A Research Of Geometrical Visualization Level On Compulsory Education Junior Mathematics Course

Visualization of Geometry is one of the important methods for mathematical research and mathematical teaching. This paper analyzes it by the following four points:(1) Through analyzing Jean Piaget's psychological theory ,children teaching and developmental theory of Vigoschy, Pro.Li's theory of concretion and abstraction, Van Hiele's grade five comprehensive level of geometry and Hoffer's grade five visualization ability,we can generalize the level of geometrical visualization of mathematical curriculum on compulsory education :0 level of visualization——recognizing normative simple geometry graphs (rectangle, square, triangle).We can observe them as a whole , but we only distinguish them by shapes.1 level of visualization——observing geometry graphs as a whole and understanding the characters of normative simple geometry graphs by shapes.2 level of visualization——being able to analyze shapes of geometry graphs, drawing simple geometry graphs with a divider, and recognizing graphs'characters.3 level of visualization——recognizing the logical relation among several characters of a graph or among several graphs; being able to apply the known proposition to demonstration of a new proposition, judging what geometry graphs they are; and basically mastering abstract-generalized ability. 4 level of visualization——during which students can start understanding syllogism method on the whole, are able to apply skillfully the known proposition to the demonstration of a new proposition, and achieve the strict level of formable thought, building Geometrical theory into a nonfigurative axiom system.Junior high school students would be labeled as 1, 2, 3 level.(2) Using classifying standard on the level of Geometrical visualization, we analyze visualization of Geometry curriculum between《standard》and《syllabus》, and through cases of concretion analyze visualization status of using Junior math teaching materials.(3) Choosing Jiajiu middle school to do a miniature teaching experiment, using questionnaire, we try seeing influence on students by boosting up Geometrical visualization. Result shows that effect by boosting up visualization is very better than decreasing visualization, and the former is helpful to students'study.(4) Through the research above, we are able to propose suggestions and problems that need to be paid attention to about Geometrical visualization of teaching material and teaching rule of following out Geometrical visualization .