Case Culture Geometric Intuition Ability Of High School Students

Geometric intuitive ability which reflects Mathematical thinking in solving Mathematical problems is the main part of Mathematical abilities. Relying on geometric intuition, people can simplify some complicated problems, broaden their thinking and find new solutions. Meanwhile, people can essentially understand the essence of Mathematics. Therefore, the cultivation of geometric intuitive ability plays an important role in Mathematics teaching and solid geometry teaching can also help students develop geometric intuition ability.Based on related concepts of analytic geometric intuition, The thesis uses some related documents and cases such as Bruna’s discovery learning method, Skinner’s operation learning theory, Polya’s plausible reasoning, Multivariate characterization of mathematics, theory of variation and Van Hiele’s the level of geometric thinking as theoretical bases.Guided by the main ideas and purposes of Mathematics curriculum standards, The thesis analyses the factors influencing the formation of analytic geometric intuition as follows, students learning situation, teachers’teaching strategy and teachers’personal quality. It also proposes a theoretical assumption---solid geometry education can help students to achieve analytic geometric intuition. Students’analytic geometric intuition can be developed by visual perception, drawing practice, diagrams judgment, practice and language training etc.Based on a record of classroom teaching in high school, teachers use "Perceived instances---Inductive definition---Preliminary determination" as the main line to help students achieve analytic geometric intuition in different dimensions including constructing geometric model, playing graphical space imagination, resolving spatial relationship, forming space logical thinking ability and remembering specific mathematical language.Combining theoretical bases and case studies, some suggestions aiming to cultivate high school students’analytic geometric intuition are given:(1) Focus on application of geometric model.(2) Emphasize on the cultivation of drawing and distinguishing graphs.(3) Develop students’imagination skills.(4) Strengthen language translation between written language, sign language and graphic language.(5) Focus on formation process of thinking and Instructional Design.(6) Pay attention to the penetration of combining numbers with graphs.