Open-ended Problems Of Mathematics And Its Teaching Research

With the implementation of quality-oriented and innovation education, the research of the open-ended problems of mathematics has gradually become hot in the process of mathematics education research. The education value of open-ended problems has already been approved by more and more mathematic teachers, and it has become a breakthrough point of implementing the quality-oriented education by the mathematic teaching with the carrier of open-ended problems.The paper is divided into five parts. The first is about the origin of the mathematic open-ended problems. It points out that the concept of "open-ended problems of mathematics" is a carrier between the "two bases" and "innovation education" on the basis of analyzing domestic and international research on the open-ended problems of mathematics.The second part defines the concept of "open-ended problems of mathematics", and analyses the characteristics and types of "open-ended problems of mathematics".The third part discusses the educational value of the mathematic open-ended problems in detail. Including the knowledge educational value of the open-ended problems, the development of the student's study ability by the open-ended problems, the training of the student's emotion and the view of the values by the open-ended problems.The forth part is to find out the students' degree of accepting the mathematic open-ended problems, the evaluation of the mathematic open-ended problems and the mathematic studying through questionnaire and interviewing. It points out that the mathematics open-ended problems not only can evaluate the students' mastering of the knowledge and the technical ability, but also can be used to evaluate the students' high degree thinking. The open-ended problems of mathematics reflect the evaluation principle of the new course standard.The fifth part mainly discusses the teaching design of the open-ended problems of mathematics on the basis of discussing the teaching view and the studying view of theopen-ended problems, including the establishment of the goal of education, the setting of the open-ended problems, the design of the teaching, the design of the studying. Then it enumerates the teaching cases to take into the elucidation. Finally it is mainly about the introspection of the teaching of the mathematic open-ended problems.