A Study On The Triangular Geometry Thinking Level Of Eighth-grade Students Based On Van Hill's Theory

"Graphics and Geometry",as one of the four major sections of mathematics in junior middle school,"Numbers and Algebra","Graphics and Geometry","Statistics and Probability" and "Synthesis and Practice",plays a pivotal role in mathematics education.Among many geometric models,triangle model occupies the highest proportion,and is closely related to congruence,similarity,rotation,translation,axisymmetry and central symmetry,etc.,which is the necessary knowledge basis for subsequent study of parallelogram and circle.Therefore,students' cognition of triangle model can be regarded as an important criterion to judge students' geometric ability.This paper uses the five-level division of The Van Hiele Theory to compile a test paper to evaluate students'thinking level of triangle knowledge,and uses the theory of geometry teaching stage for teaching practice.Comparing the teaching practice with the traditional teaching method,this paper verifies whether the triangle teaching method based on The Van Hiele Theory can effectively guide geometry teaching,and puts forward some suggestions for improvement in geometry teaching practice according to the difficulties that students encounter in solving triangle problems.The results show that:(1)At the beginning of the eighth grade,there are some students whose learning level is close to level 5--rigor,but there are also some students whose learning level is maintained at primary school as level 1--visual intuition;The majority of students are between level 3--Non-Formal and level 4--Formal Deductive,with most students at level 3.(2)There is no significant gender difference in the level of triangle thinking among eighth graders,while girls' thinking level is slightly higher than boys'.(3)Triangle teaching based on The Van Hiele Theory can effectively guide teaching practice.