The Correlation Between The CPFS Structure Of Junior High School Students And The Ability Of Mathematical Problem Solving

In Mathematics learning,the bases are concept and proposition,and the key is to improve students' ability of solving problems,thus the correlation between them is of great significance.The CPFS Structure which put forward by Professor Yu Ping with originality is recognized as an excellent cognitive structure,and it contains concept field,concept system,proposition field,and proposition system.This research aims to explore the relevance of junior high school students' CPFS Structure in function concept and problem solving ability.In order to improve the teaching process of function concept in junior high schools,and enhance students' ability of settling problems;this research investigates students'formation of this cognitive learning structure about function concept,and students'proficiency level of solving a problem,and correlation of above two variables with experimental instruments of questionnaires and interviews and with data analysis by soft-wares Excel and SPSS.Firstly,the thesis introduces the experimental background and significance,and determines research direction and method by the analysis of research status,offering theoretical bases for solving problems.Followed by a further explanation to the CPFS structure,defining the concept field and concept system,proposition field and proposition system,clearing CPFS structure related theoretical basis,which provides proposition basis for future research.The third chapter is the main part of the study which is data collection and data analysis.By data generalization and analysis,experimental results are as follows:(1)junior high school students' CPFS Structure on the basis of function concept were mostly in the middle level.(2)Junior high school students' ability to solve problems was ordinary and large differences existed among students.(3)There was a significant positive correlation between individual's CPFS structure and problem solving ability.That is,the cdearer CPFS Structure a learner had,the higher his problem solving ability was,because students who had better CPFS Structure could quickly search the knowledge of solving problem from the huge knowledge system,and vice versa.(4)In the one-dimensional linear regression analysis of correlation between learners' CPFS Structure and problem solving ability,with the independent variable of junior high school students' CPFS Structure and the dependent variable of students' problem-solving achievement,result showed that the former had a direct impact on the latter and they had obvious causal relations.At last,the researcher presents suggestions for improving students' CPFS Structure and problem solution ability based on the former chapter,and analyses the validity of this research.