How much of a class should be conceptual and how much should be procedural?
This question came up at a professional development session I led last Saturday. I tried to answer it by sharing my daily class routine and giving some examples of how I’ve taught for conceptual understanding. But as I left the session, I found myself wanting to consider the question in greater detail.
Ratio is a hot topic in pedagogy these days. Teachers think about the ratio of student talk to teacher talk. They think about the ratio of lower-order thinking questions to higher-order thinking questions. Ratio is important because it ensures differentiated instruction.
But as I tried to figure out an appropriate ratio of teaching for conceptual to teaching for procedural understanding, I realized that it couldn’t be done. Teaching for conceptual understanding is like being a vegetarian: Vegetarians don’t eat a high veggie to meat ratio; they stop eating meat. Not only that, most vegetarians stop eating meat for a reason, and that reason impacts many of their choices, not just what they choose to eat.
The same commitment applies to teaching for conceptual understanding. If you believe that math is something that can and should be understood by all students then you give up teaching rote procedure. Conceptual understanding becomes the foundation of everything you do and all the choices you make. Sure, just like vegetarians might have a little fish or egg now and then, the conceptual teacher might have to do a little “drill and kill.” But the basic belief about math making sense is always present.
This doesn’t mean that a teacher who is new to teaching for conceptual understanding can’t shift approach gradually. It means that teaching for conceptual understanding requires more than a five minute addition to the class routine. It requires a shift in mindset. To get yourself in that mindset, let me share a few things that I often see teachers who are committed to conceptual understanding do:
1. Introduce every topic in a way that relies on student sense-making.
“See how this looks like an array? That means it’s multiplication!”
2. Correct every misconception by reminding the students “why.”
“You forgot the zero. Remember how this 3 is really 3 tens? When you multiply it, it’s still going to be tens.”
3. Encourage students to ask questions and make connections.
It’s almost the New Year. Lots of people make resolutions about their diet. Maybe this year it’s time to go on a different kind of diet.
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