kitchen table math, the sequel

from Ms. K:

A quick update on Chris – he has been doing well in class. He has begun asking questions in class as well as looks for clarification or a re-explanation. I’ve gone over his homeworks and made corrections. It’s great to see the improvement he’s been making.

This is almost bizarre.

Yes, of course, preteaching is an old and honored technique.....but who would have thought???

Not me.


Rory says...

I am not surprised about pre-teaching working better for you.

I imagine that your brief tutoring gives him enough insight into the subject that when it is presented in class, he can keep up with it.

Before, I imagine that he couldn't quite keep up with the pace of presentation, got frustrated and tuned out. Then when you tried to catch him up, he was mentally discouraged.

Now, you can initially present the concept at a pace that suits him. Now when he sees the teacher present the material, he is saying to himself... "I got this!"

Obviously, Rory is right.

The class presentation is probably just moving too fast for C.; it may be that simple.

And the tuning out part -- is that a boy thing ??

Speaking as a person who has never been a boy, I think it may be. I've talked to at least 2 or 3 moms whose daughters are getting through the Phase 4 class by dint of staying up 'til midnight sweating over the homework. One mom told me her daughter tends to be anxious and is "perfectionistic." She doesn't quit.

That's not what we see around here. Nor have I heard tell of it in my many conversations with moms of boys.

If C. can't do the homework, he closes the book and we don't hear about it. That's why I have to stay on top of things; I have to watch. Every time I forget I have to watch, I end up sorry.


faster?

Maybe, when C. goes to class having worked through the material once, he's already faster.

Or, if not faster, just able to keep up. As Rory says. He's got the jist.

This whole experience is.... I'm afraid I'm going to have to resort to the word "bizarre" again.

The school must see a completely different student from the one we see. Some of you will recall the finds subject matter difficult comment from the Comment Bank that appeared on C's final report card last year re: math.

I'm sure the school considers us the ultimate exemplars of pushy parents who refuse to look reality in the face. (Your child. Not the little genius you thought he was, eh? IMS motto)

But the fact is, C. doesn't find subject matter difficult.

When I'm teaching him math -- and I'm not skilled at teaching math yet, though I hope to become so -- he finds subject matter easy.

When he's teaching himself math, which he's done, he finds subject matter easy.

He's not mathematically gifted; he's not going to be a mathematician when he grows up.

But that has no bearing on whether or not a bright 12 year old can learn beginning algebra.

A bright 12 year old can easily learn beginning algebra.

At some point C is going to "hit the wall," as Carolyn used to say ----- but that point is not beginning algebra.

Nor is it pre-algebra.

I'm having a distinctly unpleasant Big Picture moment.

Our entire country is filled with teachers, administrators, parents, and students who have no clue what material is or is not "hard" -- or, rather, what material is hard no matter how well it's taught.

So....

regular ed = special ed

In special ed, you spend most of your life telling people your kid can do more than they think.

Learn more, do more, be more, etc.

That's your job.

Same thing in regular ed.

You tell me my kid finds subject matter difficult.

I tell you he can do it.

Same difference.

..................

I don't know why people keep betting against parents.

Usually, when I've thought my kid could do something everyone else thought he couldn't, I've been right.

Parents aren't crazy -- at least, not the way educators think we're crazy.

We aren't crazy and we aren't deluded -- how can we be? We live with these kids.

When you live with a 12 year old boy you don't spend a lot of time thinking he's a genius.

In fact, you don't spend any time thinking he's a genius.

No!

The dominant emotions run to anxiety, horror, and chronic low-grade stress (just got word today: thyroid gland kaput!) --- it's not that easy to see how the 12 year old middle schooler becomes the 18 year old college student.

If the mother of a 12-year old boy thinks he can learn algebra in 8th grade and the 25 year old teacher thinks he finds subject matter difficult..... go with the mom.


update: from Rudbeckia

I can assure you that "tuning out" is an equal-opportunity behavior.

