October 8, 2011

Teaching Math: Knowing vs. Understanding

Deirdre Bailey

Each day in this process, I get a clearer idea of what powerful learning looks like. I have started to recognize what is becoming a blatant difference between kids who 'understand' and kids who 'know'. We have told them in class, we don't want 'parrots'. Parrots can recite anything we ask them to. It is not what we're looking for. Yesterday I observed a conversation in which teachers described their frustration with the time it was taking their students to 'uncover' mathematical solutions. They called it a road block and then admitted that to overcome the 'road block' they removed the problem and, 'gave them the answer', or in this case, the skills necessary to arrive at the solution.

What we, based on our prior experiences and education and even based on the way education is 'taught', assume, is that when somebody is told how to do something, they 'understand' how to do it. They don't. There are people all over the world that are capable of doing things without understanding how they're doing it, or why. As a simple analogy, how many skiers understand the physics involved in executing turns of a shorter radius than their ski? How many skiers understand that their skis have radius? As a more frightening example, how many first world home owners understand how their light switches work or understand the electrical circuits in their homes? How many adults have had mild shocks attempting to change a lightbulb because they were confused by these circuits. They can operate switches, but could they fix them? Could they pull them apart and put them back together?

Do we want schools to provide students with the necessary skills to survive or do we want schools to provide students with the ability to think, to create, to expand on what they know through critical consideration of what is possible? We believe the latter. Here is documentation of our first attempt to give power to students' own ideas instead of imparting our own.

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