I’ve said before I’m an isolationist whose methods are more reform than traditional. I try to teach real math, not some distorted form of discovery math, but I also try to avoid straight lecture. I want to make real math accessible to the students by creating meaningful tasks, whether practice or illustration, that they feel ready to tackle.
I can’t tell you that students remember more math if they are actively working the problems I give them. Research is not hopeful on this point (Larry Cuban does a masterful job breaking down the assumptions that chain from engagement to higher achievement.) Will my students, who are often actively engaged in modeling and working problems on their own, retain more of the material than the students who stare vacantly through a lecture and then doodle through the problems? Or six months from now, are they all back to the same level of math knowledge? I fear, I suspect, it’s the latter. I think we could do better on this point if we gave students less. Not Common Core “less”, in which they just shovel the work at the students earlier. But a lot less math, depending on their ability and interest, over the four year period of high school.
Four plus years of teaching has given me a lot more respect for the sheer value of engagement, though. I believe, even if I can’t prove, that the kid who works through class, feeling successful and capable of tackling problems that have been (god save me for using this word) scaffolded for his ability, has learned more than the kid who sits and does nothing. Even if it’s not math.
Anyway. There comes a moment when the teacher says to the students, “go”. Best described as release of responsibility, whether or not a teacher follows any particular method, it’s when the teacher finishes the lecture, the class discussion, or simply handing out the task the students are supposed to take on without any other instruction.
It’s the moment when novices often feel like Mork. Done poorly, it’s the lost second half of a lesson. Done well, it’s the kind of moment that any observer of any philosophy would unhesitatingly describe as “good teaching”.
I started off being pretty good at release, and got better. That is, as a novice using straightforward explanation/discussion (I rarely lecture per se) or an illustrating activity, I could usually get 30% of the class going right away, another 40% doing a problem or two before asking for reassurance, and convince most of the remaining 30% to try it with explicitly hand-crafted persuasion. And for a new teacher, that’s nothing to sneeze at. Sure, every so often I let them go to utter silence, or a forest of raised hands, but only rarely. (And every teacher gets that sometimes.)
I remember pointing out to my teacher instructor, however, that I spent a lot of time re-explaining to kids. He said “Yeah, that’s how it works. You’re going to get some of them during the first explanation, some of them while helping them through the first task….” and basically validated the stats I just described in the previous paragraph. I still think he’s right about the fundamental fact: teachers can’t get everyone right away.
But all that re-explaining is a lot of work, and it leads to kids sitting around waiting for their personal explanation—and no small number of kids who then decide why bother listening to the lecture anyway, since they won’t get it until I explain it to them again, with of course the stragglers, the last 30%, screwing around until I show up to convince them to try. Of course, I went through (and still go through) the exhortation process, telling them to ask questions, “checking for understanding”, and so on.
And it absolutely does help to make the “release” visible to the kids, “Okay, let’s be clear–we are wrapping up the explanation portion, it’s time for work, and I WILL NOT BE HAPPY if you shoot your hand up right after I say ‘go’ and whine about how you don’t get it.”
This works. No, really. Kids say “Could you go through it one more time?” before I release them, particularly after I’ve put them “on blast mode” for saying “I don’t get it” when I show up at their desk to see where they are.
But I focused on release almost immediately as an area for my own improvement. As I did so, I began to understand why release is so hard for teachers, particularly new ones.
We overestimate. We think, “I explain it, they do it.” We think, “I gave them instructions they can follow.” We think, “This is the easy part” and are already mapping out how we’ll explain the hard part.
And then we say “Fly, be free!” and the class drops with a splat. Burial at sea. Wash away the evidence.
We aren’t explaining enough. Or they aren’t listening. We aren’t giving clear instructions. They don’t read the instructions. “Too many words.”
What I have discovered, over time, is that I must halve or even quarter what I think students can do, and then deliver it at half the pace. With this adjustment, I can release them to work that they will find challenging, but doable. This is the big news, the news that I pass on to all new teachers, the news they invariably scoff at first and then, reluctantly, acknowledge to be true.
But what I have begun to realize, again over time, is that by first “dumbing it down”, I have slowly increased the difficulty and breadth of coverage I can deliver. Not a lot. But some. For example, I now teach the modeling of inequalities, modeling of absolute values, and function operations, in addition to modeling linear equations, exponentials, probability, and binomial multiplication. I don’t think my test scores have increased as a result, but it makes me feel better about what my course is called, anyway.
