Study Of The Open-ended Problems On Mathematics Teaching

With the implementation of quality-oriented and innovation education, the research of open problems has become hot in the process of mathematics education research. 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 makes mathematics teaching change from traditional authoritative mode that "teach knowledge" to self-consciousness study mode that is characterized by "encouraging study".The paper is divided into seven 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 prominent 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 advances principle,essential thought and method of designing of the open-ended mathematical problems. The fifth part puts forward three kinds of tactics of open problems teaching of mathematics: permeating tactics, subject tactics and meta-cognition tactics , and put out the cases of open problems teaching of mathematics. The sixth part analyses paradigm and criteria of evaluation of the open-ended mathematical problems. The last part points out three thinking: questions should be paid attention to in open problems teaching of mathematics; open problems of mathematics in exam; open problems teaching of mathematics and mathematics teachers' quality.