The Stage & Ingredient Principle of Problem Solving

I cannot express strongly enough the importance of learning and understanding the stage and ingredient principle of problem solving. It is the foundation for complex problem solving.

Centuries ago it was recognized that there were basic mental activity stages to problem solving. These stages are subject neutral. They will, of themselves, solve nothing. They are a guide. These stages also have been called steps, phases, processes, elements, ingredients, set of operations, elementary constituents, and others. It is desirable to standardize on one name such as stages.

Over the years, thousands of formulas have been offered for these mental activity stages. After a thorough review of the literature and selecting features from the best of them, a formula – SM-14 – is now available. It consists of 11 stages and 3 ingredients. It is complete and practical. It is long enough to cover the major stages and ingredients, but not so long as to be impractical to teach and use.

A guide or formula, being subject neutral, will not solve problems. So, certain ingredients were recognized as necessary to use at these mental activity stages. In the SM-14 formula these have been combined into three ingredients. They are applied at all stages of mental activity to actually accomplish results.

The stages and ingredients need not be followed in rigid order. Actual practice allows one to backtrack, loop, skip, stop, detour to sub-problems, coil, interplay, and other variations. “Anything goes” as long as it is ethical.

As explained later in History of Problem Solving, misunderstandings arose that caused this major principle and a good formula such as SM-14 not to be properly presented. That is why I stress that it is essential that you understand the principles explained here.

Tell your friends, associates, teachers, and others about this best site on the Internet for problem solving.

Types of Problems

There are many types of problems. Here we use the often-mentioned broad classifications.

Closed-Ended Problems. These can be both simple and difficult, but they usually have only one correct answer. They include puzzles, textbook problems, test problems, exercise problems, game theory problems. Some refer to these as problem doing or prefabricated exercises rather than problem solving.

Open-Ended Problems. These may have more than one correct answer. They are ill-structured, ill-defined, open-ended, simple, or complex. They are often referred to as real-world problems in contrast to textbook-type problems. Open-ended problems are the ones we will discuss here.

This site does not include advice and guidance on closed-ended problems. Below are links to some sites that cover them:

Decision Making and Problem Solving
The Art of Problem Solving
WebMath