Study Of The Solid Geometry Teaching Design Based On APOS Theory In Senior High School

Under the requirements of a new round of curriculum reform, collegeentrance examinations in various provinces are going through huge changes. Andchanges also take place in high school curriculums. Math has always been acourse paid particular attention to by all walks of life. While solid geometry isarranged in the first semester of grade two in senior high school, the time forteaching is short. Meanwhile, since students’ knowledge of solid geometry is nobetter than an elementary school pupil or a student in grade one in junior highschool, it is quite difficult for them to study. There are a lot of abstract concepts,rigorous and detailed expressions and mathematical logic languages in highschool solid geometry, with complicated figures and variants, as well as lots ofreasoning and demonstrations. Therefore, the use of simple traditional teachingmodel will cause students to have an ambiguous and paradoxical understandingof the concepts in solid geometry.Based on APOS theory, this paper analyzed the concept learning ofmathematics, from the abstract algebraic concepts to solid geometric conceptsand it guides the concept of the teaching process, using the four stages of thesolid geometry of APOS theory. Through activities, simulation demonstration,students get familiar with the external features in the concepts, then to theabstract intuitive graphical to reflect further on some of the issues on the conceptof variant, forming process stage. Then students, according to their own understanding of the activities and programs to be integrated into the text, couldsummarize the concept with refined language, logical language, graphicrepresentations, and finally form the object concept stage, and form the concept"schema" in their mind. On the basis of this theory, we could form a solidgeometric characteristics APOS instructional design by implementing it in ourteaching practice,and finally we can have a brief evaluation of our teachingprocess.As to concept learning, APOS theory has been demonstrated feasible. It playsan important role in helping students build their own concept system. Therefore,it could have a significant effect on the solid geometry teaching as well.This paper has carried out a systematic and comprehensive research on APOStheory teaching and solid geometry teaching design through literature analysis; ithas a sample survey on the students of grade2in senior high school using thequestionnaires. The result of the survey as well as the feedback from thequestionnaires further illustrates the drawbacks of traditional teaching forstudents to understand the concept of three-dimensional geometric. This paper,through cases, presents the advantages of APOS theory for learningthree-dimensional geometry, the problems of students’ problem solving inteaching evaluation and the reasons behind it.