Analysis Of Typical Mistakes And Attributions Of High School Students In Solving The Problem Of Combination Counting

In the Mathematics Curriculum Standard for Senior High School(2017 Edition),the counting principle unit is determined as teaching content of the selective compulsory course.Its teaching object is changed from science students to high school students,but teaching time is reduced,which is a contradiction.In high school mathematics,permutations and combinations are difficult in both teaching and learning.Learning and mastering permutations and combinations are mainly used to solve combinatorial counting problems.According to students' situation in solving combinatorial counting problems,we can know how they are getting on with permutations and combinations.However,I find that quite a few students have some typical errors in solving combinatorial counting problems in actual teaching.Based on these problems,in order to find out the reasons for this situation and find the way to solve these problems,I searcher for literatures related to errors in solving combinatorial counting problems at home and abroad and find most of the articles have been faulted for lack of cognitive analysis or too much dependence on theory.Based on these problems and the reflection in research status,I define the research content as “ Typical Errors and Attribution Analysis of High School Students in Solving Combinatorial Counting Problems ”.Through literature analysis and teacher interviews,I establish five types of problems,which consist of the interval problems,the same element allocation problems,the different element grouping problems,the different element allocation problems and the sequence-ordering problems,as error-prone problem types in solving combinatorial counting problems.On account of interview in front-line teachers,the previous measurement scale was improved and nearly three hundred high school students were tested.According to the test situation,the students' cognitive strategy path to solve different types of combination counting problems was combed.Based on the students' thinking process in specific problem solving,I make a statistical analysis on different paths of strategy in problem solving.The study finds that students show the pluralism situation in thinking strategy when they solve combinatorial counting problems.For some of the typical strategies,students are extremely prone to produce errors in solvingproblems.In this analysis,the usage and error rate of these typical strategy paths are obtained,and the root cause for students' errors are analyzed from cognitive level.Finally,the relevant teaching suggestions are given according to the results of this analysis.