The Theory And Practice Of Open-ended Teaching

A history of math teaching is just a history in which the mainbody, theory and reality are opening gradually. The opening of teaching is a necessity of our times as well as the guarantee of creativity in theory.This paper discusses the theoretical background of open-ended teaching, pointing out that the perspective on curriculum of Postmodernism, the perspective on studying of Constructivism, the perspective on mathematics of allowing making mistakes are all theoretical bases of open-ended teaching. The traditional education pays too much attention to the subject's center when concerning the relations among mainbody, theory and reality, which is above the reality as well as ignores the fact that the student is the mainbody of teaching.The opening of mathematics education is facing the modern mathematics, permeating the language, thinking and methods of modern math, facing the lives and the world, spanning a bridge which connects the "School math" and "Applied math", facing the students, emphasizing on student's full development of morality, spirit, knowledge, intelligence and physical force.We must attach great importance to cognitive goal, ability goal, furthermore, more generic objects of development. We can draw mathematical subject from the reality and common sense, organizing and guiding students to do some research work on open-ended subject encouraging them to discuss with each other or with teachers. Themulti-direction and multi-level communication will result in discovery or encourage more thinking. Open space-time for teaching, walk out of the class into the society then into a world.. From "Return on the foundation" to the "Problem solving", from "Masses' mathematics" to "Open-ended teaching", the worldwide innovation of math courses become a stage in which the teachers can pursue for opening and make it become true. More and more new models of open-ended teaching are welling out, such as Situation -teaching, Activity-teaching, Subject-teaching, Program-designing, Discuss-teaching.This paper analyses these teaching models, at the same time, drawing a conclusion that the computer-based modern educative technology is the technical support of open-ended teaching.