美国数学家和数学教育家乔治·波利亚在阐述教学的三原则时告诫教师:“在科学家的工作中,猜测几乎总是走在证明的前头.因此,让你的学生们去猜结果,这不仅调动了他们工作的积极性,并且你还教给他们应有的思维方式.”~([1])他在论述学习三原则时指出:“学习任何东西的最好途径是自己去发现.”~([1])这种以数学的猜想发现为先导的教与学原则对于学生理解数学知识、培养发现问题的意识和创新精神具有十分重要的意义, George Pollia, an American mathematician and math educator, teaches teachers in explaining the three principles of teaching: “In scientists’ work, speculation is almost always at the forefront of proof, so let your students guess the outcome This not only mobilized their enthusiasm for their work, but you also taught them the proper way of thinking. ”[1] In his discussion of the Three Principles, he pointed out:“ The best way to learn anything is yourself To discover. ”([1]) This mathematical and conjecture discovery as the guiding principle of teaching and learning for students to understand mathematical knowledge, cultivate the awareness of discovery problems and innovative spirit is of great significance,