| Permutation and combination is an important part of discrete mathematics,which is considered to be one of the hardest field to teach and learn.Each year the college entrance examination involve it but the scoring rate is low.In addition,most of domestic relevant research is the summary of teaching design and problem-solving methods.Therefore,this study mainly investigatesthe combinatorial problem-solving strategies and the types of errors among middle school students.The following research questions are answered by questionnaire and interviews:(1)What is the overall performance of middle school students in the permutation test?(2)whichproblem-solving strategy do middle school students prefer?(3)What are the common types of mistakes in the test?(4)How will the grade and gender factors influence students' understanding of permutation and combination?The results show that the overall performance of middle school students in permutation and combination is poor,the permutation problem is more difficult than combination problem,evenly distributed problem is more difficult than non-uniform distribution problem.In terms of problem solving strategies,students will use pure enumeration,system enumeration,chart and formula.When the data is smaller,the number of people using pure enumeration method will be more.Senior high school students generally use the formula method,while junior high school students prefer enumeration method.The types of errors involvesmistaken intuitive answer,calculation error,misinterpretation of the problem statement,error of order,confusing the type of object,confusing the type of cell,formula error,and forgetting the meaning of the parameter in the formula.In addition,students' performance is related with the grade and gender advantage,but the grade difference is more significant than the gender difference.According to the findings of this study,some suggestions for Permutation and combination are given at the end of the thesis. |
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