A Study On The Concept And Development Level Of The Planar Vector Concept Of Shanghai Grade 8 Students

This study adopted the theory of "mathematical understanding of growth dynamics theory", which was proposed by Pirie & Kieren(1989,1992,1994). It was regarded as a theory basis of describing individual learning process concept. The research take the way of analysis question and response during learning process in individual case, and try to learn the situation and development of Shanghai eighth grade students’ mathematical understanding when they learning the concept of plane vector.The aim of this study was to explore the differences and features among the phenomenon of "dynamic, non-linear, recursive" during the process of high and low level students learning the concept of plane vector, and also study the degree of correlation between teacher’s teaching behavior and students’ level of understanding.This research takes the method of case study from qualitative research, and the objects are eighth grade students in Shanghai Putuo District School where researcher have an internship. Picking out two samples from high level and low level,separately. And four students totally as the research objects. Then using "the concept of plane vector" as the content of course to teach those students respectively, and record the learning process of the students in a real and effective way. The tool of research was researchers’ lesson plans, and based on this theory to design the level table of development of plane vector control, which was used to analyze the learning process of students and having a further discussion about the different development of different levels students’ studying.The main conclusions of this study are as follows:1、During the teaching process, our four students both show the phenomenon of dynamic, sub level, nonlinear reciprocating.2、 The high degree students all develop to "the organization structure(7.S)" the low degree student all has the development to "observe and review(6.O)". The high degree students can be active in learning process, while the low degree students are opposite.3、The teachers taking more examples to contribute the understanding of low level students; For high level students, taking the method of same topic but with slightly changes. About enhancing the level of understanding of low degree students, takes the counter example of operation; And for high level students, adopts providing more opportunities to let them show their active learning behavior.The main recommendations of this study are as follows:1、Suggested that the teacher takes account of the student’s own concept development model in teaching, and when helping students’ develop the outer layers and occasionally return to the inner layer.2 、 When introducing the definition of plane vector, having more counterexamples to make students’ cognitive conflict, which could help them to clarify the basic definition of plane vector.3、Suggested that during progress of teachers’ assessment, except getting the correct answers, let students to show more their ideas instead of reciting symbols and formulas.