Dan Meyer, a high school math teacher, agrees (see video below). He argues that one-dimensional problem solving endorsed by math textbooks are killing students’ problem solving-skills and, worse, their interest in logical thought.
Consider your average math textbook.
They define a formula and tell you how it works. Next they give you a problem with some prescribed information and ask you to key it into the formula they just explained.
There’s no problem solving skill involved. All a student does is demonstrate his ability to plug in numbers and follow instructions.
At the end of the day, a student doesn’t know why the formula exists or how to apply it to real-world problems.
Meyer says we should give students a problem and abandon them. Let them find out what information is relevant to the problem and let them figure out how to put it together.
As a result the problem will not only get solved, but each student will know exactly why. They’ll finally appreciate why people who do math for a living use letters to represent points and they’ll understand how formulas save everyone a lot of time and finger counting.
I’m guessing you don’t have a basic algebra math book on your nightstand. I’ll even bet you don’t have the time to take offense to lazy textbook composition. But what Meyer illustrates here is applicable to teaching, training, and problem solving in any field.
Meyer rightly argues that problems shouldn’t be approached with a list of formulas, strategies, and clues. Instead, problems should be handled analytically and simply. Problem solving should be less about the answer and more about discovering the fastest, most efficient route to the answer.
Approaching a problem head-on can get results, but it can also be put you at a disadvantage. How much did you learn? Did you discover exactly how and why the problem was solved? Did you just follow the industry steps or did you beat your own path? If you ran into a similar problem would you be able to tackle it swiftly?
It’s to your benefit to approach problems from a basic, bare-bones approach. You want to know why and how you are solving the problem, not just the answer. You want to build your problem solving muscles.
Possessing the skill to look at problems in different, unbiased ways can help you formulate better, more meaningful answers. Better yet, unique problem perception can give you ammunition to fight future hurdles.
We’re learning every day. It’s important that we put down the text book and discover solutions on your own.
It’s not always about the answer. “The formulation of a problem is often more essential than its solution, which may be a matter of mathematical or experimental skill.” –Einstein