母运算和算法技巧,但学生基本运算方法不熟练,运算能力偏弱,在运算操作上存在障碍;(6)学生对解析几何中涉及的思想方法理解不深刻,不全面,忽视使用的条件,按模式套路解题,在思想方法运用上存在障碍。针对以上障碍的表现,笔者从解析几何课程、学生和教师三方面分析了障碍产生的原因,结合调查和实践,提供了以下一些克服障碍的教育教学对策:(1)加强师生之间的沟通,克服情绪障碍;(2)注重知识之间的联系,克服迁移障碍;(3)重视知识生成的教学,克服理解障碍;(4)注重运算能力的培养,克服运算障碍;(5)加强思想方法的渗透,克服应用障碍。
[Abstract]:Analytic geometry is the most important and difficult part of mathematics course in senior high school, and there are many obstacles in the course of senior high school students. In the form of questionnaire and interview, the author investigated the students in a senior middle school, including the habit, attitude and psychology of studying analytic geometry course, the students' computing ability, and the students' ability to calculate. Students' mastery of concepts, formulas and theorems in analytical geometry courses, and the application of mathematical ideas and methods contained therein. In this paper, 320 senior two students in a middle school were investigated with questionnaires and test papers. Statistics from the questionnaire show that 76.2% of the students are not interested in analytic geometry, 23% think that the biggest obstacle to analytic geometry is the complexity of the calculation process, 15% think that the formula is too much to remember, and 14% do not use the method of thinking. The accuracy rates of the two analytic geometry questions in the test paper were 32% and 8%, respectively. The author carefully analyzed the results of the investigation and consulted a large number of data, and concluded that the following problems existed in the study of analytic geometry: (1) the learning goal was unclear, and the learning emotion of analytic geometry was indifferent; (2) the study was utilitarian, and scores were valued. (3) the course of Analytical Geometry integrates functions, vectors, triangles and so on, but students have a poor grasp of the basic knowledge they have learned. There are obstacles in knowledge transfer. (4) Analytical Geometry course has many definitions and is easy to be confused. As a result, there are obstacles in the application of the concept definition. (5) Analytical geometry problems involve a large amount of computation and involve alphabetical operations and algorithmic skills, but the students are not proficient in the basic operation methods and are weak in computing ability. There are obstacles in the operation of operation; (6) students do not have a profound understanding of the thinking methods involved in analytic geometry and ignore the conditions of using them. They solve problems according to the pattern routine and have obstacles in the application of thought methods. In view of the performance of the above obstacles, the author analyzes the causes of the obstacles from three aspects of Analytical Geometry course, students and teachers, and provides the following educational and teaching countermeasures to overcome the obstacles: (1) strengthening the communication between teachers and students; To overcome emotional obstacles; (2) to pay attention to the relationship between knowledge, overcome the obstacles of transfer; (3) to pay attention to the teaching of knowledge generation, to overcome the obstacles of understanding; (4) to pay attention to the training of operational ability, to overcome operational obstacles; (5) to strengthen the penetration of thought and methods and to overcome the obstacles of application.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
本文编号：2276831
[Abstract]:Analytic geometry is the most important and difficult part of mathematics course in senior high school, and there are many obstacles in the course of senior high school students. In the form of questionnaire and interview, the author investigated the students in a senior middle school, including the habit, attitude and psychology of studying analytic geometry course, the students' computing ability, and the students' ability to calculate. Students' mastery of concepts, formulas and theorems in analytical geometry courses, and the application of mathematical ideas and methods contained therein. In this paper, 320 senior two students in a middle school were investigated with questionnaires and test papers. Statistics from the questionnaire show that 76.2% of the students are not interested in analytic geometry, 23% think that the biggest obstacle to analytic geometry is the complexity of the calculation process, 15% think that the formula is too much to remember, and 14% do not use the method of thinking. The accuracy rates of the two analytic geometry questions in the test paper were 32% and 8%, respectively. The author carefully analyzed the results of the investigation and consulted a large number of data, and concluded that the following problems existed in the study of analytic geometry: (1) the learning goal was unclear, and the learning emotion of analytic geometry was indifferent; (2) the study was utilitarian, and scores were valued. (3) the course of Analytical Geometry integrates functions, vectors, triangles and so on, but students have a poor grasp of the basic knowledge they have learned. There are obstacles in knowledge transfer. (4) Analytical Geometry course has many definitions and is easy to be confused. As a result, there are obstacles in the application of the concept definition. (5) Analytical geometry problems involve a large amount of computation and involve alphabetical operations and algorithmic skills, but the students are not proficient in the basic operation methods and are weak in computing ability. There are obstacles in the operation of operation; (6) students do not have a profound understanding of the thinking methods involved in analytic geometry and ignore the conditions of using them. They solve problems according to the pattern routine and have obstacles in the application of thought methods. In view of the performance of the above obstacles, the author analyzes the causes of the obstacles from three aspects of Analytical Geometry course, students and teachers, and provides the following educational and teaching countermeasures to overcome the obstacles: (1) strengthening the communication between teachers and students; To overcome emotional obstacles; (2) to pay attention to the relationship between knowledge, overcome the obstacles of transfer; (3) to pay attention to the teaching of knowledge generation, to overcome the obstacles of understanding; (4) to pay attention to the training of operational ability, to overcome operational obstacles; (5) to strengthen the penetration of thought and methods and to overcome the obstacles of application.
【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6
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