1.1 What is Problem Solving?

Many books have been written in an effort to analyze and teach problem solving skills. Perhaps an even more fundamental question than the one posed in the title of this section is: What is a problem? Here are a few:

• one is at the bottom of Mt. Baker and wishes to be at the top
• one wishes to find the greatest common divisor of two numbers
• two children are listening to the Canucks hockey game but they are supposed to be sleeping
• a large mailing list needs to be sorted alphabetically so as to search for duplicates
• a wood-burning stove must be supplied with wood for the winter
• a teacher wishes to analyze a number of test scores and generate letter grades for report cards
• a grade six French student needs to memorize some verbs.

Just as the bare fact of a problem is a different thing to different people, so also is the process in view to solve them:

• To a high school algebra student, problem solving is the name for a formalized kind of game.
• To the owner of a business, it is finding the way to maximize customer satisfaction and profits.
• To a counsellor, it may involve restoring a client's self esteem and re-building broken relationships.
• In the information sciences domain, it is often thought of as the process whereby raw data is given meaning and thereby transformed into information or knowledge.

All these and many more situations that could be added to these lists have two things in common that make them "problems." These elements are:

(a) a current state of affairs, and

(b) a desired state or goal that is different from (a)

The problem solver seeks to use some process to transform the perceived current state (a) into the desired state (b.) In the narrowest sense, problem solving is the operation of some process by which the transformation of states is achieved. In a broader sense, problem solving encompasses both discovering the problem and the finding of an appropriate process, and not just the execution of the solving strategy after it is found. That is;

Problem solving is the description of current states and desired goals, and the finding and using of means to achieve those goals.