A Research On The Diagnostic Test And Improvement Strategies Of High School Students' Thinking Level In Stereoscopic Geometry Based On The Theory Of Van Hiele

Three dimensional geometry is one of the core content of high school mathematics curriculum,and it is also one of the key contents to be examined in the college entrance examination.It is a mathematical subject studying the relationship between the size,shape and position of the real world objects,which helps to cultivate the students' space imagination ability,geometric intuition ability and reasoning ability,so there is the rich education value.During the teaching process,it is found that students have many difficulties in learning the three dimensional geometry.Therefore,based on the senior one students,this paper discusses how to improve the level of students'thinking in the process of learning the three-dimensional geometry.First,the geometry of the Usiskin and Atebe compilation is adapted to think about the level of the test volume,and it will be used as a pre-test volume to examine the geometry level of thinking of the senior one students before they learn the three dimensional geometry.Second,according to the analysis of the test results of students in learning plane geometry problem,van Hiele's theory of teaching strategies will be combined.Then according to van Hiele's thought of the high school mathematics curriculum goal level model and the "curriculum standards" in the learning activities of students in the level of testing and positioning,a solid geometry teaching content level of thinking and ability analysis framework will be formed.As a later test volume,the effectiveness analysis of the teaching is tested by the difference between the pre-test and post-test.This study finds that level of plane geometric thinking level and the students learning solid geometry of three-dimensional geometric thinking level is positively correlated.Students are relatively weak in graphics application ability,language communication ability,and reasoning computing capability.They lack understanding of the mathematical way of thinking.They lack the initiative and ability to form new knowledge and methods of cognitive structure of the.All of these directly lead to students' lack of good problem-solving strategies in the face of specific problems,and they cannot solve the problem smoothly.Through the comparative analysis of two classes,it is considered that the strategies of the three dimensional geometry teaching can be as follows:1.Apply van Hiele's teaching stage design to organize teaching.Especially in front of the class,students will be strensthened to communication.Students' specific situation will be understood deeply through assignment,testing,and the results of the pre-test.Especially for students at lower levels,the new curriculum related to old knowledge gaps will be done.In the classroom,the appropriate teaching content will be chosen and the corresponding teaching objectives will be determined,so that students of different levels will have a harvest.2.By emphasizing to specific physical around for the operation of the objects and requiring making common geometry models,students will grasp the characteristic of three-dimensional graphics and spatial position relationship through intuitive.Thus,they will have the ability to grasp the overall pattern formation,so that they can not only correctly understand graphics,but can also construct the graph correctly,and gradually the students' ability of space imagination will be developed.3.By promoting students'understanding of mathematical knowledge,and regulating the language expressions of students,the students' logical thinking ability will be improved.4.In solving the problem of the relationship between the space positions,the application of mind map should be paid attention to.It will help students sort out problem-solving ideas.In teaching,the teaching of mathematical thinking methods,such as transformation,analogy,movement change,plane and dimension reduction,ascending dimension and so on should be attached great importance to,which will improve students'mathematical thinking,such as image thinking and logical thinking.5.Students are asked to draw knowledge network chart and network diagram,such as solid geometry preliminary knowledge network chart,proving spatial position relation network graph,and the dihedral angle method of network diagram,which help students clarify the logical relationship between knowledge and methods,and on this basis,mutual understanding will be enhanced to develop flexible application ability.