A Survey And Research On Geometric Intuitive Ability In The Field Of "numbers And Algebra" Of Third-year Junior High School Students With Different Cognitive Styles

"Mathematics curriculum standard of compulsory education(2011 Edition)" clearly puts forward that geometric intuition is one of the 10 core concepts of mathematics curriculum standard,and emphasizes that geometric intuition should be paid attention not only in the teaching of geometric content,but also in the whole mathematics teaching.In this paper,through sorting out the literature,we know that there are few literatures on students' geometric intuition from the perspective of algebra at this stage,and the empirical research on geometric intuition also needs to be further strengthened.Therefore,this paper starts from the field of number and algebra to study geometric intuition,and then combines with students' cognitive style to find the differences between students from the psychological level,so as to teach students in accordance with their aptitude and make up for the experimental data gap in the current theoretical research.This research mainly adopts the methods of literature analysis,survey and case interview,aiming at starting from the definition of cognitive style and geometric intuition,combining with the mosaic graph test(CSFT),geometric intuition test questions and interview data,comprehensively analyzing the current situation of geometric intuition ability of junior three students with different cognitive styles in the field of number and algebra,so as to improve the current level of number and algebra The emphasis of geometry intuition in teaching is to respect students' individual differences and teach students in accordance with their aptitude,so as to find teaching strategies suitable for students with different cognitive styles.Through the analysis of the survey results,this paper draws the following conclusions:1.There is no gender difference in the cognitive style of junior three students,and there is no significant difference between different classes.2.The average level of geometric intuition of junior three students in the field of number and algebra has reached the requirements of the new curriculum standard,but the ability varies from dimension to dimension.Among them,the level of graphic intuition is obviously better than that of simple symbol intuition and substitute intuition.3.There are significant differences in the scores of the third year students in different representation forms of the same topic.The overall performance of the third year students with pictures is better than that of the third year students without pictures.4.The students of grade three in junior high school are more inclined to solve inequality,travel encounter problem,multiplication formula and finding regular calculation problems in geometry,and more inclined to solve absolute value problem,travel opposite problem,set Wayne diagram and function image in algebra.5.There is a significant correlation between the number of junior three students and the geometry intuition and cognitive style in algebra field,and the field independent students have higher scores in geometry intuition than the field dependent students.6.No matter whether the title is given or not,the geometric intuitive performance of field independent students is better than that of field dependent students.And they are most affected by the presence or absence of graphics in the simple symbol intuition,followed by the substitute intuition,and finally the graphics intuition.7.Different explicit and implicit topics have relatively little influence on the field independent students,but have a greater influence on the field dependent students,especially in the graphics represented by function and polynomial multiplication.8.The students of field independent and field dependent type are less aware of using graphics to solve problems in algebra problems such as number axis(absolute value),travel problem,Wayne graph set,function image and point graph(regular calculation).9.There is no gender difference in the development of geometric intuition in the field of number and algebra.10.There is a significant correlation between geometry intuition and mathematics achievement of junior three students,and the students with better geometry intuition also have better mathematics achievement,which shows that cultivating students' geometry intuition is conducive to the improvement of mathematics achievement.