[By John Palinksi.]
In problem solving, the difference between a solution and a resolution is important to understand. The American Heritage Dictionary defines a resolution as "an explanation, as of a problem or puzzle," while a solution can be thought of simply as the answer to a problem. A resolution is a way of looking at, explaining and writing up a problem in a systematic fashion.
Whereas solutions only include the answer, writing a resolution encompasses previewing, specializing, generalizing and reviewing the problem. The first step to problem solving is reading and understanding the question. After the problem is understood, it is important to think about what is known about theproblem and about the topic and writing down these thoughts is often helpful. Beginning actual work on the problem involves specialization, simply trying specific cases, beginning with random examples and then using more systematic examples. Throughout the specialization process, it is important to keep notes about your progress and Rubric writing is a valuable tool. In Rubric writing, upon reaching a point where you can go no further, write "Stuck" and then try to continue by using prompts such as "If I knew this, I'd be able to figure out this." When an idea arises that you think may help you, write "Aha!" followed by your statement. The next step, generalization, involves trying to move from the specific to the general. Using those discoveries that have been made, attempt to generalize about a larger case. A final step requires reviewing and reflecting. Review what you have learned from the problem and reflect on which techniques helped you solve it. This step is a very important step because the techniques used on one problem are often helpful on future problems.