Tests And Correlation Analysis On Mathematics Cognition Levels Of Grade Eight Students

Qingpu Experimental Research Group had conducted two large scaleMathematical Cognition Tests on grade eight students in 1990 and 2007. The resultsshowed that, on the first three cognition levels (Calculation Level, Concept Leveland Comprehension Level), students' performance in 2007 were much better thanthat of the students 17 years' ago. But on the topmost level (Analysis Level),students' performance has no any improvements 17 years later. This result waswitnessed by some international comparative studies. So how to improve ourstudents' performance on the topmost mathematics cognition level will be a big issuein Chinese mathematics education.Based on Qingpu Experiment, the author of this paper will focus on thefollowing works:Firstly, the framework of mathematics cognition levels used in QingpuExperiment will be described in more details. This paper will use a system ofindicators to describe the four levels and construct a series of tests to assess students'cognition levels. In order to draw more information from the tests, this paper will usethe modern Item Response Theory (IRT) to analyze the items used in these tests.Secondly, the author will use a series of tests on different mathematics cognitionlevels to assess sample students from Suzhou city. The purpose of this work is notonly to confirm the results of Qingpu Experiment, but also to reveal students'cognition behaviors on tasks that need the topmost mathematics cognition. Theresearch shows that the results from Suzhou sample students are consistent to thosefrom the Qingpu Experiment. Besides, the author will also analyze the characteristicsof doing high level mathematics tasks from different students, which include thediscussion of gender differences.Thirdly, the paper will do some relative analysis, which includes the correlationsof different levels of mathematics cognition tests, and mathematics cognition tests tonormal mathematics tests or teachers' assessments. The initial results show asfollowing:(1) All the four levels of mathematics cognition tests are showed correlativity,among them, there is high correlative relationships between the tests onConcept Level and on Comprehension Level, and low correlativerelationships between the tests on Concept Level and on Calculation Level.(2) There are positive correlation between the mathematics cognition tests andthe normal mathematics tests, but the degrees of the correlation are different on different cognition Levels. The highest correlativity appears on theconcept level and comprehension level, and the lowest appears on theanalysis level. That means the normal mathematics tests are mainly focus onthe mid-levels of mathematics cognition.(3) Teachers' assessments to students are significantly related to themathematics cognition tests, especially on the concept and comprehensionlevels. These results means in somewhat that teachers usually put moreattentions on normal mathematics tests, and few attentions on abilities ofsolving non-routine mathematics problems.Fourthly, the paper will analyze factors that might affect students' mathematicscognition levels from the following three aspects: students' own mathematics literacy,mathematics curriculum and teaching methods. Some evidences show that studentsusually achieve higher mathematics cognition levels if they have better mathematicsknowledge bases, using problem-solving strategies consciously, high metacognitionlevels and positive belief and attitude. The paper also found that there are only a fewmathematics items which belong to the fourth level of mathematics cognition inpresent textbooks and teachers also put few attentions to the teaching of the topmostlevel of cognition as well as the gifted education.Finally, the paper puts forward some suggestions on the teaching of higherlevels of mathematics cognition based on the above researches, such as: giving moreemphasis to high level mathematics reasoning, encouraging students to make newproblems and generalization, using more open-ended problems, and so on. The paperalso calls for people to support mathematics gifted education in China. Accordingthe perspectives of the author, the excellent mathematics gifted education dependsnot only on the special educational systems, but also on the professional levels ofteachers.By the way, the author has to say that due to the number of the sample studentsin Suzhou, it is difficult to use IRT in the research and the author also need moreefforts on the qualitative analysis of the factors which effect students mathematicscognition levels.