构造法在高中数学中的应用探究

发布时间：2019-06-18 21:25

【摘要】：随着社会更加文明化,对人才学历的要求也越来越高,而高考是人才成长至关重要的一步。就数学而言,要在高考中取得高分,关键是做题方法的选择,这样才能省时省力又有效果。因此,本文将研究一种重要的数学方法,即构造法。文章将主要从四个方面着手,研究数学构造法。首先,对于数学学科构造法,在国际数学发展进步中的作用做一简单总结。然后,探索研究使用数学构造法去解题的优点、原则、方法、类别区分,以及在中学数学学科教学中的典型题型(高考题)。在用数学构造法解题时,应遵循相似性、直观性、熟悉化等原则。求解数学题,通常根据问题所设条件以及结论——直接构造；转换变更条件以及结论的形式——间接构造,这是用构造法解数学题的最基本方法。高考题中便有很多典型的构造例子,而本文就其中的函数、方程、递推关系、图形、向量、对偶式等,做一详细探究,并且对它们每个类别的解题模式进行探讨。其次,笔者选择一个具体教学案例,探究数学构造法在实际教学中的应用以及渗透,让学生切身体会到数学构造方法的巧妙和美。最后,针对老师如何进行引导学生,以及学生如何自主学习提出一些行之有效的方法。
[Abstract]:With the development of the society, the requirements for the education of the talents are getting higher and higher, and the college entrance examination is a crucial step in the growth of the talents. In the case of mathematics, to get high marks in the college entrance examination, the key is to make the choice of the method of the problem, so that time and labor are saved and effective. Therefore, this paper will study an important mathematical method, that is, the construction method. The article will start from four aspects, and study the mathematical construction method. First, it is a simple summary of the role of the mathematical subject construction law in the progress of international mathematics development. Then, the article explores the advantages, principles, methods and categories of the use of the mathematical construction method to solve the problems, as well as the typical problems in the teaching of middle school mathematics. In solving the problem with the mathematical construction method, the principles of similarity, intuition and familiarity should be followed. Solving the mathematical problem is usually based on the conditions and the conclusion _ direct construction of the problem, the change condition and the form _ indirect structure of the conclusion, which is the most basic method for solving the mathematical problem by the structural method. There are many typical structural examples in the high-test questions, and the function, equation, recurrence relation, graph, vector, dual-type and so on in this paper are discussed in detail, and the problem-solving model of each category is discussed. Secondly, the author selects a specific teaching case, explores the application and penetration of the mathematical construction method in the practical teaching, and makes the students feel the skillful and beautiful of the mathematical construction method. Finally, how to guide the students, and how to study and put forward some effective methods.
【学位授予单位】：西北大学
【学位级别】：硕士
【学位授予年份】：2016
【分类号】：G633.6

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