During the pandemic quarantine, I decided it would be cool to train myself to do a handstand. So I started spending a few minutes each day trying to do handstands. I would kick my feet up and try to gradually kick them a little higher and hold them there a little longer. The best way to teach myself to do a handstand, I figured was to just start doing them until it finally worked.
Turns out, it isn’t. The way to learn to do a handstand is to regress and progress. You don’t start out doing the actual handstand  you start out doing a regressed version of it, then progressing into a slightly harder version, then a slightly harder version, until you can do the real thing. Here is a 20second video showing a particular progression that has three preceding moves to learn before the handstand, and then even a level to proceed to beyond it. This week in math, my curriculum calls for me to teach my class how to solve an algebraic equation like, say, this one: 6(2x + 1) – 3 = 4x – 5 The best way to teach this, math curriculum would tell you, is to spend a few minutes a day showing them and reviewing the steps to do this. Each time we practice, it’ll feel a little better. The best way to learn to solve an algebraic equation like this, one would assume, is to just keep practicing it until it finally sticks. Actually, I’ll bet it isn’t. The best way to learn to solve a complex algebraic equation, I’d wager, is probably more like the best way to learn a handstand  regress and progress. Before you can solve an equation like the one above, you'd need to be able to solve one like this:
But that isn’t how the curriculum works. The curriculum says that in the grade I teach, students learn how to do the last one (or two). Why start there, you’re probably asking? I’m glad you did, and there’s a perfectly logical reason.
They were supposed to learn all the other ones last year. And isn’t that, my friends, how math becomes terrible? “This year, you have to do a handstand. You were supposed to learn all the previous steps last year. So this year, it’s handstand from the start.” I’m using a specific math skill to make a point, but the truth is, this is how math buries kids every year. It builds upon what you learned last year. And if, for whatever reason, you didn’t learn it last year, or you forgot it, well too bad. This is where we’re starting, so you’re starting with us. Learning math should be more like learning a handstand.
I think everybody comes out of that doing better handstands and feeling better about fractions.
A lot better. The only small problem is that expecting a teacher to be able to regress and progress every student in his or her class in every math strand as far back or as far forward as is necessary is completely unreasonable. Oh yeah, that. Great idea, but it won’t work the way the system is set up. So throw out the idea. Or, change the system. When I talk about “the system,” I mean the general way a math class (and every class) is set up. The system works like this:
Here is a great video of Graham Fletcher explaining how the fractions strand progresses from kindergarten through 4th grade.
Something I hope you noticed is that the progression of fractions in this video is just like the progression of moves in the handstand video earlier. If you take out any mention of “grade level” from the system, this shows how understanding a critical strand of math progresses from the very beginning to the very end. Learning math, it turns out, is a lot like learning to do a handstand. If a student was to drop into a 4th grade class and start learning fractions there, it wouldn’t work. He wouldn’t have learned the skills prior to fourth grade that what he’s learning now is built upon. He doesn’t need to start learning fourth grade fractions just because he’s the age of a fourth grader. He needs to regress back to where he can comfortably start, then progress, just like I did when I was learning to do a handstand.
My school manages to teach math to about 1,200 kids with 10 “regular” education teachers. Broadly speaking, that’s 120 kids per teacher, or 4 classes of 30. Each of these teachers is assigned to teach an entire grade level of math  all five of the strands listed above  in either 6th, 7th, or 8th grade to their 120 kids. The numbers for a single teacher works like this: 5 strands of math, covering 1 grade level, in 180 days, for 120 kids. As the system always does, everything is based around the agebased grade level of the students.
In doing so, there isn’t room for regression or progression  everything is about the grade level. The teacher in each grade level only knows and teaches within that one grade level for each strand.
What if we shifted that, and instead of a teacher focusing entirely on one agebased gradelevel, he or she was focused on one multiyear strand of math? For our ten teachers, that would mean setting it up like this:
Let’s just say I teach the algebra strand. I get 7 weeks with a group of kids (still 120 over 4 class periods) to regress and progress them as far as possible within that strand.
Rather than being an expert on five strands of math (all the 7th grade ones), I’m an expert on three  the 6th, 7th, and 8th grade algebra strands. Rather than starting everybody in one place and limiting everybody to one ending, I can regress students to where they need to start and carry them as far as they can go  different for every student. How does that get managed instructionally  teaching different levels to different students on the same day? There are already schools experimenting with this structure  particularly in math  with great results. I am in the midst of experimenting with this structure for the very algebra skill I described earlier. I prerecorded a series of lessons spanning from 6th gradelevel through 8th grade on this skill, and I assigned students to begin at different places depending on their readiness, then allowed them to selfpace. How’s it going? In short, a whole lot better than if I just threw everybody into the current grade level with no regard for what they learned (or didn’t learn) last year. Some students reached the prescribed "grade level" finish line in under two weeks. Some are going on their fourth. But here’s the real payoff  everybody truly understands the skill at the level they’ve reached. No one has wasted any time floundering with a level of the skill they aren’t ready for.
At least 45 are going to make it to an algebra handstand this year, and the rest will be ready to do one in short order next year, which is still on schedule.
Here's the craziest thing  I truly feel like if I had started this with them in 6th grade, every single one of them would have met the 8th grade standard by the end of 7th grade. Based on what I saw, nearly every student made two grade levels worth of progress in one year’s worth of time. It wasn’t the same two grade levels for everybody, but that’s still a lot of progress. Do that for enough years in a row, and just imagine where kids end up, even if they start out “behind” for their age; rather than miserably fighting through (and not mastering) one year’s worth of math they weren’t ready for, if properly regressed, they comfortably move through two.
Maybe we should buck the system.
Maybe learning math should be more like learning a handstand.
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About MeI'm an awardwinning teacher in the Atlanta area with experience teaching at every level from elementary school to college. Categories
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