Cognitive Diagnosis On Trigonometric Function Of High School Based On Rule Space Model

In recent years, the foundation education course’s reform has already become the main melody of national education reform. And one of the problems is the educational assessment. The mathematics curriculum standards of high school put forward:“evaluation should run through the whole process of mathematics learning, not only to play its screening and selection function, but also to highlight the incentive and development function.” In most of current research, the complication of mathematical test is still mainly based on classical test theory and the analysis of test results is based on a general score in the teaching of our country, which is unable to provide the diagnostic information for the remedial teaching and weaken the effect of the evaluation on the educational guidance. The development of cognitive diagnosis theory provides a new way to explain the test results and to understand the inner psychological of the students. Therefore, the dissertation tried to conduct the application of mathematics teaching evaluation by the rule space model of the cognitive diagnostic theory as the guide, and the high school trigonometric function as the carrier.Many methods such as literature analysis,questionnaires,Item Response Theory,Rule Model were employed in the research. Two major components of the research process are as follows:Part1 The Development of Diagnostic Measurement Instrument of Trigonometric Function First,attributes model of trigonometric function was constructed based on materials such as mathematics curriculum standards of high school, examination standards, mathematics test of college entrance examination. And the suggestion was sought to frontier teachers by questionnaire survey. Then the preliminary diagnostic measurement of trigonometric function was developed, and R software was used to estimate the performance parameters of items. Finally, we pick out the good performance of items to form a formal measurement instrument with low measurement error.Part2 Analysis on the Diagnostic Results of Trigonometric Function At the beginning,the attribute code matrix which links between attributes modes and items’ attribute code was constructed. Then we applied Matlab software to estimate 23 virtual subjects’(θ_Ri,ζ_Ri)and 260 realistic subjects’(θ_xi,ζ_xi), so as to classify subjects according to rule points. Finally, we used the compute program to calculate subjects’ attribute mastery probability and employed statistical method to explore characteristics of attribute mastery.The research has found that: the diagnostic instrument we developed in this research has good reliability and validity; rule space model can be employed in the diagnostic analysis of trigonometric function; subjects have good performance in the majority of attributes of trigonometric function, but solution triangle and its application and transformation are needed prompt remedy; significant difference in attribute mastery between text、science, schools have proved; there are seven knowledge states and three learning paths in subjects; the learning paths can effectively guide class remedy teaching, a diagnostic report is personalized and favorable for self-remedy.