On The Internal Networks Of Middle School Students' Mathematics Knowledge-Elementary Function

D. Ausubel says, "If I had to reduce all of educational psychology to just one principle, I would say this: The most important single factor influencing learning is what the learner already knows". The function of teaching is to link new knowledge to pre-existing knowledge. That is to say, teachers need to be aware of the knowledge their students have at various stages so they can provide appropriate instruction.There is a tendency in mathematics education: Educators usually appraise the students' knowledge networks according to theses of psychology and pedagogy, etc, while teachers may estimate them by textbook and experience. Then were the children's internal knowledge networks the same as the assumption of educators? What is the common ground of children's knowledge network on mathematics? What are the characters of the internal networks of mathematics knowledge at various stages between different students? The answers to these questions will not only provide the reliable features of children's internal mathematics knowledge network to our educators, help them to adjust the misunderstanding of them, but, also, will propose the way that students' internal knowledge is structured at various stages and attach to some practicable advices for teaching.This paper focuses on the elementary function knowledge, begins with the investigation of the internal networks of middle school students. In this foundation, it makes comparative analysis among students' internal networks of different grade, different sex as well as different studies performance, and then comes to following conclusions:1. In the initial period of studying certain content, students' internal knowledge network is dynamic, but along with their study, the knowledge tends to be stable;2. While grade elevating, students' polymerization thought ability develops, but the disperse thought ability weakens;3. Students of different grade have remarkable difference among their knowledge networks and such difference obviously manifests the guidance function to students' knowledge networks constitution by strengthened training;4. Boy-student and girl-student display different superiority in their internal knowledge network;5. Students with different mathematics performance have obviously difference in their internal knowledge network.Therefore, teachers should comprehensively and accurately grasp student's existing mathematics knowledge network and its cognition characteristics, arrange their institution accordingly, in order to improve students' performance, while students must consciously establish the mutual relation among their knowledge, construct the highly effective mathematics knowledge network.It will take us well beyond earlier investigations based on simple achievement measures and will feed the development of increasingly useful theories of mathematics learning and teaching.