preteaching not reteaching

I've had a revelation.

For two years now a lot of us have been saying reactive teaching is bad. (hit refresh a couple of times if the page doesn't come up)

That's why I've been attempting to teach a separate, coherent curriculum here at home.

Unfortunately, teaching a separate, coherent curriculum here at home is not happening. Christopher is too old, has too much other homework to do, is too defiant and independent, etc. I'm sure there are other parents who could make this work, but seeing as how it is now April and C. has made his way through only 20 lessons in Saxon Algebra 1/2, obviously I'm not one of them.

So I've been teaching reactively all year long. It's been the standard Phase 4 Survivor show, two parents trying to keep their kid alive in "accelerated" math in Irvington. Reteaching at night, correcting C's homework and having him re-do problems he missed (never, ever done at school), pulling problems for extra practice from 10 different textbooks & workbooks, Googling for more problem sets when the workbooks don't have what I need, spending hours creating my own problem sets targeted to the material Ms. K has taught.

Two years of this.

Then, last week for some reason, instead of reteaching whatever it was Ms. K had covered in class that day, I taught the next thing.

Actually, I remember now why this happened.

Christopher came home from school and said they'd started learning about linear equations. For months I had been dreading this moment. The topic is so intricate, with so many moving parts, that I simply could not imagine how on earth C was going to learn linear equations in this course.

C. told me they'd learned slope.

yikes

What about slope, per se? I asked.

Ms. K had taught the formula for finding the slope from two points:

slope = y₂ - y₁ / x₂ - x₁

That seemed like a bit of a strange place to start - shouldn't one begin by showing kids what the slope is on a coordinate plane and how to count squares to determine rise and run, then setting up the ratio slope = rise / run?

I don't know. Maybe math brains do better with symbolic abstractions than with the "visual aid" of the coordinate plane..... ?

In any case, C. had the formula down cold, but of course had no idea whatsoever what it meant and didn't care to know, either. This is one of the many ironies of our situation. The school speaks only of the kids "understanding" math, never of the kids "doing" math, but I'm the one teaching understanding, or trying to. The accelerated math course is purely procedural.

Memorize this, memorize that.

So naturally I sat C. down and made him watch me graph some linear equations; then I showed him how to determine "rise" and "run" on the graph and taught him the mnemonic device I came up with when I was trying to teach myself this topic:

rise / run sounds like "raisin," or "raise" / (r)un

Then I gave him a few graphs and had him practice finding the rise, the run, and the slope on each one.

In my own mind this was just another off-the-cuff session of reactive teaching, nothing new.

C., however, recognized at once that we'd crossed a line. I was teaching something Ms. K had not.

He didn't like it. "She isn't going to teach that! That's not what we're doing!" etc.

But the next day C. came home and, when I asked what they'd done in math, said cheerfully, "Oh, she taught us that thing you showed me last night and I already knew how to do it."

That was a first. In math, C. is never the kid who knows more than the other kids. Except on the subject of unit multipliers, of course. C. is the only child in his class who has been taught unit multipliers outside school. On the two occasions Ms. K has taught unit multipliers, C. has had the satisfying experience of being the most mathematically advanced kid in the room. I owe this to Kitchen Table Math. I'd never even heard of unit multipliers until Dan K brought them up on the old site and everyone else chimed in.

After that I taught unit multipliers to myself (they're in Saxon 8/7) and then to Christopher.

C.'s homework that night was more of what he'd done the night before with me and then again in class with Ms. K, so there wasn't any reason to go over it again, and it was obvious he was going to be able to do his homework quickly.

So I decided to teach the next thing.

I didn't know what the next thing might be in his class (curriculum map, anyone?), but it occurred to me that it didn't really matter. Whatever it was, I'd be close enough.

So I decided to give him some linear equations in standard form and have him practice converting them to slope-intercept form.

Bingo.

She taught that next.


priming

At that point it became blindingly obvious to me that what I was doing is called "priming" by behaviorists, and that, furthermore, priming is what I should have been doing all along.

Priming means, essentially, that you pre-teach the material before the classroom teacher teaches it. It's a classic method in special ed, I believe.

So that's what I'm now doing. I could kick myself for not thinking of this sooner.

Priming is a classic mode of creating the conditions for success, as opposed to trying to ward off looming failure, which is what a lot of reactive teaching and tutoring amount to.

With priming you could probably get tremendous bang for your buck so long as you had a teacher willing to tell you what's going on in class. (It's possible Ms. K would do so, but she can take weeks to answer an email so I probably won't bother asking.)

You teach the material one-on-one, which means you can give your child the exact explanation and practice he needs.

Then, when the teacher teaches the material, your child is ahead of the game, he can easily follow the classroom instruction, and he benefits from a second "dose" of practice. Priming means that classroom instruction suddenly becomes far more effective simply because the student possesses knowledge to build on and consolidate.

The tutoring happens before the student needs it.

We did this for just 3 days in a row last week: Monday, Tuesday, and Wednesday.

On Thursday C. had a quiz that he forgot was coming up, forgot to tell me about, and forgot to study for.

sigh

He finished 10 minutes early and had time to check his answers.

It'll be interesting to see how he did, but I'm expecting some kind of B, and I wouldn't be surprised by a low A.

So this is the new regime.

Priming.

I'm curious to see whether priming -- priming under conditions of zero communication with the classroom teacher, that is -- will be a big improvement over the after-the-fact reactive teaching I've been doing.


preteaching not reteaching
success!
success, part 2
more preteaching results in the offing
preteaching saves the world
preteaching wonders of the world