Research On Geometry Teaching In The 7th And 8th Grades Based On Van Hiele Theory

It is generally recognized among students that the plane geometry is a nodus in junior high school mathematics for its high demand of spatial imagination and abstract thinking.As a guide for students to acquire knowledge,teachers need to ponder over the means which can help students to understand geometry from perceptual to rational,and from concrete to abstract based on the student' cognition.The Van Hiele's theory,one of the most influential geometric learning theories based on the Piaget's theory of cognitive development,was proposed by Van Hiele couple according to their teaching experiences.Our study,based on the content of congruent triangles and the Van Hiele's theory used in junior high school,aims to investigate the following aspects:(1)the levels of geometrical thinking and the statement of geometrical learning of students in grade seven and eight.(2)the rationality of content arrangement of congruent triangles in mathematics published by Shanghai Education Publishing House for seven and eight years students according to the Van Hiele's theory,as well as the reasons of teaching congruent triangles within two semesters.(3)the methods of teaching mathematics among students within different levels of geometrical thinking and promoting their abilities of learning geometry.To begin with,students in grade seven and eight have filled in the questionnaires in order to investigate the statement of learning geometry and the levels of geometric thinking.The data shows that the geometrical thinking levels in students from the same grade were significantly different.However,the geometrical thinking levels in eighth grade students were obviously higher than those in seventh grade after a one-year study on geometry course.Subsequently,analysis of the purpose of teaching congruent triangles within two semesters and conclusion of the points in modest adjustment of content in the class,according to the arrangement of teaching materials related to congruent triangles.Finally,with examinations data of geometric thinking levels,combined with results of questionnaires,requirements of Mathematics Curriculum Standard for Compulsory Education(2011),and the five stages in the learning of geometry based on the Van Hiele theory,a skilled educational strategy was proposed to make the learning schedules of congruent triangles in second semester of seventh grade students and right triangles in first semester of eighth grade students.