Understanding is so misunderstood

Anytime you go "meta" on a topic--when you start talking about what you're talking about, thinking about what you're thinking about--there is a hall of mirrors feeling to the enterprise. Before you know it you've lost your way. Perhaps that's why epistemology is such a bitch. It departs from the worst kind of circular question: How do we know what we know? Oh, God, your pained brain cries out, Can't we just be happy and grateful that we do sometimes arrive at understanding and not worry how? Unfortunately, when you are in the business of helping others to understand, you have to know the process intimately so that you can take your young charges there reliably and consistently, rather than leaving it up to fortune's whims.

As Wiggins and McTighe point out, there are many cases where knowledge mimics understanding but--like a $25 Chinatown Rolex and the real thing--it takes training to see the difference. Compare, for example, someone who can follow a recipe to someone who can really cook. If you show the recipe-follower your pantry and ask him to make a meal from its contents, he'll be lost. But the cook can draw on his fund of general knowledge about sweet and savory flavors, proportions, and techniques and apply it to the specifics of what's on hand to come up with a successful improvisation. Obviously, we want our students to be more like a chef and less like a bachelor who can make beautifully al dente Kraft Mac & Cheese but absolutely nothing else.

The most pernicious aspects of knowing masquerading as understanding are when students give a right answer purely by luck and we teachers give them and ourselves a pat on the back. Reflexive responses to cues (think about a dog who gives you his paw anytime you have a treat, even when you ask him to roll over or play dead) are Skinnerian examples of conditioning that devalue both learner and teacher. To see how vulnerable this knee-jerk learning is recall the example of the word problem that is easily solved with the Pythagorean Theorem but doesn't have the flashing neon markers screaming USE A SQUARED PLUS B SQUARED = C SQUARED. Most students could easily solve it but don't understand the theorem well enough to apply it to a situation outside the artificial diagrams in their textbooks and class chalkboards. Like the bachelor cook, they are at a loss even when the variation presented is as minimal as having noodles and cheese on hand but no reassuring blue cardboard box.

Our goal as teachers should be to encourage students to become flexible, adaptable, conceptual thinkers and doers through properly designed units rather than trying to cram more and more facts into their heads. Untethered, uncontextualized facts have a funny way of being forgotten (amnesia), lying there never to be used (inertia), or, worst of all, contributing to a false sense of confidence in students who are sorely mistaken (fantasia).