Research On Cognitive Diagnostic Test For Primary Fraction Word Problems:Structure And Measurement

Objective:(1)To prepare two sets of cognitive dignostic tests for fraction word problems,and to provide reliable tools for children with learning difficulties.(2)To construct a cognitive model of fraction word problems which can provide a theoretical basis for students correctly solving the score application problems.(3)To diagnose students’cognition mistakes in solving problems and classify the attribute mastery patterns.Methods:According to Mayer’s classical theory and Yang Dong’s primary school children’s mathematical problem solving cognitive model,the cognition attributes of fraction word problems were found.Based on the cognitive diagnosis theory,the cognitive dignostic test of fractional word problems was compiled.Determine the delimitation of the test by expert assessment and ROC curve method.After a total of three surveys,the formal tests were administered to 1300 students,with 1253 valid questionnaires(683 boys and 570 girls),the effective rate of which is 96.38%.Based on the seqG-DINA model,the students’ attribute mastery patterns were classified and the error strategies were analyzed.Using the non-equivalent design of anchor test,the Tucker’s linear equivalent method under the classical test theory was used for the equivalent study.Results:(1)Item quality analysis,the difficulty parameter of volume A is between[-3.605,0.689],the average difficulty coefficient is 0.569;the difficulty parameter of volume B is between[-3.571,0.264]and the average difficulty coefficient is 0.85.The volume A discriminatory parameter is between[0.4,2.5],the average discriminatory coefficient is 1.66,the volume B discriminator parameter is between[0,5,2.5],and the average discriminatory coefficient is 1.335.(2)The analysis of reliability and validity of the test,the internal consistency reliability of the volume A(B)is 0.810(0.774),and the split-half reliability is 0.656(0.662).The maximum information function value of volume A is 11,and the maximum information function value of the volume B is close to 7.The cognitive diagnostic reliability of volume A is 0.829,that of volume B is 0.866,both greater than 0.8.Structural validity and internal validity are mainly adopted.HCI indicators are used for structural validity,and the average HCI indicators for volumes A and B are 0.887 and 0.825.The internal validity is based on the rate of mastering patterns,and the percentages of volume A and B are more than 80%.(3)Demarcation and detection rate,through ROC curve method,the delimitation points of volume A is 20 points,and that of volume B is 23 points,which are basically consistent with the demarcation points evaluated by experts.The detection rates were 25.7%and 21.9%respectively.(4)The analysis of cognitive diagnosis results,a total of 19 ideal mastery patterns are obtained.The diagnostic results based on the seqG-DINA model included guessing parameters and slipping parameters.Except for the guessing parameter of item 9 and the slipping parameter of item 1,the guessing parameters and slipping parameters of the remaining 11 items in volume A are less than 0.4.Except that the guessing parameters of item 3 and item 8 in volume B are greater than 0.4,and the guessing parameters and slipping parameters of the remaining 11 items are less than 0.4;The analysis of attributes mastery probability,In general,students have poor mastery of attributes A3(fractional multi-step operations),A6(identify implied conditions),and A7(arithmetic representation),the probalities of which are less than 80%.Students have a probability of more than 80%for other attributes.Students with difficult mathematics learning have poor mastery of the seven attributes of fraction word problems;The analysis of attribute mastery pattern,there are 81.07%and 83.31%of the students successfully classified in volume A and B seperately.The 62 students with mathematics learning difficulties are all classified into non-ideal mastery patterns.Conclusions:(1)The cognitive diagnostic tests are of good quality,good reliability and validity,and it can be used as a screening tool for students with learning difficulties.(2)19 ideal mastery models are obtained based on the seqG-DINA model.More than 80%of the subjects are successfully classified.All students with mathematics learning difficulties are classified into non-ideal mastering models.(3)The weakest attribute for students to master is the arithmetic representation.