The Research Of Relationship Among Number Sense,Mathematical Efficacy And Mathematical Performance

Number sense is the concept which is refered widely in the field of psychology and mathematical education, bringing up number sense of students is one of the main aims of new mathematical curriculum reformation, the bourgeoning, forming and developing of number sense become the important issue naturally. The concept of self-efficacy which is developed by American psychologist Bandura was applied in the field of education aboard, and mathematical efficacy as one of concrete form of self-efficacy affects mathematical study deeply. Understand the relationship among number sense, mathematical efficacy and mathematical performance better is necessary to mathematical ability brought up and mathematical performance improved. There are two parts in this research:Studyâ… : Revise"The Scale of Number Sense of Elementary Fourth-graders"to get a scale of number sense which is adapt for the fourth-greaders of elementary school students, and also to supply a effective tool of measurement for research aboard in this field; when we get the scale, according the result of measurement, we take a analysis about its rationality, verify its discrimination, reliability and validity; if the scale is eligible, we take a formal test, and the explore the developmental level and characteristic of elementary students in our country, which are able to supply credible reference data for the researche and practice work.Studyâ…¡: Research the relationship among number sense, mathematical efficacy and mathematical performance with the same subjects, and compare the impaction number sense, mathematical efficacy to mathematical performance, the impaction number sense, mathematical performance to mathematical efficacy.We have got such conclusions by analyzing the stuff:1 The scale of number sense of elementary four-graders which we revised has well reliability and validity, the alpha and split-half coefficient of each dimension of the scale are both more than 0.6 except the dimension of combining and dividing numbers, and the reliability and validity of whole scale is more than 0.8.2 The elementary four-graders in number sense ranging form best to worst is understanding the meaning of number, comparing numbers, calculating numbers, combining and dividing numbers, developing different computation.3 The characteristic of number sense of elementary four-graders is that: boys are better than girls , but the difference is not significance; students living in urban are better than who are living in rural, and the difference is significance in many dimension.4 The characteristic of mathematical efficacy of elementary four-graders is that: there is no vast difference between different genders of students, but there is vast difference between city and country.5 The correlation coefficient of number sense and mathematical efficacy is 0.323(p<0.01); the correlation coefficient of number sense and mathematical performance is 0.602(p<0.01); the correlation coefficient of mathematical efficacy and mathematical performance is 0.372(p<0.01).6 The regression coefficients of number sense and mathematical efficacy to mathematical performance are 0.538 and 0.201 which achieved significant level both; the R2 in the bivariate regression model is 0.399, that is to say, number sense and mathematical efficacy can predict 33.9% of mathematical performance; the predicting power of number sense and mathematical are 26.0% and 13.6%, number sense is better than mathematical efficacy in predicting mathematical performance.7 Mathematical efficacy is the mediating variable of number sense and mathematical performance, the coefficient of mediating effect is 0.064 which achieved significant level; the path coefficient of direct effect is 0.474 which achieved significant level too. So the style of mediating effect of mathematical efficacy between number sense and mathematical performance is part mediating effect.