I appreciated some of the disagreement that got aired as a response to my last piece, on discovery. In particular, some told me that guided-inquiry or discovery really is more memorable than other forms of instruction.
Either because the stuff you learn from discovery is more meaningful (and hence more memorable):
…or because discovery involves surprise, and surprises are more memorable and lead to stronger learning:
I’m not satisfied with either of these arguments.
The thing about discovery activities is that the new idea — by definition of discovery — comes at the end of the activity. That means that kids are spending most of the activity thinking about stuff besides the new, often difficult, idea. It takes time to understand new ideas — to make them meaningful, to “own” them — and most of the time in a discovery activity is spent thinking about other stuff.
That’s certainly the case for the triangle angle activity that I critiqued in my post. While working on the activity, a student’s attention is drawn to many mathematical things — the angles, protractors, adding angles — and only very little of the time is spent thinking about what exactly a triangle’s angles sum to. (This is especially true if the idea is truly new to a student — they’ll only be thinking about the sum once they discover it, towards the end of the activity.)
It’s also true in the trapezoid/triangle area task that I shared. There was a ton of excitement precisely because my class hadn’t discovered the relationship between bases and area yet. That was where the joy was coming from — that also means that they were thinking about the discovered relationship for comparatively little of the time spent on the activity.
As I argued in the original post, that’s OK for me. It was fun and beautiful, and kids should have a chance to articulate slippery patterns and feel the pleasure of discovery. That’s part of math that I enjoy sharing with kids.
Anyway, that’s my response to the idea that discovery is more memorable because it’s more meaningful. Ideas are meaningful when you have time to get used to them, and that’s precisely what gets lost in a discovery activity.
As far as the idea that guided inquiry is surprising, and surprising stuff is more effective: why can’t you structure an explanation to elicit prior knowledge and surprise students? Aren’t explanations sometimes surprising? I think they can be.
Of course, how to craft effective explanations — that surprise and really engage students — is not easy, but it doesn’t get any easier if we don’t talk and write about it. That was part of my argument in Beyond “Beyond Explaining.”
This is all theory, though. What happened in class today, after the weekend, after the memorable discussion on Friday?
I ask them to find the area of a trapezoid and…it’s like Friday never happened.
Hold on what do you mean the same as a triangle?
Could we go over this again?
The only kid who remembered how to find the area of the trapezoid — and I promise this is true, and not just me making up details to annoy advocates of discovery — was the kid who had connected Friday’s lesson to a formula that she once knew.
No guys, it’s the sum of the bases times half the height.
This is sort of surprising and disappointing. Friday’s class was so good! And nearly everybody was involved in the inquiry/discovery/discussion. It felt wonderful and it was fun.
That class, for me, was discovery that’s about as good as it usually gets. And yet it failed to stick over the weekend.
And yet this isn’t that surprising. The kids didn’t get a chance to practice the idea on Friday because we spend the class time uncovering some super-cool math. Kids need practice to remember ideas, and discovery takes a long time. This is just how it goes.
But if it’s not surprising, it’s also not disappointing. It was a lot of fun, and everybody was involved. It’s not what my class is like every day, and it would probably frustrate kids if it were.
So, at least this time, anecdote matches argument. And since we started practicing finding the area of trapezoids today, it’s getting a lot more meaningful for my kids.