A Survey On The Cognitive Level Of High School Students' Number Sequence And A Case Study From The Perspective Of CPFS Structure

Sequence is a special function model which contains rich mathematical ideas.It is a key content in high school mathematics and plays a very important role in the cultivation of students' mathematical ideas.However,through the investigation and research,it is found that many students' cognitive level of number sequence is low,they can not extract and apply effective mathematical information in effective time to solve the problems related to number sequence,and they have great difficulties in learning number sequence knowledge.CPFS structure is a unique and excellent cognitive structure of mathematics learning,which is composed of concept field,concept department,proposition field and proposition department.A good cognitive structure can help students quickly accept new knowledge and assimilate new content.Therefore,it is of great practical significance for mathematics education to study the excellence of students' cognitive structure,the cognitive level of sequence and the relationship between them.The case study is based on the subject content of classroom teaching as the carrier,is the representation and description of the teaching problem processing method,can reflect the process and teaching ideas of teachers' teaching design,use the case study to analyze teachers' teaching and students' learning,and provide the basis for practical research.Guided by CPFS structure theory,this paper compiles senior high school series test paper and questionnaire to understand senior high school students' cognitive level of series,and puts forward some teaching suggestions to optimize students' cognitive structure of series,aiming to provide some help for senior high school students' learning of series.In this study,526 senior high school students of different levels from grade two and grade three in three middle schools in Qiannan area were selected as the research objects by using the methods of questionnaire survey and interview survey.Their cognition level of number sequence was analyzed,and then the effective questionnaires were statistically analyzed by using spss25.0:(1)Most of the students are in the low-level CPFS structure group;(2)there are differences in the cognitive level between male and female students;(3)the cognitive level gradually improves with the increase of students' grade;the higher the cognitive level of high school sequence,the better the CPFS structure.The main reasons for students' low level of sequence cognition include:(1)Students don't understand the related concepts of sequence;(2)students don't master the mathematical ideas contained in sequence;(3)students' learning methods are poor.Based on the above research results and causes,the following teaching suggestions are put forward:(1)We should pay attention to the essence of the number sequence concept and present the concept domain from various angles;(2)pay attention to the students' cognitive structure to lay a solid mathematical foundation;(3)give full play to the role of mind map to construct a good cognitive structure.