Research On The Influence Of Enumeration Method In Combinatorial Problem Solving Of Senior High School Students

The problem of permutation and combination is an important content of high school mathematics.It has a long history of development and has a wide range of applications.The content and academic requirements of this knowledge are also put forward in the "General High School Mathematics Curriculum Standard".The research on the status quo of permutation and combination learning,learning barriers and problem-solving strategies at home and abroad is relatively rich,but few pieces of literature have studied the impact of specific problem-solving strategies on the permutation and combination counting problems,especially the enumeration method,which is a basic and extremely important strategy.Based on this,this paper proposes the following three research questions:(1)What is the current situation of high school students using an enumeration to solve permutation and combination problems?(2)Does high school students use enumeration to solve permutation and combination problems relate to their ability to solve such problems?(3)What are the characteristics of effective enumeration implemented by senior high school students in solving permutation and combination problems?Taking the students in the first and second grades of senior high school as the research object,the survey was conducted by issuing questionnaires and test papers.Through the analysis of the questionnaire,it is found that the current situation of students’ use of the enumeration method in solving the problem of permutation and combination counting is that students of all grades do not have a high level of understanding of the enumeration method.The second grade of senior high school performs better than the first grade of senior high school,and there is no gender difference.In addition,there is no grade difference in the use of enumeration method,source,effect,difficulty and influencing factors.Through the quantitative analysis of the test paper,we know that in the problem of permutation and combination counting,senior high school students’ problem-solving ability is insufficient,but the use of enumeration can promote the improvement of students’ ability of permutation and combination counting.Through qualitative analysis of the other test paper,the overall characteristics of effective enumeration are summarized,including clear symbolic representation,organized problem-solving strategy and orderly structural expression.Finally,some teaching suggestions are put forward for the teaching of the enumeration method in permutation and combination counting.On the one hand,teachers should enhance their awareness of the importance of enumeration in learning and solving permutation and combination knowledge,while paying attention to teaching methods.On the other hand,teachers should strengthen the guidance of students’ standardized problem-solving training and help them develop effective enumeration problem-solving habits.