kitchen table math, the sequel: preteaching not reteaching

Saturday, April 21, 2007

preteaching not reteaching

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

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 saves the world
preteaching wonders of the world

Exo said...

So that's called "priming'? Thanx, now I know what I do...)

Instructivist said...

But doesn't priming require some kind of clairvoyance, especially with Mrs. K?

Catherine Johnson said...

exo - how do you do priming??

Catherine Johnson said...

instructivist

But doesn't priming require some kind of clairvoyance, especially with Mrs. K?

lol!

You may remember my story about a friend who spent her year with Ms. K having a nervous breakdown for that very reason.

It was quite a drama -- I could hardly believe it. She kept trying to get ahead of the game, and she never, not once, managed to predict the game!

She was the opposite of Wayne Gretsky! (going where the ball is going to be)

A couple of things.

Number one, I don't know if you read the post about the parents I know who actually are starting to predict Ms. K's twists, turns, and tests (at least two parents taught Venn diagrams before Ms. K put them on a test without teaching the topic).

It's possible I'm starting to develop "clairvoyance" where Ms. K is concerned.

But number two, as chaotic and fragmented as C's math knowledge is, he does have quite a lot of it.

Look, ma!

Lots of math inside my head!

I guess what I'm saying is that he really does possess quite a bit of "background" or "prior" knowledge and that makes a difference. Even if I teach a different concept within the topic from what Ms. K teaches the next day, he's still going to show up with more prior knowledge than he would have without the preteaching.

And by now more is more; any extra he gets at home he probably can "access" and use in class.

I hope so, at any rate.

We'll see.

Exo said...

Catherine, my son is in K-grade (which makes "predicting" game a bit easier.
In Reading - I teach him using phonics workbooks + make up my own explanations and always refer to differences and similarities in Russian (I make it parallel to teaching reading in Russian) For example, I was explaining vowels and consonants as "girls" and "boys" - just to make him understand the difference in reading 'A" and "I" in words such as "plan" and "plane" - see, there's a "girl" letter at the end?
And he was able to read such words correctly in class (oh, dreaded WL=Balanced Literacy!). The teacher was sooo happy, "Your boy is a natural reader!" He-he.
In math I simply go by the Russian math book for 1st-graders - and we are up to multiplication by 4 now. He is not going to be taught it for at least a year yet (if they will teach multiplication table at all!), but he just loves it. So in this we are ahead of the train.
As other skills - I make him to re-tell stories I read to him. Or create a story looking at the picture. One thing I have to remind myself is to do it in English as often as I do it in Russian.

Catherine Johnson said...

exo

Perfect!

If I had it to do over again, I would engage in pre-teaching in phonics and in math.

C. learned to read "on his own" -- that is, he suddenly began reading a couple of weeks after his teacher told us, correctly, that he was at risk of a reading disability because his handwriting was so poor.

The school uses balanced literacy, which means, in our case, that he did receive some training in phonics and phonemic awareness.

(Apparently 10% of kids who've had systematic instruction in phonics and phonemic awareness "spontaneously" begin to read. I've forgotten the source of that statistic; it's one of the books written for parents about phonics and phonemic awareness. Louisa Moats wrote the foreword, as I recall.)

Nevertheless, I strongly suspect that he didn't receive enough phonics instruction to ward off significant spelling problems.

I was shored up in this suspicion when our district posted online a terrific report on the multi-sensory class for at-risk kids at the K-3 school.

One of the symptoms that a child may be at-risk is difficulty spelling.

Anyway, in spite of the fact that C. did learn to read and his reading comprehension is high, I would teach him phonics. (I may yet do it; I ordered Engelmann's book for that purpose.)

C. learned math very well in K-3, I believe.

However, the Singapore books are so terrific that I'd use them as "real" enrichment.

Anonymous said...

This is fabulous. I've been pre-teaching, but now I have the word "priming" to add to my vocabulary.

In math, I always try to stay ahead of the school curriculum. That way, too, my kids respect what I've taught them first, with lesser regard for the way they learn it in school.

I use pre-teaching in another way, too. I pre-teach social agendas and values. That way, when the same topic comes up at school, they say, "You were right mom, they said it exactly as you predicted. Boy, are they off the wall."

That's much better than trying to fix what they've learned in school, because when it's done in that order, the kid often tries to defend the school.

Pre-teaching, or priming, is quite a useful device for being the teacher in charge.

Dickey45 said...

Check out UCSB Koegel booklets on autism - one is on priming.

Catherine Johnson said...

Right!

That's why I linked to it!

We love the Koegels; they're our gurus.