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

Two tests after I began my new preteaching-not-reteaching regimen, Christopher has an average grade of 87.7 in his math class.

This is up from a C second quarter, a C+ 3rd quarter.

All from preteaching.

Ed says that with preteaching C. is getting "a second look."

The improvement we're seeing is almost bizarre.

I'm kicking myself for not thinking of this sooner, but otoh I wouldn't have predicted that simply having the second look occur in class instead of at home would have an effect of this (seeming) magnitude.

Plus I'm spending very little time on this -- maybe 10 or 15 minutes at most? I spend only a few minutes demonstrating and explaining the procedure; then C. does 2 or 3 problems, which take another 10 minutes.

That's about it.

I also have him do some practice equations from workbooks. That's part two: I'm having him try to gain speed at the foundational skills he's using in the class problems.


tutors and teachers

It's probably time for me to sit down and study Ericsson's "The Role of Deliberate Practice in the Acquisition of Expert Performance," (easily found on Google) seeing as how it contains this passage:

Research in education reviewed by Bloom (1984) shows that when students are randomly assigned to instruction by a tutor or to conventional teaching, tutoring yields better performance by two standard deviations—the average tutored student performed at the 98th percentile of students taught with the conventional method. Interestingly, the correlation between prior achievement and achievement on the current course was reduced and corresponded to only about 6% of the variance for the tutored subjects as compared with around 36% for students taught with conventional methods.

Apparently we've moved from tutoring to tutorial.

We'll see.


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

C. took another test this week, and came home saying it was "easy."

"Easy," on the last test, translated to a score of 80, which is only 4 points above the 76 he received on the reteaching test prior. Four points is four points; I'll take it. But it's not as large a gain as I'd like to see.

However, that was the test he forgot about and took cold. There's never been a time, in the entire two years he's been in this class, that he could have taken a math test cold and scored an 80.

He studied for the test he just took. Unfortunately, he had to study almost entirely on his own because we went to the candidate's forum.

It'll be interesting to see how he does.

Regardless of his grades, it's obvious that preteaching is absolutely the way to go. I can tell by working with C. that he's getting the material, not struggling horribly with it, not lost at sea -- none of that stuff.


short attention span theater

One of the gigantic advantages of preteaching is that attention lapses in class aren't fatal.

If C. misses a point, or spaces out for a minute, or gets distracted by the other kids (apparently the class is rowdy) he can get back on track because he's already learned and practiced the material once.

My neighbor told me that next year's teacher gives reading assignments in the book.

The kids read the text (in theory), and come to class knowing a little something about the material that's going to be taught.

That sounds like heaven.

With C.'s class, every day can bring a fresh surprise!


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

So last night I taught Christopher how to find the equation of a line given two points.

Today Ms. K taught the kids how to find the equation of a line given two points.

I'm on a roll.


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

Christopher finally got his quiz back, the one he took after I started my brand-new preteaching-not-reteaching regime.

He got an 80!

This is on a quiz he forgot about, didn't tell me about, and didn't study for.

Just walked into the class cold and took it.

Even better, the other kids didn't blow him out of the water. A couple of the class stars got scores in the 80s.

This is the way to go.

I'm also having him do KUMON-like practice every night to build speed. For whatever reason, he's not giving me vast quantities of grief about it. I've said "You need speed" so many times (scroll down), and related the need-for-speed to athletics so many times....maybe it's just sunk in.

Spaced repetition, the Key to life. Water wears away rock.

Also, it's a bit easier getting a middle school kid to do extra math if you say, "Go solve these 10 equations as fast as you can."

Makes the whole thing sound less onerous.

I've been using two workbooks:

• Instructional Fair's Algebra 1 ISBN 0-7424-1788-3
  
• Skill Builders Algebra 1 ISBN 1-93221-010-5

This is an amazingly low-stress way to remediate the school.

Extraordinary.

Just sorry it took me two years to think of it.


preteaching not reteaching
success!
success, part 2

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