竞赛数学中组合问题的教育价值研究
发布时间：2019-01-03 16:31
【摘要】：基本上所有的大型数学竞赛都会考组合题,然而这类题目大多对具体的数学知识的要求并不高,不需要太多的解题方法、技巧,但是它们要求学生具有较高的数学思想与观点,而这些大多不是看几本书就能拥有的,而这恰好是数学竞赛最原始的目标.那么竞赛数学中的组合问题究竟具有怎样的教育价值?这正是本文所要探寻的.本文首先分析了国内外在竞赛数学中组合问题价值方面相关的研究,再将竞赛数学中的组合问题分成三类：计数问题、存在与构造性问题以及组合极值问题,然后对这三种不同类型的问题,分别举例论述其对于学生个体的教育价值：有利于掌握何种知识、提高什么能力、启迪哪些数学思维、如何促进学生的身心发展等。在此基础上,本文对竞赛数学中组合问题的具体教学提出了三个教学策略,并由此设计了一个用图论方法解决竞赛数学中组合问题的教学案例。
[Abstract]:Basically all the large-scale mathematics competitions will take the combinatorial questions. However, most of these kinds of questions do not require a high level of specific mathematical knowledge, and do not require too many problem-solving methods and techniques, but they require students to have a higher degree of mathematical thought and viewpoint. And most of these are not just a few books, and that's the original goal of the math contest. What is the educational value of the combinatorial problem in competition mathematics? This is exactly what this article wants to explore. This paper first analyzes the research on the value of combinatorial problems in competition mathematics at home and abroad, and then divides the combinatorial problems into three categories: counting problem, existence and construction problem and combinatorial extremum problem. Then the three different types of problems are illustrated with examples to illustrate their educational value to students: what knowledge to master, what ability to improve, what mathematical thinking to enlighten, how to promote the development of students' body and mind, and so on. On this basis, this paper puts forward three teaching strategies for the specific teaching of combinatorial problems in competitive mathematics, and designs a teaching case for solving combinatorial problems in competitive mathematics by means of graph theory.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G634.6
本文编号：2399619
[Abstract]:Basically all the large-scale mathematics competitions will take the combinatorial questions. However, most of these kinds of questions do not require a high level of specific mathematical knowledge, and do not require too many problem-solving methods and techniques, but they require students to have a higher degree of mathematical thought and viewpoint. And most of these are not just a few books, and that's the original goal of the math contest. What is the educational value of the combinatorial problem in competition mathematics? This is exactly what this article wants to explore. This paper first analyzes the research on the value of combinatorial problems in competition mathematics at home and abroad, and then divides the combinatorial problems into three categories: counting problem, existence and construction problem and combinatorial extremum problem. Then the three different types of problems are illustrated with examples to illustrate their educational value to students: what knowledge to master, what ability to improve, what mathematical thinking to enlighten, how to promote the development of students' body and mind, and so on. On this basis, this paper puts forward three teaching strategies for the specific teaching of combinatorial problems in competitive mathematics, and designs a teaching case for solving combinatorial problems in competitive mathematics by means of graph theory.
【学位授予单位】：湖南师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：G634.6
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