The Theoretical And Technique Research During Diagnosing Geometric Analogies Ability Of Primary And Middle School Students

Cognitive diagnosis can help people better understand human internal psychological rules and its processing mechanism, and diagnose the strengths and weaknesses of individual cognition, and promote development of the individuals. Embretson(1999),Stout(2002) and Leighton & Gierl(2007) all think , cognitive diagnosis is new research topic, the actual value of cognitive diagnosis is also unceasingly apparent in practice,and cognitive diagnosis is the new testing paradigm in the 21st century. Geometric analogies are analogical reasoning based on geometric figure. The ability that Geometric analogy measured is at the core of general intelligence. Using cognitive diagnosis to research geometric analogical reasoning, it help to better understand the essence of geometric analogical reasoning, and help better understand students’analogical reasoning ability’s strengths and weaknesses, and improve students’ analogical reasoning ability.This study discussed three important theoretical and technical problems during using HO-sRUM and HO– DINA to diagnose students’geometric analogical reasoning ability. First of all, we put forward cognitive model involved in solving geometric analogies based on the literature survey, and validate cognitive model by means of oral report method and LLTM respectively. Second, this study first estimate parameters of the two models using the higher-order approach given by de la Torre & Douglas(2004). In order to explore estimated precision and properties of HO-DINA and HO-sRUM, we use the Monte Carlo simulation method to simulate various situations to evaluate models performance. It include three researches, the first is to explore parameter estimated precision of HO-DINA and HO-sRUM in different experimental conditions while the attributes are independent. The second is to examine model robustness of HO-DINA and HO-sRUM in different experimental conditions while the attributes are independent. Third, we use Monte Carlo simulation method to investigate the influence of diagnosis accuracy based on different levels of item parameters under four attribute hierarchical structures. Finally, this study adopts HO-DINA and HO-sRUM model to evaluate the students’geometric analogical reasoning ability, and evaluated diagnostic result from model data fitting inspection and diagnosis of quality. Research shows that:(1) Oral report method and LLTM model results show that cognitive attributes involved in solving geometric analogical reasoning test are seven types of transformations. Transformations include two kinds change, namely spatial displacement and spatial distortions. Spatial displacements include rotation, reflection, and exchange. Spatial distortions include size, shading, shape and number. LLTM model result also shows that cognitive component for the greatest impact on item difficulty is reflection, followed by rotation, the minimum is number.(2) In all cases, the precision of item and person parameters is preferably great for HO-sRUM and HO-DINA. In high cognitive structure and low level slip and guess parameters condition, the precision of item and person parameters is higher. The results also show that, when the more items measure an attribute, the attribute classification accuracy is higher. At the same time, the result also shows, HO-DINA model has certain robustness, however, HO-sRUM model has certain robustness in low complex Q-matrix circumstances, but in highly complex Q-matrix circumstance, the precision of item and person parameters of HO-sRUM model is relatively poor, but it does not result in serious mistake. For four hierarchical structure, attribute marginal match ratio gradually decreases in lower strata. Attribute marginal match ratios between four hierarchical structure are high, convergence and linear’s pattern match ratio is lower than unstructure and divergence’s.(3) From the data fitting inspection and quality of diagnostic results, the diagnostic result of HO-sRUM model is the best. The results of this study indicate that students’attribute master proportion that HO-DINA estimates than HO-sRUM’s . 4-8 grade students’mastery of 7 key attributes on geometric analogical reason is goodish in total. But there exists significant different effect between diffirent grades. The result also indicated that the sixth grade is the fastest development period for geometric analogical reasoning abilities. The cognitive error of students can be categorized into three types, all of them are related to attribute 2.