Everyone has problems. They come with being alive. Problems are unwelcome and often unexpected. They don’t solve themselves. If it goes away, it’s not really a problem, unless it comes back. Some problems are big, many are small, some are harmful. All require some effort on our part. Problems are persistent circumstances. They cause doubt, uncertainty and anxiety.
We have many metaphors for problems and their goals. We say we are “hitting a dead end” or are “stuck in the mud.” We describe the feeling of “being lost” or “having no clue of what to do.” We describe solution hunting as “searching” or “getting over obstacles” or “getting around roadblocks.”
Problems tend to be content specific. The solution to one problem (6 times 5) doesn’t help us with a different problem (which shoes to wear with jeans). But there are some general commonalities. When faced with a problem we create a mental representation of it. The representations include the problems current state (what’s wrong now) and its goal state (what success looks like). Since these mental models take up memory space, they are often called search spaces or problem spaces. They are called search spaces because we are searching for a solution.
When we encounter a problem, there is a lot of emphasis on its nature. There is problem finding, problem definition, problem shaping and problem solving.
Problem finding is an application of creativity. You must be able to notice what is missing. It also means extending the search from a small problem to discover larger problems or underlying causes.
Problem definition is identifying the characteristics of the situation. Problems can be divided into two general categories: well-defined and ill-defined. Well-defined problems have a limited set of options, and the initial state and the outcome state are clear. Examples include calculating the total price of an order, converting gallons to liters and predicting the flight of an arrow. Games are typically well-defined. The rules of go, checkers and chess are well-defined (also called well-structured). Winning might not be easy but the problem itself is clear.
Ill-defined (ill-structured) problems don’t have as many limits. Calculating your taxes is well-defined but deciding to be honest is an ill-defined process. Examples of ill-defined problems include deciding what caused a war, predicting the weather, and deciding what to buy as a housewarming gift.
It doesn’t take much to move from well-defined to ill-defined. The Tower of Hanoi task is a well-defined problem when there are 3 poles, regardless of how many disks are involved. But it is an ill-defined problem when there are 4 or more poles. It changes from being solvable with an algorithm to being an ill-structured task with seemingly infinite options.
Problem shaping is the manipulation of components to convert a problem into something more manageable. It is approaching it from a different angle. Problem shaping often involves framing the issue from different perspectives until you find a version of the problem you can solve.
Problem solving is the use of ad hoc methods in an orderly manner. Ad hoc is one of those fun Latin phrases that are usually misused. We tend to use it for unplanned, shoot-from-the-hip procedures. We think it is a random process because we have ad hoc committees that explore random topics. But ad hoc means “for this” or “for this specific purpose.” An ad hoc method applies to a specific situation or knowledge domain. Most of our problem solving techniques work on some problems but not others.
We approach a problem’s solution in an orderly manner. We define the problem and select which ad hoc method to apply. Solving math problems is not the same as solving inter-personal problems. Each domain has techniques which will work better than others.