Investigation And Research On The Current Situation Of High School Students' Permutation And Combination Learning

Combination has developed rapidly since the middle of the last century,and their achievements have been widely applied in various fields and disciplines.But according to the existing research,students still have some difficulties in solving the problem of counting.Therefore,it is of practical significance to understand students' current learning status in order to improve students' learning and teaching.Through reading and analyzing the relevant literature,the author confirms that the four research questions in this paper are: high school students' overall mastery of the three combinatorial models of permutation and combination,what types of errors high school students have in permutation and combination problem solving,according to the four steps of Polya's problem solving,what proportion of errors occur in each step of high school students' solving permutation and combination problem,and their differences.Whether there are differences between students of different levels or not.The author chooses 279 students from three levels of science classes in the second grade of a high school in Shijiazhuang as subjects for investigation and research.(1)The correct rate of solving problems in the student distribution model is lower than that in the selection model and the segmentation model,and the types of errors in the distribution model are obviously more than those in the other two models.The mastery level is lower than selection model and segmentation model.(2)There are nine types of errors: examination errors,confusing object errors,intuition errors,counting principle errors,sequence errors,elimination errors,unsystematic enumeration,formula errors,and calculation errors.(3)The proportion of students' errors in the two steps of understanding problems and drawing up plans is much higher than that of drawing up plans..(4)The conclusion of the study on the difference.In the test of permutation and combination,there are differences between different sexes.Further analysis under the combination model shows that there are gender differences under the selection model and thedistribution model,and there is no gender difference in the segmentation model.There are also differences among students at different levels.Finally,according to the research conclusion,some teaching suggestions are put forward for permutation and combination.In daily teaching,teachers should pay attention to the teaching of basic principles and basic concepts,pay close attention to the types of errors in the steps of understanding the topic and drawing up a plan,correct them in time,make paired learning of different genders to reduce gender differences,and suggest that teachers should try the teaching of three combinatorial models.