A Research On The Measurement Of The Mathematics Problem Schema Based On IRT

A new round of curriculum reform of basic education has been fully implemented. The second article of the overall objective, which is put forward in the curriculum standards in mathematics of full-time compulsory education (trial version) drawn up by the Ministry of Education, poses explicitly that students should learn to observe and analyze the reality in mathematical way of thinking, to solve the problems in daily life and in other disciplines, which may help enhance the awareness of using mathematics. It can be seen that the new round of curriculum reform of basic education puts more concern on problem-solving. In order to develop students'ability of problem-solving, we should firstly know the factors which can affect students'ability of problem-solving. Based on the research of problem-solving by predecessors, we know that one of the most important factors which affect the ability of problem-solving is the problem schema of the related problem. Therefore one of the research purposes of this paper is to better measure students'mathematical problem schema.This paper, under the guidance of item response theory, through scoring the production of 0,1 "one out of four" multiple-choice questions, forms a set of test scale. Through the actual measurements towards students, this test scale can give detailed and exact data which would be, under the guidance of item response theory, analyzed by using the three-parameter logistic model. Firstly, the Unidimensionality of data's would be tested through the principal component factor analysis by using the software SPSS. Secondly, the collected data would be estimated through software ANOTE1. 03. The parameters includes the difficulty of the project, the discrimination, the guessing probability, and the value of subject's ability。When estimating the parameters, the software ANOTE1.03 does Assessment of Model-Data Fit at the same time. This paper not only gives the report of the model - fitting test, but also gives the detailed parameters of each project. Then according to the related theories based on item response theory, the project selection would be done. Such as deleting a project whose model data which is not fitful, and deleting one whose guessing probability is too much over. Through the aforementioned selections, the projects which own superior performance would be selected and then forms a set of testing scale. Finally, Item Characteristic Curve and Item Information Curve would be drawn in order to analyze under what condition each item and the whole test can provide the most information. Then through Test Information Function, the standard error of measurement can be calculated which can replace the traditional reliability coefficient.