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Math : History :: Construction : Gardening

I was talking to Ms. L, a history teacher:

“You teach like you’re working in a garden. You’ll plant a seed one place, pull a weed in another place. You’ll prune something one day, and the next day you’ll water something completely different.”

“Yup,” she said, “I just putter around, doing a little bit here, and a little bit there, but planning the whole time for the big effect, and when we get to the end of a unit, everything fills in, and the students have a big giant cornucopia of understanding.”

“Nice!” I replied. “I can’t teach like that. Learning math is like building a house. The knowledge builds on itself. First you need to lay the foundation. Then you frame it. Then you add plumbing and electrical. After that, the roof, insulation, sheetrock, and then all the internal fixtures.”

“You’re right” she agreed, “in math everything builds up, resting on something else. You can’t teach division before addition, and you can’t teach calculus before they learn algebra.[1]”

We taught different subjects, and we recognized that those subjects reflected different modes of thinking, that those different modes of thinking required different modes of learning, and had structured our classroom styles appropriately.

The Faculty Room is talking about whether or how students should be grouped.

I haven’t collected real data, but I’ve asked around, and I’ve got a gut feeling (and this is reinforced by the demographic of responders to those questions): Heterogenous grouping causes a lot more difficulty in math than it does in other subjects. That difficulty is directly related to the difference related above.

I have been to dozens of trainings on differentiated instruction. Not one single one of the techniques we learned in those trainings was applicable to math. I’ve heard administrators and professors tell us that we need to differentiate our instruction, without any clue as to how to actually do so. (Generally those who attempted to give advice only demonstrated how woefully little they understood math.) The few administrators I’ve had with a math background were unanimous in their appreciation of the difficulty2 of the task.

I can’t argue that homogenous grouping is a panacea, either. The emotional toll and lack of successful role models in the bottom groups can be crippling. I know – that’s what I’m teaching right now. I see it every week. And yet, those kids are going to have a much greater chance of success next year because they had a chance to work on their foundation and will have something solid to build on.

So, why is it that the advocates of heterogeneity can recognize that one size fits all is bad for students, but insist on treating all academic disciplines the same?

1 I’m willing to be wrong on this. I suppose it is possible, in at least some cases, to teach the concepts without the foundation. But that understanding will lack rigor, and be hugely missing in the abstraction that I talked about yesterday when i was trying to write this post.

2 It is not completely impossible. I have managed to design some lessons that allow for a broad range of skills. Those are great teaching – I get out of the way, and students discover the knowledge for themselves. The more advanced students discover more, the less advanced proportionately less. But they are also the exception – most lessons build heavily on previously developed concepts, and a students success is very related to how well they understood those previous concepts.