| Probabilistic literacy is a necessary mathematical literacy for citizens.The curriculum standard(2022 edition)has arranged the learning of probabilistic concepts for students from grades 5 to 9 in compulsory education.However,how to diagnose the cognitive development of probability concept is an urgent problem to be solved.Therefore,based on the theory of cognitive diagnosis,this study develops a cognitive diagnostic assessment tool of probability concept for students from grade 5 to 9.Through literature research,four cognitive attributes of randomness,sample space,probability estimation and probability comparison are extracted,and a "three-level branching" probabilistic cognitive process model is constructed.On this basis,the adjacency matrix(A matrix),reachability matrix(R matrix),ideal mastery mode,test item mode and ideal response mode are generated,which together constitute the evaluation framework of this study.The test items were compiled according to the assessment framework,and after two expert consultations and three pre-tests,three rounds of revision,the assessment tool planned to be developed in this study was finally generated,namely,the Diagnostic Test of Probability Concept Cognition for students in Grades 5-9.The proposed assessment tool was used to test the quality of 947 students in grades 5-9 from 2 schools in J City,S Province,East China.The results showed that:1.The explanatory degree of cognitive attributes to the difficulty of the topic was 87.1%,higher than 60%,and reached the level of significance.namely:the four cognitive attributes extracted were reliable;2.2.The average value of HCI index is 0.816,higher than 0.6.that is,the constructed hierarchical relationship of attributes is reasonable;3.The Templin reliability index was 0.926,greater than 0.7,that is,the reliability of measurement tools was high;4.The test Q matrix has good validity,and the measurement tool has high validity;5.The test items have good fitting effect,suitable difficulty and good differentiation;6.913 students had fitting parameters greater than-2,accounting for about 96.4%,that is,96.4%students responded well.In conclusion,the assessment tools developed in this study are of high quality and detailed,which can be used to diagnose the cognitive development of probability concepts of students in this class.Using this tool to diagnose students from grade 5 to grade 9,the results show that:1.Overall,students are in a higher attribute mastery mode,and the attribute mastery increases with the growth of grade.Grade 8 is the highest,and grade 9 has a slight decline,which is caused by the decline of "probability comparison";2.In the initial stage,Grade 5 students showed the best performance in randomness,followed by sample space and probability estimation,and poor performance in probability comparison;3.The development speed of cognitive attributes from fast to slow is:sample space,probability comparison,probability estimation,randomness;4.Randomness and sample space are relatively stable in grade 6,and probability estimation is relatively stable in grade 7;5.In this learning section,probability comparison has the most significant degree of development,followed by probability estimation and sample space,and the degree of randomness is relatively small.Based on the diagnosis results,this study draws a path map of the cognitive development of probability concepts for grade 5 to grade 9 students,and marks one major path,one minor path,and several other potential paths,in order to provide guidance and reference for the assessment and teaching of probability content. |
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