Research On The Van Hiele Level Of Thinking Of Sophomore Students ' Learning Analytic Geometry

Hyperbolic curve is a part of analytic geometry,there are differences between stereoscopic geometry and analytic geometry,but all rely on reasoning thinking.Based on the " Curriculum Standard of Mathematics of senior High School(2003)"(hereinafter referred to as "Curriculum standard")on the requirements of hyperbolic and its position in the college entrance examination,as well as the differences in students ' thinking,this paper is based on Van Hiele theory,combined with the collegeentrance examination,"Curriculum standard" on the requirements of hyperbolic,A scale of the level of Van Hiele thinking was developed to measure the sophomore students ' learning hyperbolic,the test questions corresponding to five levels were compiled according to the scale,88 sophomore students in a middle school were selected for testing and interviewing,and finally,according to the results of the tests and interviews,the level of Van Hiele thinking of sophomore students after learning the hyperbolic content was studied,The main conclusions of the study are as follows:(1)After learning the hyperbolic curve,the adjacent Van Hiele level of thinking is moderately correlated,and the development of level of the lower is the basis of the development of the higher.(2)Sophomore after learning the hyperbolic content,the students reached the level of Van Hiele thinking 2 on the whole,but with the increase of thinking level,the average score obtained by the students showed a downward trend.(3)Students in the level of Van Hiele thinking 0 overall development is relatively smooth,but some problem is the mindset does not know the strange analytic style or image to do the appropriate operation before the identification.(4)in the level of Van Hiele thinking1,The main problem is that most students are incomplete in the description of the definition of hyperbolic curve,and a few students can not distinguish hyperbolic curves from hyperbolic properties at all.(5)in the level of Van Hiele thinking 2,problems focus on the students ' understanding of hyperbolic definition,nature is not deep enough,not comprehensive enough,so they can not establish the relationship between hyperbolic definition and nature better.(6)The main problem of students 'in the level of Van Hiele thinking 3 is that students are not able to establish the relationship between hyperbolic curve and other knowledge to form knowledge relation network,and can not use the knowledge learned to carry out effective deductive reasoning synthetically.(7)Students in the level of Van Hiele thinking 4 completion situation is very unsatisfactory,the ability to explore the existence of sexual problems is quite weak.In addition,the characteristics also puts forward some teaching suggestions to help students transition from the existing Van Hiele level of thinking to the higher according to the specific answer situation and existing problems of the students.