Investigation And Research On The Development Of The Geometric Thinking Level Of The Ninth Grade Students

As an important part of mathematics,geometry plays an important role in cultivating students' thinking.Judging from the actual situation of geometry teaching in China,it is the junior high school that can really reflect the geometric characteristics.Because the primary school mainly stays at the intuitive level,and the geometry of the high school needs to rise to the level of the theory,the geometry of the junior high school just plays a role in connecting and connecting.The similar triangle is a difficult point in the junior high school's geometric content.It is a turning point from the identity transformation to the similar transformation learning.Therefore,it is significant to investigate the level of geometric thinking of the similar triangle content among the ninth grade students.In this study,80 ninth grade students from a public junior high school in Mudanjiang City,Heilongjiang Province were selected as the research object.The school is a key junior high school in Mudanjiang City,and 20% of the 95% enrollment rate can enter national key high schools.Since there are no special classes in the ninth grade of the school,the two randomly selected classes can represent the overall ninth grade of the school,and even to some extent can reflect the ninth grade students in some ordinary prefecture-level cities and counties.This study uses a questionnaire survey method,based on Fan Hill's geometric thinking level,to investigate the students' geometric thinking level on similar triangles.This study excludes Fan Hill's five levels,which are generally recognized in the education industry as students who have reached a fully acquired level 0 and a level not covered by junior high school geometry4.Focus on the study of ninth grade students on level 1,level 2 and level 3.At the same time,with the help of the four-dimensional vector introduced by Gutiérrez et al.To represent Fan Hill's geometric thinking level,the points in the three-dimensional space are used to present the acquisition situation of the ninth grade students at three levels,which is also an innovative point of this research.The research results are as follows:(1)The current status of the geometric thinking level of the similar triangle content in the ninth grade students: students have fully developed at level 1,78% of whom have been fully obtained at level 1;56% of students at level 2 have achieved "high level of acquisition "And above",11% of them are "fully acquired";there is more room for development at level 3,of which 73% of students are still at "medium level" and below;students' development at level 2 is between level 1 and level 3;(2)Therefore,it is not difficult to find that the development of students' geometric thinking at these three levels has a certain correlation,and they are extremely significantly related to each other.This means that when cultivating students' geometric thinking,teachers should pay attention to it when training at a lower level;(3)There is no significant difference in the geometric thinking of similar triangles between boys and girls.As for the learning of similar triangles,there is no phenomenon that boys are better than girls,so teachers do not need to teach men and women differently.