Mathematics Teaching To Generate

Teaching generation doesn't come from imagination; it is based on broad theory, including epistemology, life science, learning science, knowledge science, and curriculum science. To consider on the side of the learning, teaching generation is talked about contrasting to accept, the character of learning accept is exceeded and developed by generation. To consider on the side of the teaching, teaching generation is talked about contrasting to pre-design, the character of teaching pre-design is renewed and modified by generation.Point of view from epistemology, teaching is a process that students obtain individual knowledge by teacher's help, and students' cognition can be transformed from ignorance to unknown, from unknown to awareness, and from awareness to gnosis. Point of view from infqrmatics, learning is a process that can generate new information by reciprocity between interior information and exterior information. Generative information can become generative knowledge by absorbing, generative information can also become generative resource by revealing, and generative resource can result in generative teaching, including generative teaching aim, generative content of courses and generative teaching tactics. Point of view from complexity cognitive science, the system of teaching generation has lots of characteristics, including nonlinear, uncertainty, self-organization and dynamic condition. Point of view from system science, the system of teaching generation is an information processing system, which consists of both information field and thinking system, and including dynamic system, condition system and tactics system.Personal mathematics knowledge is different from book knowledge; it is generated by one's own master. Investigative research shows clearly that single received way of extension knowledge squeezes generating of personal mathematics knowledge, personal mathematics knowledge reflects discrepancy in quantity, quality and function, and received process of personal mathematics knowledge is short of individual thinking participation generally. Generative resource is dynamic resource, which is produced in the course of teaching. By analysis of investigative consequence of generative resource, we can acquire some major apocalypses as follows: we should adequately understand the value of generative resource, and actively exploit and use generative resource, and try hard to improve teaching intelligence of using generative resource.In order to become the idea of mathematics teaching generation true, teacher should guide students developing inquiry learning, including obtaining on oneself by thinking, reflecting on oneself by inquiring, and converting on oneself by comprehending. To this end, teachers must have three basic qualifications, including teaching ability which can conduct generation, strong teaching resource consciousness, and teaching wisdom which can answer generation. Teacher should clearly understand the theory of heuristics on guiding students to learning, and master appropriate tactics and timeliness tactics on heuristics. Teacher must change designing idea from rigid and static teaching designing into elasticity and dynamic learning designing. At the same time, teaching canonical form should become from single to multielement, teaching model should become from static state to dynamic state, and teaching tactics should become from meticulous to coarse.