I'm just talking about myself here, so please don't take this as a criticism of anyone else. I am truly struggling with this, and maybe I will come to a realization that you already have, that maybe it's a bit unrealistic to think that some day I'll be able to "teach without telling" all year. And anyway, I really have no idea how anyone with a fixed curriculum and a limited amount of time, which is pretty much every high school teacher in the world, would realistically do that. So for the time being, I'll settle for minimizing the passive learning and maximizing the active learning as much as possible. On the other hand.....
Maybe, sometimes, telling is okay!
For example, after you've made your students think, struggle, discuss, compare, and wonder, then it's okay to tell them what's what, or at least better than if you just told them at the outset. I've always felt that it's okay after you've made them sort of suffer a bit, because then they appreciate the relief your facts offer them.
I think I did a pretty good job of that this year in my trig functions unit. I completely rearranged things, and eliminated a few "lessons" at the outset, by having them graph the trig functions without knowing they were trig functions, and without any preconceived idea of what the curve would turn out to be. Once they'd done their graphs, they compared with their peers, and I actually heard them wondering - Is this what it's supposed to look like? Why does it look like this? What kind of math operation would give this kind of curve?
They decided that the wave was the right one, and I told them, yes that's right, and then moved on to explain how trig gets into the act. Next year, I'll try to coax that out of them somehow. But it felt right to validate their intuitions at that point. They were not passively absorbing information at that point - they were primed and very ready to receive it.
I think it's also okay to "tell" once the right question has been asked. In my second year of teaching, I remember having a breakthrough during one of my classes. WARNING: THERE WILL BE MATH!
The Secret to the Good Split
I was doing the grade 9 factoring unit, and we had just finished factoring by grouping, wherein
this: 2x² + 2x + 3x + 3
becomes this: 2x(x + 1) + 3(x + 1)
which then factors into this: (x + 1) (2x + 3)
From there we went to factoring trinomials like this:
2x² + 5x + 3
which can be done by splitting the middle term like this:
2x² + 2x + 3x + 3
so that the grouping can be done as above. But the thing is, you have to split that "5x" just the right way, otherwise, the grouping doesn't work. There are plenty of bad splits (eg 4x + 1x would be a bad split), but only one good split, and you could sit there and try them all until you hit the good one, or....you can use the secret!
I remember deciding to myself, right there in front of my class, that I wouldn't tell them the secret until someone asked me. So I just kept putting examples on the board, taking their suggestions for the split and working through the example. Sometimes they hit on the right one right away, and sometimes, happily, they did not. Finally, one student, Richard, sensed that I knew more than I was letting on, and asked The Question. "Miss, how do you know how to split it?"
|Before The Secret - Trial and Error|
So as much as I'm trying to stop telling, I suspect there is a time for it. And I don't think we should just fall back on the old argument "Well, if we don't, someone else on the internet will, so what the heck?" I am also, like a lot of people, dazzled by the prospect of my students answering their own questions, and self-validating to boot, to become completely self-sufficient.
But is that an unrealistic goal to set everyday? And is there a place for telling?
What do you think? I would really love to know.
PLEASE TELL ME!
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