| Mathematics problem solving(MPS)is an important but relatively weak area in the quality monitoring and evaluation of preschool mathematical education.In order to connect with the value orientation of international early children's mathematics learning and evaluation and the goal of primary school mathematics curriculum,and monitor and promote preschool children's mathematical learning and development from the perspective of MPS and micro knowledge structure,this study firstly aimed to develop a cognitive diagnosis assessment tool of problem-solving in the field of “number and operation” for 5-6-year-old children.Furthermore,the second purpose of this study was to apply the tool to assess 5-6-year-old children's MPS and intervene children's MPS based on the assessment results.Study 1: The cognitive diagnostic test of problem-solving in the field of “number and operation” for 5-6-year-old children(CDT-MPS test for short)was developed.Firstly,the cognitive model of “number and operation” problem-solving for 5-6-yearold children was constructed.The cognitive model included three cognitive components(mathematical knowledge and skills,semantic understanding,and quantitative reasoning)with 11 cognitive attributes(cardinality concept,set comparison,addition and subtraction within the range of natural numbers to 10,combine semantic understanding,result-unknown change semantic understanding,change-unknown change semantic understanding,consistent language comparison semantic understanding,inconsistent language comparison semantic understanding,addition and subtraction inverse reasoning,addition composition reasoning,one-to-many correspondence reasoning).Secondly,the cognitive diagnostic test was developed.The results of quality test indicated that the cognitive model was reasonable.The CDT-MPS test had good reliability and validity,including 35 items.One-to-one interview and 0-1 score system were used,and the test time was about 30 minutes.Study 2: The cognitive diagnostic assessment(CDA for short)of 5-6-year-old children's “number and operation” problem-solving ability by applying the CDT-MPS test was conducted,to test the value of using CDT-MPS test to monitor preschool children's mathematics education.Firstly,the MPS ability of 680 children from 13 urban and rural kindergartens in Shanghai,Hunan and Henan were investigated.The results indicated that the whole sample's overall MPS ability was at a medium level,and the mastery of mathematical knowledge and skills was better than the mastery of semantic understanding and quantitative reasoning.Althouth there was no significant difference in the overall MPS ability among the uraban children,there were significant difference in the overall MPS ability between urban-rural and rural-rural children as well as between different genders and different-level kindergartens.Furthermore,there were different strengths and weaknesses in the mastery of the 11 cognitive attributes of the children from different regions,urban and rural areas,gender and different-level kindergartens.Secondly,the development of MPS ability of 245 children from 4 kindergartens in Shanghai were investigated at two time points within seven months.The results indicated that the children's overall MPS ability was significant improved.However,the progress speed of mastering the 11 cognitive attributes was different.There was no significant difference in the progress of the children from different-level kindergartens.The progress in MPS ability of boys was significantly greater than that of girls.Study 3: The educational intervention research was carried out based on the results of the CDA in study 2.The subjects included 60 children from two classes in the same kindergarten in Shanghai.They were five intervention groups: addition and subtraction within the range of natural numbers to 10,change semantic understanding,addition and subtraction inverse reasoning,addition composition reasoning,and one-to-many correspondence reasoning.Each kind of intervention group included 12 children and was conducted once a week(30-40 minutes each time)and lasted 8 weeks.The results indicated that the intervention of change semantic understanding and addition composition reasoning had significant effect.Each kind of intervention needed not only different core experience,but also common basic mathematical skills and intervention measures.All in all,there were some advantages and difficulties in using cognitive diagnostic theory and technique to develop and apply CDA tool in the field of preschool mathematics.This study may provide some valuable experience for future applied research.The CDT-MPS test can provide rich information for preschool mathematics education quality monitoring,and help educational administrative agencies understand the strengths and weaknesses of mathematics eudcaton in different regions and kindergartens from the micro level.This study may provide some experience and inspirations for the future research of educational intervention based on the results of CDA.However,it still faces great challenges and needs more exploration. |
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