Thematic Teaching Of Polyhedron And Revolution Solid Based On Van Hill’s Theory

Solid geometry is one of the important contents in high school mathematics curriculum,in which the content of “polyhedron and revolution solid” also plays an important role in cultivating students’ spatial imagination ability,mathematical calculation ability and logical reasoning ability.In recent years,the curriculum standards of high school mathematics show that Thematic teaching has many advantages,and encourage and advocate front-line teachers and education researchers to develop theme-based teaching.In addition,Van Hill theory,the five stages of geometric thinking level follow the law of students’ thinking development,and can connect the knowledge of different difficulty levels of the same geometry in series.Therefore,this study chooses the mature Van Hill theory to guide the themebased teaching design in geometry.For the content block of " polyhedron and revolution solid " in high school solid geometry,based on the assessment of students’ learning difficulties and weaknesses in solid geometry,by re-integrating and improving related teaching content,a reasonable and effective theme-based teaching scheme is designed,to help students form a solid and logical knowledge chain based on geometry.In this study,firstly,based on the curriculum standards,the feasibility analysis of the Thematic teaching of polyhedron and revolution solid based on Van Hill theory is carried out,and the Thematic teaching design process of polyhedron and revolution solid based on Van Hill theory is formed.Secondly,this study investigates and tests the current situation of learning polyhedron and revolution solid,to understand students’ learning difficulties and weaknesses in solid geometry.Then,based on the geometry theory of Van Hill,the curriculum standards and textbooks of compulsory education and senior high school are sorted out and analyzed.At the same time,by referring to the relevant contents of the textbooks of Suzhou Education Edition and Beijing Normal University edition,the knowledge points belonging to the same geometry are linked vertically and enriched horizontally.Furthermore,aiming at students’ main problems and weaknesses,with "cube","regular triangular pyramid" and "sphere" as the theme content and the development sequence of Van Hill’s geometric thinking level as the logical relationship,three specific thematic teaching cases are designed,so as to improve the difficulties of students in learning solid geometry and help students form a logical and closely related knowledge chain.Finally,the experimental research and teaching effect analysis of this teaching design are carried out.After the research,the following conclusions are drawn:(1)The combination of Van Hill theory and thematic teaching is feasible,and the polyhedron and revolution solid thematic teaching design process based on Van Hill theory is formed.(2)Students’ grasp of the concepts,properties and theorems of polyhedrons and revolution solid is not deep and firm enough,and they are weak in understanding and solving problems such as the section of geometry and the relationship between the positions of lines and planes.(3)Three thematic teaching cases based on Van Hill theory are designed.It includes "cube" themed teaching case based on Van Hill theory,"regular triangular pyramid" themed teaching case based on Van Hill theory,and "sphere" themed teaching case based on Van Hill theory.(4)Through the teaching experiment,the average score of the students in the posttest is slightly higher than that in the pre-test,which indicates to some extent that this teaching program can help students overcome learning difficulties and effectively master knowledge.