The Study Of The Present Situation Of Permutation And Combination Of Grade 12 Students

With the explosion of information in the past decades,permutations and combinations play an important role in our life.For example,the arrangement of timetable in school,the possible result of a lottery,the molecular structure of DNA,and the coding in computers all depend on the knowledge of permutations and combinations.Permutation and combination,which has a long developing history,always makes students feel challenging.Knowing the strategy but fail to apply it,applying the methods but fail to get the correct result,getting right answers but not confident in it are typical for students in permutation-and-combination problem-solving.This dissertation intends to explore the grade 12 students' learning of permutations and combinations in Shanghai by addressing four research questions:(1)Whether the factors like gender,interests in mathematics,and understanding level of mathematics would lead to students' different performance in learning permutation and combination?(2)What are the typical mistakes students would meet in permutation-and-combination problem-solving?(3)What is the level of grade 9students' mathematical understanding of permutation-and-combination in Shanghai?(4)What reasons for the mistakes when students solve permutation and combination problems?I choose the questionnaire which is designed by Batanero and modify the questionnaire slightly.This questionnaire is used to conduct an investigation and research on students of grade 3 in high school who randomly selected about permutation and combination learning in Shanghai.Firstly,I use Crosstabs and Correlations of SPSS 23.0 to conduct difference analysi and analyze the overall situation of 49 students;Secondly,I choose knowledge of statistics to analyz details of wrong questions under three combinatorial models;Fianlly,I establish the framework of knowledge analysis to interpret the students' problem solving process and find the causes of students' mistakes from the perspective of semiotics on the basis of ontology and semiotics theory.I draw the following conclusions through my own empirical research and analysis:1:In the learning process of permutation and combination,there is no difference between the gender and the students' liking for mathematics and the learning of permutation and combination,but there is significant difference between the students' mathematical level and the learning of permutation and combination;2:The eight wrong types of Permutation and combination are as following: repeat order type,the topic type,type of formula,calculation,intuitive type,object type,enumeration type;3:In data analysis,students' overall mastery of permutation and combination knowledge is low.In the process of permutation and combination learning,students' mastery of selection model knowledge is better than that of distribution model and segmentation model,but the degree of mastery of distribution and segmentation model is the same but low;4: There are three reasons for mistakes in students' permutation and combination problem solving from the perspective of semiotics:(1)Lack of basic concept of symbol;(2)Misunderstand or do not understand the wording of the question;(3)Can't understand the symbols that used to solve the problem(including symbols of permutation and combination and symbols which are used to solve problems).In the end,I not only give some teaching suggestions but also give the corresponding examples for illustration through conclusions and my own understanding.