Research On The Relationship Between The Mathematics Cognitive Structure And Logical Reasoning Ability Of Junior High School Students

As a very important mathematics ability,logical reasoning capability has a more significant status as the explicit formulation and determination of the mathematical core accomplishment.This article has researched the logical reasoning capability of the junior middle school students and discussed that whether the cognitive structure of mathematics is a factor to affect the capability of logical reasoning,and also specifically discussed the relationship between the cognitive structure of mathematics and the logical reasoning capability.This research conducted the test of mathematical cognitive structure(referring to the CPFS test paper)and the test of logical reasoning capability(referring to the table developed by Yuping and Yanqing)to analyse the current situation and the relationship between them.As a result,six conclusions can be summarised with some educational suggestions:(1)The mathematical cognitive structure of the junior middle students is generally at a low level;the results of school B is better than that of School A,the results of the two schools have a significant differences.There is no much difference between genders,however from the descriptive statistics,boys' performance is worse than the girls' within the low awareness group,and better than girls' in the group of middle and high cognitive groups.(2)The overall logical reasoning capability of the junior middle school students is in the upper middle level,their performance in deductive reasoning is better than that of reasonable reasoning;the results of school B is better than that of school A,and there are significant differences in both total score and other reasoning dimension.The total score and and other reasoning dimension results between different genders has relatively small gap,and found no much difference after conducting the independent t-Test.(3)There is a significant positive correlation between mathematical cognitive ability and logical reasoning capability of junior high school students,the Pearson index is 0.515.(4)Significant difference of junior middle school students can be seen between different cognitive structure groups and logical reasoning capability;the logical reasoning capability between the low cognitive structure group and the middle,high cognitive structure groups also has significant difference,however,logical reasoning capability is similar for the middle and high cognitive structure groups.(5)In the low cognitive structure group,the average score of girls' logical reasoning capability is higher,however,in the middle and high cognitive structure groups,the average score of boy's logical reasoning capability is higher.Nevertheless,the logical reasoning capability does not have significant differences between boys and girls within each cognitive structure group.(6)The regression equation between logical reasoning capability and mathematical cognitive structure of junior middle school students is Y=0.359X+51.7 which performs a moderate positive correlation;mathematical cognitive structure has a significant predictive effect on logical reasoning ability.