| Objectives:(1)To develop a set of test papers(Scale A and B)for cognitive diagnostic assessment of decimal division towards pupils,aiming at providing an effective and feasible tool for screening the children who may have difficulty in learning decimal division.(2)To build a cognitive model of decimal division for pupils(based on the results of the cognitive diagnostic assessment),which can provide a theory basis for improving their ability in decimal division.(3)To analyze the response pattern and error type the children have in learming decimal division,which can support the construction and application of the model from the perspective of data.Methods:With the Cognitive Design System(CDS)as the compilation method,McCloskey's theory of semantic representation as the theoretical basis for cognition,and CTT/IRT parameters and decimal division error types as the basis to select items,a cognitive test for decimal division was drew up.In this resaerch,seven cognitive attributes as well as the logical relationship were developed,which could be confirmed by expert evaluation and oral report.The test papers we proposed are divided into Scale A and B,each of which has 27 items.And the cutoff score was determined by combining expert evaluation method and ROC curve method.After 3 surveys,1294 valid samples(725 boys and 569 girls)were collected out of 1435 questionnaires with effective return-ratio 90.17%.Finally,the analysis of response pattern and error type they have in learning decimal division was carried out based on DINA model.Results:(1)The quality analysis of the item revealed that the difficulty indexs of Scale A and B were[-3.309,0.507]and[-3.413,1.701],the average values of which were-1.134 and-1.084,respectively.On the other hand,the discrimination index of Scale A was[0.478,2.241]with the average value of 0.903>0.7,while the discrimination index of Scale B was[0.435,1.938]with the average value of 0.860>0.7.(2)The Maximum information fiunction of Scale A(B)was 20(15),the Cronbach a coefficient was 0.670(0.821),the split-half reliability was 0.670(0.625),and the reliability based on the cognitive diagnostic test was 0.72(0.80).The content validity showed that the normal children's scores were significantly higher than the difficult pupils;the construct validity revealed the HCI value of the Scale A(B)was 0.63(0.57),both were more than 0.3;the external validity showed that the passing rate of the school types(good,middle,poor)differ significantly in each attribute.(3)The cutoff scores of Scale A and B were 14 and 13,respectively,the overall detection rate of which was 8%.(4)The results of cognitive diagnosis based on DINA model:14 typical assessment models and 15 ideal master models were obtained.From DINA model,the guessing parameters of Scale A and B were[0.1260,0.5660]and[0.0587,0.5398],respectively;and the error parameters of Scale A and B were[0.0067,0.2590]and[0.0335,0.3900],respectively.The probabilities of attribute Al,A2 subjects mastered was more than 90%,that of A5,A6,A7 were less than 80%;In Scale A(B),388(567)children were assigned to the ideal master model among 563(731)children,and the rate is 68.9%(77.6%).955 children were reasonably classified,which accounts for 73.8%;79 children who have learning difficulties with decimal fractions were successfully classified.54 of them were discriminated among 7 typical response patterms,the rest were discriminated among 9 Non-ideal patterns.Conclusions:(1)The item parameters basically accommodated the requirements of cognitive diagnostic test,the reliability and validity of the test were good,and all indicators also reached the surveying demands;(2)The cognitive attribute model of primary division of students is reasonable and effective;(3)Children perfodrm poorly on calculation program execution in fractional division learning;(4)the cognitive diagnosis realized the classification of the children who have difficulty in learning decimal division as well as the analysis of error rules. |
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