| Everyone’s life is closely related to permutation and combination problem,permutation and combination is also a big difficulty in high school mathematics learning,because of its complex and varied types of questions,high school students are prone to logical confusion when analyzing specific problems,resulting in difficulties in learning permutation and combination.The purpose of this paper is to understand the problems encountered by high school students in learning permutation and combination based on combination model and Bollea problem solving theory,and finally to provide effective teaching suggestions and learning suggestions for front-line teachers in the teaching of permutation and combination and students in the learning of permutation and combination.First of all,through the literature research method,the existing research results and theories on high school students’ permutation and combination learning difficulties are integrated.At the same time,according to the requirements of permutation and combination in the Curriculum Standards for Common High School Mathematics(2017 Edition),the key and difficult points of the knowledge points are analyzed based on the basic counting principle.Then the research method combining questionnaire survey and test paper survey is adopted to understand students’ learning of common question types and methods through the test paper,which provides data support for collecting error types and analyzing the causes of learning difficulties.The questionnaire mainly understands students’ learning status from four dimensions,and then interviews some students and teachers who participate in the test.Secondly,statistics and analysis are carried out on the data obtained from the survey,and the following three conclusions are drawn: First,the most errors occur in the distribution model and the least in the segmentation model.In the allocation model and the selection model,the number of counting principle errors and operation errors is obviously higher than other error types in the model,and the number of operation errors in the segmentation model is much higher than other error types.Secondly,the error rate of the planning step is more than 50% in the allocation model and the selection model,while the error rate of the implementation step is close to 50% in the segmentation model.Thirdly,students have some problems in permutation and combination learning,such as loss of interest in learning and weak foundation,among which the factors affecting learning difficulties include teachers’ teaching style,their own personality and class learning atmosphere.On the other hand,the introduction method of teachers’ teaching is relatively simple,and the introduction of mathematical cultural background and practical life examples is rather boring,which fails to stimulate students’ interest in mathematics learning.Finally,according to the types of statistical errors and the results of questionnaire analysis,the causes of students’ difficulty in learning arrangement and combination are found out and targeted teaching and learning suggestions are provided to front-line teachers and students.First,teachers should return to teaching materials and pay attention to basic knowledge in teaching;Add appropriate combination model;To strengthen the differentiation of error-prone questions;Pay attention to students and understand students’ thinking.Secondly,students should ensure effective learning time every day,learn to actively construct knowledge framework,learn to reflect and consciously exercise calculation ability in the learning process. |
