High School Students' Geometrical Thinking Level And Its Teaching Application Research

High school geometry is a significant substance of mathematics in senior high school,which playing an important role in training students' geometric thinking.If the students' age groups and psychological characteristics can be sufficiently considered in geometry teaching,it is able to improve the level of students' geometric thinking efficiently.This thesis will mainly discuss the level of students' geometric thinking and its application in the teaching of solid geometry.First of all,this thesis illustrates the research status of geometric thinking,then studies Van Helie's theory of thinking level,Piaget's cognitive development theory and other correlative theories.We know the situation about students' geometric thinking level in Yancheng city,Jiangsu province by the way of questionnaire.On the basis,we propose four levels of high school students' geometric thinking: descriptive level?representational level?formalizational level and critical thinking level.Then characteristics of these levels of thinking and their teaching applications are systematically discussed.We get conclusions by applying the concept of dihedral angle?three perpendicular line theorem?properties of parabola?line-plane vertical?space geometry volume and straight-line equation etc,then designing teaching cases according to these.The effectiveness of designing cases is verified by questionnaire feedback information.At last,we summarize the paper and make a deep reflection on geometry teaching in order to provide reference for the later research.