The Research On Educational Values Of Combinatorial Problems In Math Competitions

Every large math competitions will test combinatorial problems, however, solving this them does not require too much specific knowledge of math. We don’t need too much problem-solving methods and techniques to solve them but higher ideas and views, which one can not get them by reading just a few books. That is exactly the most original purpose of math competition. What kinds of educational values do they have? This paper is written to solve it.Firstly this paper analyzes the research of educational values of the combinatorial problems in math competitions and then classifies these problems into three categories:counting problems, the problems of existence and structure, problems of combinatorial optimization. After that, the paper demonstrates the educational values of each category by illustration:it helps students to master which knowledge, to improve which ability, to enlighten which kind of mathematical thinking, and how to promote the development of the students etc.This paper gives three strategies in teaching combinatorial problems in math competitions further, and designs a teaching case about how to use graph theory to solve these problems.