The Relationships Study Between Mathematics Self-Efficacy And Function Problem Solving Of Ninth-grade Students

At the end of twentieth century,mathematics educational circles began to pay more attention to the study of noncognitive factors in mathematical problem solving.In recent years,as one of the noncognitive factors that influence the problem solving,mathematics self-efficacy has become the focus of the researchers.This study aims to discuss the relationships between mathematics self-efficacy and function problem solving of students in ninth-grade.This study uses a self-developded “mathematics self-efficacy scale” and a“function problem solving test“ as research tools,through questionnaires and individual interviews,to launch a combinational research with qualitative and quantitative analysis.This research is divided into the following three stages:(1)Pre-test stage.Taking the 127ninth-grade students in a school as the object,the pre-test of the research tools are carried out.After item analysis,reliability and validity test,the research tools are modified.(2)Formal test stage.The revised research tools are tested in 142 ninth-grade students in a school.(3)Interview stage.We interview some students with similar mathematics ability in high,middle and low mathematics self-efficacy groups,respectively.Through investigation and interview,the following conclusions are obtained:1.Most of the ninth-grade students have very high mathematics self-efficacy,but the function problem solving performance is lower.There are 53.96% students who overestimate their ability to solve function problem and only 33.09% students whose mathematics self-efficacy is consistent with the function problem solving performance.Boys overestimated their ability to solve the problem more than girls.2.Mathematics self-efficacy can effectively predict the problem solving performance.Regression analysis showed that,there is a binary linear regression relationship among sense of mathematics self-efficacy,mean bias score of mathematics self-efficacy and function problem solving performance,and the regression equation is y=0.575x1—8.853x2,where x1 represents the sense of mathematics self-efficacy and x2 represents mean bias score of mathematics self-efficacy.The regression equation's Adjusted R Square is 0.992.3.Mathematics self-efficacy affects the processes of function problem solving.It through selection processes affects people's goals selection and setting in problem solving,through motivational processes affects people's effort and persistence in problem solving,and through cognitive processes affects people's cognitive construction and the generation and use of problem solving strategy in problem solving.4.The problem contexts have a certain effect on the performance of mathematics self-efficacy and function problem solving.Students' problem solving self-efficacy and problem solving performance in the abstract contexts is higher than that in the real contexts.Finally,on the basis of the research conclusion,this paper gives some suggestions for reference only to improve the students' ability of problem solving and the students' level of mathematics self-efficiency.