The Cognitive Diagnosis Research On The Sixth Grade Students’ Word Problem Solving

Problem solving is an important research direction of international mathematical education,and it is the important and difficult contents for the primary school students.As a new generation of measurement theory——the cognitive diagnosis theory,has broken through the traditional measurement only on the macro level,therefore this study just recardsthe cognitive diagnosis theory as the theoritical instrument in the research of diagnosing the internal psychological process for the primary students’ problem solving,and mainly concentrates on the sixth grade students’ level and lack of knowledge structure on the problem solving and provide the basis for the remedial teaching.First, this study applied Mayer proposition analysis, combining Shalin&Bee symbol network analysis to classify the elementary algebra word problems in structure and quantity structure situation,and establishes an elementary algebra word problems bank resources.Then separated out two components corresponding to seven cognitive properties on solving the algebra word problems,The operating components: A1(basic arithmetic operations), A2(multi-step operation), A5(identify the implied conditions), A6(Mathematical representation), A7(the formalalgebraic strategy);and the schema components:A3(basic quantitative relationship),A4(complex knowledge schemata).Establish the hierachical relationship between the construction of seven attributes(cognitive model);Based on cognitive model and AHM prepare test paper and implement diagnosis for 531 students of grade six in about 11 classes.Finally using the software of multilog 7.0 and the matlab programming about the range attribute weight multistage score of AHM to realize the diagnostic evaluation of the ability of subjects and attributes master pattern classification. Draw the following conclusions according to the results of the diagnosis:(1)On the overall properties master pattern classification:the 531 subjects were divided into 21 kinds of attributes modes,just as only mastering the A1 attribute or failed all.On the average master level,A1(basic operation)and A3(basic quantitative relation)are belong to the ideal properties which had been acquired,and A4(complex knowledge schemata)and A7(formal algebra strategies)are of the weak properities for the whole students.(2)On the differences between genders and the urban and rural areas on the knowledge state:original scores differences between urban and rural is much obvious,the students number of rural areas on the high scores is relatively more concentrated,and more than half of the people focused on between 64-71 points.On the attribute mastering models, the number of boys is much higher than girls accounting for most of the models;Differences between urban and rural areas were more significant in the A1-A7 attributes,and the gender differences is only significant on A4 attribute.(3)On the differences between the outstanding students and the underachievers of the knowledge state: the A1-A7 properties are controled relatively stable by the high ability subjects for the probability between 0.962 to 0.994,for the lower scores subjects the average attributes probability of A2、A4 and A7 are less than 0.4,particularly the A4(complex knowledge schema)and A7(formal algebraic strategy)are less than 0.3.On the average probability of mastering attributes the outstanding students are obviously superior than the underachievers.In view of the conclusion above,come up with some remedial teaching suggestions:(1) strengthening the A4 and A7 properties of remedial teaching;(2) strengthening the teaching of basic properties to breakthrough the difference between urban and rural areas;(3)analysing the underachievers’ knowledge state,timely adjust to the teaching design;...