A Survey Of High School Students Solving Permutation And Combination Problems

Permutation and combination problems are two kinds of important counting problems based on the basic counting principle,which does not involve new calculation methods,but requires higher thinking ability.Therefore,logical reasoning,mathematical abstraction and mathematical operation literacy can be improved through the study of permutation and combination.At the same time,permutation and combination problems often appear in the way of realistic situations,which can not only cultivate students’ rigorous logical thinking ability and ability to analyze and solve problems,but also increase the interest of mathematics and cultivate students’ interest in mathematics learning.In this study,the following four questions are studied through test papers and student interviews:(1)How well do high school students solve permutation and combination problems?(2)What mistakes do high school students make when solving permutation and combination problems,and what are the reasons for these mistakes?(3)How is the ability of high school students to solve permutation and combination problems related to their Chinese scores?(4)Is there any ethnic difference in the ability of high school students to solve permutation and combination problems?The results show that high school students,after three years of study,by the third year of high school,the overall performance on permutation and combination problems is good,but the problem transfer ability is poor,and the performance is poor when facing new situations and new problems.In terms of problem-solving strategies,the proportion of students using enumeration method and graph method increased with the difficulty of the problem increasing.The main error types include non-systematic enumeration,wrong understanding of the problem,repeated or omitted counting errors,confused object types,formula errors,order errors,counting principle errors,grouping errors.Permutation and combination problem solving ability is significantly related to Chinese performance.There are some differences among students of different nationalities in solving permutation and combination problems.Finally,according to the results of the survey,some teaching suggestions and suggestions are put forward.