Open Problems Of Mathematics And Its Teaching

With the implementation of quality-oriented and innovation education, the research of open problems has gradually become hot in the process of mathematics education research. The education value of open problems has already been approved by more and more mathematics teachers, and the teaching taking open problems as carrier has become a breakthrough point in which implements quality-oriented education. The open problems teaching of mathematics has reflected that Problem solving is the central thought for mathematics education, and it is wise choice when mathematics teaching changes from traditional authoritative mode that "teach knowledge" to self-consciousness study mode that is characterized by "encouraging study".The paper is divided into five parts. On the basis of analyzing domestic and international research on open problems of mathematics, the first part points out that studying how open problems enter daily teaching will be further problem to be solved. The second part defines the concept "open problems of mathematics", and analyses its characteristics and types. The third part analyses several questions that exist in mathematics education at present, then fully affirms education value of open problems, and thinks mathematics teaching is necessary to introduce open problems. The fourth part investigates the teaching situation of open problems through the forms such as questionnaire and interview etc, believes the teaching situation of open problems is not optimistic at present, and analyses four reasons :(1)important guide effect of high school and college entrance examination ; (2)open problems teaching has no regular operation mode , and requires teacher has high quality ; (3) ready-made open problems that suit mathematics teaching is less , and teachers' ability to design open problems is relatively poor ; (4)open problems teaching requires teachers to have open teaching ideas , and most teachers still stick to pastteaching ideas . Toward the investigating and analyzing reasons (2),(3), the fifth part puts forward three kinds of tactics of open problems teaching of mathematics : permeating tactics ; subject tactics ; and meta-cognition tactics , and combines these three kinds of tactics and put out the case of open problems teaching of mathematics . Finally, this paper points out three questions which should be paid attention to in open problems teaching of mathematics, namely, open problems teaching of mathematics and open-approach mathematics teaching; open problems teaching of mathematics and performance of "two bases"; open problems teaching of mathematics and closed problems teaching of mathematics.