A Study On The Level Of Mathematical Self-concept And Function Problem Solving In High School

The process of mathematics problem solving,not only need students have solid knowledge base,but also the active thinking,the attitude in the face of difficult mathematics problems.All of them can effect the results of mathematics problem solving.Ability and attitude are equally important in the process of mathematical learning.In addition,focusing on students' development of emotion and attitude is also one of the basic goals of mathematics curriculum reform.Actually,In many learning affective problems,the psychological traits associated with mathematical problem solving are rarely taken seriously by researchers.Even so,we can ' t neglect the importance of improvement of mathematics problem solving.Therefore,it is helpful to understand the psychological characteristics of the students when he learn about functions and then to improve their function learning.In order to make up for the shortage of the existing research,this research survey on the relationship between mathematics problem solving and mathematical self-concept.It is a meaningful attempt for improving senior one students'learning of function.This research can be divided into two parts.First of all,from the sight of qualitative study,through the comparison and analysis of the existing literature at home and abroad,understanding the current situation of function' s problem solving and mathematical self-concept in the round.And then defining the concepts such as problem solving and mathematical self-concept.According to the requirements of curriculum,researcher complete the function test volume.After two trials,the test paper achieves satisfactory reliability and degree of distinction.Secondly,from the perspective of quantitative research,this study used the self-made function test and Marsh self-description questionnaire to investigate the three classes of two high school students.After the survey of questionnaire,the following conclusion can be drawn:(1)Currently,the overall level of mathematical self-concept of senior one students is not very high.The main characteristics is some people realized the importance of thinking and method,but they still can' t do well in function study.On the other hand,On the other hand,the level of emotional self-concept is higher than the ability self-concept level.(2)When senior one students solve the function problem,they have trouble in solving complex function 'domain.They can' t realize the role change of the domain of complex function,external function,and built-in function;(3)When senior one students solve the problems about function analytic expression,they do better in solving the external function according to the complex function than knowing the type of function to solve the analytic expression of function;(4)When senior one students solve the problem with new concept,their performance is not satisfactory.The main reason is the fear of challenge.(5)Dividing the students into three group according to the score of emotional self-concept,the results showed that there was a significant difference between two groups,except the middle score group and low group;(6)Dividing the students into three group according to the score of ability self-concept,the results showed that there was a significant difference between every two groups.The research result means that the level of ability self-concept can predict the result of problem solving.(7)Dividing the participants according to the score of emotional self-concept and ability self-concept respectively,study its independent effect on the three kinds of function problem.The results showed that only a few dimensions does not exist significant differences.