A Study Of High School Mathematically Gifted Students On The Understanding Of Combinatorial Mathematics

Combinatorial mathematics is an important branch of mathematics and an excellent material for cultivating mathematical thinking.The current educational research on Combinatorial Mathematics mainly involves the permutation and combination within the scope of college entrance examination,but there are few educational studies on the content of extracurricular combinatorial mathematics.Problems of permutation and combination in class is relatively simple for mathematically gifted students.So the researcher also wants to know their understanding of extracurricular combinatorial mathematics.In this study,by consulting the literature and summarizing the data,the problem framework of combinatorial mathematics is drawn up.On the basis of the framework,four kinds of combinatorial mathematics tests are formulated,which are permutation and combination in class,combination counting outside class(without advanced method),combination counting outside class(with advanced method)and combination construction.Each test has a pre-test and a post-test,supplemented by the teaching of combinatorial mathematics,and the researcher interviews students and teachers after the post-test.The research questions of this study are:(1)How about the understanding of combinatorial mathematics among mathematically gifted students.(2)What changes have taken place after teaching?(3)What are the main mistakes of mathematically gifted students in combinatorial mathematics?(4)What are the emotional attitudes of mathematically gifted students towards combinatorial mathematics?The results show that:(1)Mathematically gifted students have a relatively high level of mastery of permutation and combination in class,but a relatively low level of mastery of combination counting(without advanced method),combination counting(with advanced method)and combination construction,and there is no significant difference in scores among the three.(2)Different combinatorial mathematics contents have different teaching effects.Permutation and combination in class and combination structure have significant teaching effects in this study,while combination counting outside class(without advanced method)and combination counting outside class(with advanced method)have no significant teaching effects.(3)The main types of errors in combinatorial mathematics test for mathematically gifted students are repeated counting,omission counting and problem understanding errors.(4)The mathematically gifted students are more interested in combinatorial mathematics.This study can provide some reference value for the future teaching and evaluation of mathematics gifted students.