Research On The Actualities Of Pupils’ Geometric Thinking Level Based On Van Hiele Theory

"Mathematics Curriculum Standard for Compulsory Education(2011)" takes "graphics and geometry" as one of the four parts of mathematics curriculum content,highlighting the essential position of "geometry" in the process of mathematics learning and teaching.Geometric thinking can reflect students’ thinking process of analyzing and solving geometric problems and is a critical support for students to learn geometric knowledge.Therefore,the investigation and analysis of this part of content has important theoretical value and practical significance.Van Hiele theory is consistent with the law of students’ physical and mental development,which is of great guiding significance to the learning and teaching of "graphics and geometry".This thesis uses the methods of literature,classroom observation,text analysis and interview to study the geometric thinking level of students.And it constructs the analytical framework of the sixth grade students’ geometric thinking level based on Van Hiele theory of geometric thinking level,curriculum standards and the content of the first volume of the sixth grade textbook.Through the data analysis of the scores of the unit tests,the present situation of geometric thinking level of the sixth grade students in Jinan L School is grasped.Through classroom observation,text analysis and interviewing with students and teachers,this thesis deeply analyzes the existing problems and influencing factors in the development of students’ geometric thinking level in this school,and puts forward reasonable suggestions based on Van Hiele theory of geometric teaching stages.It is found that the geometric thinking of students in sixth grade in Jinan L school mainly focuses on the analysis level,a small number of students’ geometric thinking stay at the visual level,and there is room for the development of non-formal deduction level;There are gender differences in students’ geometric thinking level;Class factors have no significant effect on students’ geometric thinking level;There is a significant correlation between the level of geometric thinking.Through deep analysis,it is found that there are the following problems in the development of students’ geometric thinking: it is difficult to grasp the elements of graphics and their relations,and geometric thinking still stays at the visual level;The ability of geometric reasoning is low,and the transition of geometric thinking level is slow;The concept of space is weak,and the level of non-formal deduction is low.In order to promote the improvement of geometric intuition ability,the development of spatial concept,and improve students’ geometric thinking level,this thesis based on the existing problems and reasons,combined with Van Hiele theory of geometric teaching stage,puts forward the following suggestions: with the help of preschool consultation stage,fully understand the learning situation;Pay attention to the stage of guiding orientation,stimulate students’ interest;Using the elucidation stage,establish the knowledge structure;Rely on the free orientation stage,cultivate divergent thinking;Grasp the integration stage,improve the level of geometric thinking.