Cognitive Diagnosis Of Primary Mathematics Spatial And Graphics Problem Solving:Comparison0-1Scoring With The Grade Scoring

Mathematical problem-solving ability is an important indicator of students’ mathematical literacy,develop problem-solving skills is an important goal of elementary mathematics education.Space and graphics are a major part of primary school mathematics learning. The traditional evaluation methods and test theory studies currently in use can not reveal internal psychological process of student problem solving, and as the core of a new generation of diagnostic tests of cognitive theory developed is a good solution to this problem. But domestic research always focus on the theoretical research, practice of less. Someone is not yet solved the problem of spatial and graphical systematic research, its research focuses on graphical reasoning section. For lack of previous studies, this study used the rule space approach from both theoretical and empirical aspects studyed the space and graphics cognitive diagnosis of elementary mathematics.Theoretical research used Leighton, Gierl, and Hunka’s (2004) no structured, linear, convergent and divergent four basic attributes hierarchy, compared marginal match ratio and pattern match ratio of four kinds spatial hierarchy method of classification rules of0-1points and grade score.Empirical research used Primary Mathematics Space and Shape cognitive diagnostic test as test tools, studied1106students of five primary schools of Zhejiang Jinhua and Wenzhou.For lack of previous studies, this study used the0-1points and grade score’s rule space approach to diagbose students’ spatial and graphics problem-solving ability, and also compared the results.The main conclusions of theoretical research are as follows:(1) Different scoring methods and different structures and the interaction between the two levels can affect the accuracy of PMR.In the0-1scoring,the PMR of unstructured was significantly lower than structured, but no significant difference between structured.Under the grade scoring, no structured, divergent and convergent is significantly lower than linear.And no matter in which hierarchy,the PMR of grade scoring was significantly higher than0-1points.(2) Different scoring methods and different structures and the interaction between the two levels can affect the accuracy of MMR.In the0-1scoring,the MMR of unstructured was significantly lower than structured, but no significant difference between structured.Under the grade scoring, the MMR of four hierarchys are high.And no matter in which hierarchy,the MMR of grade scoring was significantly higher than0-1points.The main conclusions of empirical research are as follows:(1) The space and graphics test which based on cognitive diagnosis theory is with good psychometric properties, good reliability and validity. Using item response theory and hierarchical regression method, we found that cognitive content property and cognitive skills properties are the mian reasons which influent item difficulty and primary space and graphics mathematics problem solving.(2) Sixth grade students are good at basic arithmetic and basic knowledge of space and graphics,and weak in transpose,schematic representations and identification implied condition.Teachers and students should pay attention to it.(3)There is big difference between the diagnosis of students’ knowledge and property master probability of0-1scoring space and grade scoring method’s rule space approach. Grade scoring diagnostic information on student learning is more meticulous than0-1scoring.