In mulling this development, I have concluded, tentatively, that I’ve become a better teacher. Or at least a better curriculum developer. That is, I don’t think “dumbing down” itself has led to my increased coverage or my students’ ability to handle the topic. But I’ve gotten better at the “release”, at developing explanations and tasks that allow the students to engage in the material.
It’s possible I’ve been unwittingly participating in a positive feedback loop. As I get better at the release, at correctly matching their ability to my tasks and explanations, the students are more likely to listen, to try to learn, to dig in to a new task and give it a shot. So I get bolder and come up with ideas for more complex subjects.
I dunno. Here’s what I do know: effective release requires willing students. The able students are willing by default. The rest of them need something else.
Put it another way: the able students have trust in their own abilities. The kids who don’t trust in their own abilities need to trust me.
No news there, that trust is an essential part of teaching. But I’m only now considering that my lesson sequencing and content might be an essential element in building the trust the students need to take on challenges.
Eighteen months ago, I wrote an essay that captured the moment when teachers realize that their students don’t retain learning. They demonstrate understanding, they pass tests demonstrating some ability, and then two weeks, three weeks, a couple months later, it’s gone. (Every SINGLE time I introduce completing the square, it’s a day.)
The “myth” essay describes what happens after release. That is, after the teacher realizes that students didn’t understand the lecture, didn’t understand the worksheet, are goofing off until the teacher comes around to give one on one tutoring, after the teacher does the additional work to get the instruction out, the kids seem to get it. And then forget it all completely, or remember it imperfectly, or rush at problems like stampeding cattle and write down anything just to have an answer.
So consider this the companion piece: the front end of classroom teaching to the myth’s back end.
But in fact, it’s all part of the same problem. And, as I said in the first essay, teachers tend to react in one of two ways: Blame or Accept. Many accepters just skedaddle to higher ability students. I’m teaching precalc this year and have some interesting observations on that point. But leave that for another essay.
I’m an accepter:
Acceptance: Here, I do not refer to teachers who show movies all day, but teachers who realize that Whack-a-Mole is what it’s going to be. They adjust. Many, but not all, accept that cognitive ability is the root cause of this learning and forgetting (some blame poverty, still others can’t figure it out and don’t try). They try to find a path from the kids’ current knowledge to the demands of the course at hand, and the best ones try to find a way to craft the teaching so that the kids remember a few core ideas.
On the other hand, these teachers are clearly “lowering expectations” for their students.
And that’s me. I lower expectations. I do my best to come up with intellectually challenging math that my students will tackle. I don’t lecture because the kids will zone out; instead, I have a classroom discussion in which the kids live in some terror that I might call on them to answer a question, because they know I won’t ask for raised hands. So they should maybe pay attention. I have no problem with students taking notes, but for the most part I know they don’t, and I don’t require it. I give them a graphic organizer with key formulas or ideas (or they add them). I periodically restate the critical documents they should save, tell them I designed the documents to be useful to them in subsequent math classes, double check them periodically to see if they have the key material.
Dan Meyer sees himself as a math salesman. I see myself as selling….competence? Ability? A sense of achievement?
Whatever. When you read of those studies showing that math courses don’t match the titles, you’re reading about courses I teach. I teach the standards, sure, but I teach them slowly, and under no circumstances are the kids in my algebra II class getting anything close to all of second year algebra, or the geometry students getting anywhere near all the geometry coverage. That’s because they don’t know much first year algebra, and if you’re about to say that the Next New Thing will fix that problem, then you haven’t been paying attention to me for the past two years.
But at some point, maybe we’ll all realize that the issue isn’t how much we teach, but how much they remember.
Be clear on this point: I do not consider myself a hero, the one with all the answers. I am well aware that many math teachers see teachers like me as the problem. Many, if not most, math teachers believe that kids can learn if they are taught correctly, that the failings they see are caused by previous teachers. And I constantly wonder if they are right, and I’m letting my students down. While I sound confident, I want to be wrong. Until I can convince myself of that, though, onwards.
I began this essay intending to describe a glorious lesson I taught on Monday, one in which I released the kids and by god, they flew. But I figured I’d explain why it matters first.