数学美在中学代数教学中的应用

发布时间：2018-04-25 23:00

本文选题：数学美 + 代数　；参考：《广西民族大学》2017年硕士论文

【摘要】：由于我国的社会主义国情,自新中国成立以后高考成为了我国重要的选拔人才的制度。但随着时间的推移,高考所带来的弊端也日益呈现。学校和家长一味的追求卷面高分,使得学生对数学学习陷入了枯燥无味的死循环。国家教育部门也逐渐重视这一问题,针对传统的应试教育而提出了素质教育。素质教育倡导全体学生的全面发展,因此它更重视对学生学习兴趣的培养,即让学生发现数学中也是存在着美的。笔者通过翻阅大量的文献发现,我国学者不仅对数学美的理论进行了研究叙述,还将数学美与课堂的实际教学联系了起来。但针对于数学美如何与中学代数进行整合,让学生发现代数中的数学美从而提升代数学习兴趣这一方面的研究还是相对来说较少。本文通过文献法对相关理论进行了整理,从代数概念的教学以及代数证明两方面出发,对其进行了阐述。对于代数概念可以从以下三个方面展开教学:(1)善于利用数学故事激发学生的代数学习兴趣;(2)利用螺旋式教学方式,加深学生对代数概念的深入理解;(3)在教学中结合数学史让学生进行数学感悟。而对于解代数证明题时可以从数学美的特征——和谐美、简洁美、严谨美、奇异美、对称美这五个方面出发,简化运算扩充证明思路。另外本文采用了问卷调查法对湖南省常德市某高级中学高三学生中的代数数学美的现状进行了数据收集。并从学科特征、学生、教师、社会这四个方面出发对数据进行了分析,力求将理论与实际调查相结合。此外,笔者试图在理论与实践的指导下,将数学美与高中代数相结合,设计了正弦定理与二项式定理这两个教学片断。最后,对本论文做出了一个总的小结。
[Abstract]:Due to the socialist national conditions of our country, the college entrance examination has become an important system for selecting talents in China after the founding of new China. However, with the passage of time, the drawbacks of the college entrance examination are becoming more and more. The school and the parents blindly pursue the high grade of the volume, which makes the students fall into a dull dead cycle of mathematics learning. We also pay more attention to this problem and put forward quality education in view of the traditional exam oriented education. Quality education advocates the overall development of all students. Therefore, it pays more attention to the cultivation of students' interest in learning, that is, to let students find that there is also a beauty in mathematics. The theory is discussed and the beauty of mathematics is linked to the actual teaching in the classroom. However, the research on how to integrate mathematics beauty with middle school algebra, let the students find mathematical beauty in algebra and improve the interest of Algebra Learning is relatively less. From two aspects, the teaching of algebra concept and the proof of algebraic proof are expounded. The concept of algebra can be taught in the following three aspects: (1) good at using mathematical stories to stimulate students' interest in Algebra Learning; (2) use spiral teaching methods to deepen students' deep understanding of the concept of algebra; (3) combine teaching in teaching. The mathematics history lets the students carry on the mathematical understanding. And for solving the algebra proof problem, we can simplify the proof of the expansion of the arithmetic from the five aspects of the features of the beauty of mathematics, the beauty of harmony, the beauty of succinct, the rigorous beauty, the strange beauty and the symmetry of the beauty. In addition, this paper adopts the questionnaire survey method for the algebra of the senior high school students in a high school in Changde, Hunan. The data is collected from the four aspects of the subject characteristics, the students, the teachers and the society. The author tries to combine the theory with the actual investigation. In addition, the author tries to combine the mathematical beauty with the high school algebra under the guidance of theory and practice, and designs the sine theorem and the binomial theorem, two Finally, a general summary of this thesis is made.

【学位授予单位】：广西民族大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：G633.6

【参考文献】