Purpose
The purpose of this page is to share with web surfers my 22 years of experience in the area of teaching problem solving. I will do this by demonstrating specific problem solving strategies which can be found by using the links to the left. This site was designed to use the links sequentially, but it is not mandatory to do so. Each link will also provide two problems for the web surfer to try and solve independently. Although any age group can learn from my selected problems, most of them are geared towards high school students.
Source
Most of my problem solving influence has come from my own teaching experience which will be included on this site. I will however model my problem solving process after George Poyla's steps to solving a problem :
Poyla is considered an authority figure in the field of problem solving by many mathematicians around the world and each of his steps can be found in his book "How To Solve It".
Definition of Problem Solving
A teacher, student, or psychologist may each have their own definition of "problem solving", but according to George Poyla, in order for an individual to "problem solve" he must experience heuristics. This is a mental process which includes a blockage and forces one to solve a problem without an immediate plan of attack to the solution. It is not a process by which a person merely follows a recipe or algorithm to the answer. Consistently working on heuristic problems which require a variety of problem solving strategies makes for a more successful overall problem solver in today's society. Working on non heuristic problems does have it benefits as well. They can exercise the mind and build up one's repertoire of problem solving strategies which can be used as a tool to solve heuristic problems.
When will we ever use this?
This is the dreaded question that comes up sooner or later in every math teachers classroom. I would guess that some teachers fear this question simply because they are tired of hearing it or perhaps they do not have a good answer.
Here is my answer to the question : "When will we ever use this?" A student solves math problems not just to obtain a solution, but to understand the strategy used to solve the problem in hopes that he can mimic it later in life. Sure, the exact problem that a student is currently working on may never be duplicated in his future life. However, the problem solving strategy he is using may be repeated continuously throughout his life time. The more a student practices problem solving strategies, the better the student becomes as a problem solver in today's society. For example, a student attempts to solve a problem by using the problem solving strategy "Draw A Picture", and that same student may use that same strategy later when building a new deck in his back yard or explaining to his colleagues a new solution to a work schedule. Solving math problems whether it be in a General Math or Calculus class can contribute to ones success in life which is filled with challenging problems that require solutions. Problem solvers in today's world is in high demand and math problems which require a variety of problem solving strategies will help individuals prepare for the work skills that will be expected of them.
© COPYRIGHT 2007 Simone (Sam) Powell All Rights Reserved.