Below are quotes from some of the world’s greatest scientists that will help inspire your creativity:
Tag: einstein
Sometimes how you articulate or look at a problem is more important than the solution. I’m paraphrasing Einstein, of course.
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
Pic Cred: http://www.flickr.com/photos/paul-w-locke/ / CC BY-NC-SA 2.0
Why are you always in the longest line at the grocery store, post office, or in the slow lane of traffic?
You might think you suffer from Murphy’s Law. You sigh and think that everything that could go wrong does go wrong with sinister ruthlessness. These poor souls even have a Facebook group.
Or, you might think that it’s a trick of the brain. You reason that you only notice long lines simply because they are the ones that are memorably infuriating. The short, can-I-help-you?, lines never exactly bought real estate in your memory because they were so quick and effortless. You conclude that long lines are a symptom of your faulty memory.
In any case you’re wrong.
The truth of the matter is–you generally are in the longest line and in the slowest lane of traffic. This happens because, on average, big lines have more people in them. You are more likely, on average, to be in a longer line. This happens because long lines, by their evil nature, require more people. More often than not you help make long lines the way they are. After all, someone has to. This doesn’t mean you always get stuck in long lines. It just means, on average, you do.
Our thinking about lines is a type of bias in thinking. We don’t always look at the right facts in the right ways. In the case of long lines we selected specific events to study and incorrectly deduced we were either prone to bad luck or victims of observational hiccups. We rarely pause to think that maybe, just maybe, we are, on average, going to be stuck in the longer queue.
This bias, this mental stumble, can have serious implications for how we look at numbers and data. Suppose, in a simple exercise, you wanted to rate the best sales people in your company. You look at how long everyone worked and how much they have sold, draw up averages, and start to compare the numbers. Should the results be taken seriously? Not really. They don’t factor in where exactly the sales people are working for one. Neighborhoods, population, and local income, big factors in sales, are absent from the results.
The point is simple. When you have to make a big decision based on numbers and data make sure they aren’t pushing you to towards a particular conclusion. Data, along with your perceptions, can be biased. Be wary of selection biases creeping up on your choices. The crucial thing to ask before making a decision is whether or not some bias if forcing your hand. Like Einstein said, “We can’t solve problems by using the same kind of thinking we used when we created them.”
