The last step in problem solving is not necessarily the most important—they’re all important—it’s the one that I think is the most overlooked: you need to test your solution. Another way to put this is to “check your work.”
Solving a problem, especially a challenging one, is exhilarating. It’s a sense of accomplishment and we naturally want to pat ourselves on the back. But the rude but necessary question is this: how do you know you’re right?
Sometimes my students get so excited that they were able to apply some newly acquired knowledge to a lengthy problem that they skip this step, missing a critical element of the question or forgetting a minus sign, ultimately getting the question wrong. On a more serious level, imagine what would happen if a new medicine arrived on the market with claims of treating a grave illness–cancer, say–but without any evidence of testing for its efficacy. Not only would that medication likely be useless, it may actually be dangerous.
When you think you’ve solved a problem, don’t be too certain. Check your work. Test your solution.
How to Solve Any Problem:
Step 1: Get Your Mind Right
Step 2: Identify and Clarify the Problem
Step 3: Break It Down
Step 4: Identify and Gather Your Resources
Step 5: Send in the Wolf
Step 6: Test Your Solution