Problem-solving can be seen broadly as changing a situation from one state to another. This view covers a host of human endeavors. Most often, the end state is a goal or objective. Problem-solving methods can be categorized as either trial and error or the use of a recipe. A recipe is a method with a proven track record of success. Trial and error, however, tries an approach that has not yet been done successfully. The task of baking oatmeal raisin cookies can be done by trial and error, combining various ingredients. With careful experimentation, you might expect to eventually produce a batch of oatmeal raisin cookies suitable for consumption. But you would also expect to produce, in the process, several batches of either soggy mush or inedible bricks.
By following a recipe for oatmeal raisin cookies, you can produce an excellent batch on your first attempt. The key lesson here is to use a recipe whenever you can. Recipes originated through trial and error. Using a recipe lets you benefit from the experience, lessons learned, and discoveries of others. A recipe allows you to avoid repeating the mistakes others have encountered and to save both time and money.
When no recipe exists for exactly what you want, an excellent approach is to start with the recipe closest to your goal and apply trial and error to modify it. You are essentially starting further along the learning curve toward a recipe that meets your requirements. Adding some chopped macadamia nuts to your oatmeal raisin cookie recipe is one example. This particular modification may be unusual, and there is no guarantee you will like it. Starting from a proven recipe to attempt this combination still avoids a lot of unnecessary mistakes.
Jamie
How Math Works