Investigation And Research On The Status Of High School Students' Permutations And Combinations Learning

Permutation and combination is an important part of probability and statistics,and is closely related to life.The study of permutation and combination is not only conducive to the development of high school students' thinking ability,but also conducive to the penetration of mathematical thinking methods.Although the formula is not difficult to remember and the knowledge is not complicated,the diversity of permutation and combination problems and the abstraction of the concept of permutation and combination of words will make students confused and even unable to start.So,what is the status quo of permutation and combination learning? Can arrangement and combination be used as a carrier to improve students' core literacy? Do students have irreconcilable obstacles during the learning process? Is this obstacle everybody has or is it just an example? How to overcome it and put forward feasible suggestions.Based on metacognitive theory,this paper finds out the students' attitudes,habits,attributions of success and failure to permutation and combination,and their mastery of knowledge.With the help of APOS theory,a test paper is designed to objectively test the students' learning effect in the four stages of operation,process,object and schema of permutation and combination concept understanding,and whether there are problems.The SOLO theory is applied to analyze the results.Through student interviews,we can understand the causes of the wrong answers in the test papers,and provide a basis for the analysis of permutation and combination learning disabilities;through teacher interviews,we can objectively understand how students perform in permutation and combination classes,and then provide effective reference for the suggestions in the following text.The conclusions of this study are summarized as follows: 1.The substantive construction of permutation and combination from example intuition to concept formation has not been completed,especially the reflection on internalization is not deep enough.2.Understanding the formal meaning of the formula of permutationnumber and combination number is not thorough enough.3.There is no effective and good psychological schema for permutation and combination,and the ability to deal with the problem of permutation and combination synthesis is not good.According to SOLO theory,the cognitive level of students in permutation and combination learning is in the level of M(multi-structure).In this paper,the types of errors students make in dealing with permutation and combination are mainly divided into calculation errors,model recognition errors,conceptual understanding errors of permutation and combination,equivalence position errors,problem interpretation errors,sequence errors,etc.According to these types of errors,the main obstacles of students' learning arrangement and combination are divided into psychological barriers,cognitive barriers,operational barriers and environmental barriers.Finally,the causes of the obstacles are analyzed,and the corresponding teaching and learning suggestions are put forward.