THEORY OF POLYA
George Polya : The father Of Modern Problem Solving
George Polya was born in Hungary in 1887. After receiving his Ph.D. at the University of Budapest, where his dissertation involved questions in probability, he taught at the Swiss Federal Institute of Technology in Zurich. In 1940 he came to Brown University in the United States and then joined the faculty at Stanford University in 1942.
In his studies, he became interested in the process of discovery, or how mathematical results were derived. He felt that to understand a theory, one must know how it was discovered. Thus his teaching emphasized the process of discovery rather than simply the development of appropriate skills. To promote the problem-solving approach, he developed the following four steps:
1. Understand the problem.
2. Devise a plan.
3. Carry out the plan.
4. Look back.
Polya’s accomplishment includes over 250 mathematical papers and three books that promote his popular approach to problem solving. His famous book “How To solve It”, which has been translated into 15 languages, introduced his four-step approach together with heuristics or strategies, which are helpful in solving problems. Other important works of Polya are Mathematical Discovery, Volumes I and II, and Mathematics and Plausible Reasoning, Volume I and II.
Polya, who died in 1985 at the age of 97, left mathematics with an important legacy of teaching for problem solving. In addition, he left the following “Nine Commandments for Teachers”.
1.Be interested in your subject.
2.Know your subject.
3.Realize that the best way to learn anything is to discover it by yourself.
4.Find information but know-how, mental attitudes, the habit of methodical work.
5.Let learn guessing.
6.Let learn proving.
7.Look out for such features of the problem at hand as may be useful in solving the problems to come-try to disclose the general pattern that lies behind the present concrete situation.
8.Do not give away your whole secret at once- let the students guess before you tell it – let them find out by themselves as much as is feasible.
9.Suggest it; do not force it down their throats.