Cognitive Diagnostic Assessment On Primary School Grade Four Students’ Arithmetic Word Problem Solving:Compare GRM-RSM And GRM-AHM

Cultivating the problem-solving ability of students is one of the important tasks in the mathematical courses of compulsory education. Arithmetic word problem solving is the key part of mathematics problem solving in primary school. Traditional academic test and evaluation report can’t reveal the student’s internal cognitive structure. But Cognitive Diagnostic Assessment based on cognitive model, diagnoses students’ knowledge by cognitive diagnostic test. It provides useful information for remedial instruction. Currently, the multi-level scoring item or structural response item is the main content of examination reform program at home and abroad, because the kinds of questions can reflect students’thinking process of problem solving. However, studies on cognitive diagnosis are more focused on the development and application of cognitive diagnostic models of scores0-1. There isn’t yet study which compares GRM-AHM and GRM-RSM from theory and practice aspects. The two models applied to the case that contains a hierarchical relationship and multilevel score. Therefore, this study is based on three methods of GRM-AHM-A (A), GRM-AHM-3A (3A) and GRM-RSM, cognitive diagnostic assessment for primary school grade four students’ arithmetic word problem solving. This paper is divided into two parts of simulation and empirical studies.Cognitive diagnostic tests couldn’t choose all item inspection patterns in the developing tests. In the simulation study, there were four tests, which measured7items (Q1),16items (Q2),30items (Q3),53items (Q4). We wanted to explore the variation and difference of Pattern Match Ratio (PMR) and Marginal Match Ratio (MMR) of three methods. Empirical study included constructing cognitive model, developing cognitive diagnostic test and cognitive diagnostic assessment. The subjects were888students of grade four from6schools in3different areas of Zhejiang. We got the following results:1. There were two factors. A factor was cognitive diagnostic classification method, the other was test Q. PMR was affected all main effects and two-factor interactions. On condition Q1, the PMR of GRM-RSM was significantly lower than A’s and3A’s. But there were no significant differences between the last two methods’. On condition Q2, the PRM of A was significantly higher than3A’s and GRM-RSM’s.3A’s PMR was significantly higher than GRM-RSM’s. On condition Q3, the PMR of3A was significantly lower than A’s and GRM-RSM’s. But there were no significant differences between the last two methods’. On condition Q4, the PRM of GRM-RSM was significantly higher than A’s, A’s PMR was significantly higher than3A’s. When method A and3A were used, Q2’s PMR was the highest, Q4’s was the lowest. When GRM-RSM was used, Q3’s PMR was the lowest, Q2’s was the highest.2. MMR was also affected all main effects and two-factor interactions. On condition Q1and Q2, the MMR of GRM-RSM was significantly lower than A’s and3A’s. But there were no significant differences between the last two methods’. On condition Q3, the MMR of method3A was significantly higher than A’s, method A’s MMR was significantly higher than GRM-RSM’s. On condition Q4, the MMR of method3A was significantly higher than GRM-RSM’s; GRM-RSM’s MMR was significantly higher than A’s. When method A and3A were used, Q2’s MMR was the highest; Q4’s MMR was the lowest. When we used the GR-RSM, Q1’s MMR is the highest; Q2’s MMR was the lowest.3. Mathematical content knowledge and cognitive skills were defined through cognitive analysis, thinking aloud, experts discuss. The two components could80.3%predict difficulty of items. The HCI and HCIM index associated with the cognitive consistency were0.62,0.74, which indicated the fitting degree of cognitive attribute hierarchies was good, and the cognitive model was fully justified.4. Having developed a cognitive diagnostic test of arithmetic word problem solving in grade four was based on the top-down ideas of cognitive diagnostic theory, which has a good measure of liquidity. The analyzes of CTT and IRT showed lower overall difficulty of the test items, discrimination of items was ideal, and the Crobach’s Alpha of the test is0.743.5. The results of application of three methods of cognitive diagnostic assessment on arithmetic word problem solving suggested that there was a big difference between the results of three kinds of cognitive diagnostic classification methods. There were53kinds of knowledge methods.888subjects’knowledge states were categorized into44kinds when using methods of GRM-AHM-A and GRM-AHM-3A. While using method of GRM-RSM,888subjects’were classified into34kinds.