用信息技术重塑波利亚的问题解决理论——研究框架的构建及展望

Information Technology Reshaping George Polya's Theory of Problem Solving

在简述乔治·波利亚生平及其问题解决理论的基础上,指出信息技术应用于问题解决能够拓展解题者思维的深度和宽度,以图形计算器技术为例,给出信息技术应用于解题的四个步骤,重塑波利亚的解题表,搭建用信息技术重塑波利亚解题理论的一个框架,通过案例对重塑后的解题表做实际应用,并指出整合信息技术创新波利亚问题解决理论和数学方法论的若干研究方向。

In brief review of George Polya’s life and his theory,it’s pointed out that he application of information technology expanding the problem-solver’s depth and width in thinking.Taking the graphing calculator as an example of IT,this paper gives four steps of problem solving with information technology application,and reshapes George Polya’s table of problem solving.Setting up a framework of problem solving with IT to reshape George Polya’s problem solving theory,this paper takes some conclusions relating Fermat’s conjecture for prime numbers for a concrete example and put forward some research directions.