reactive teaching

We probably should call this page things we think we've learned.

We are feeling our way, and one of the main reasons we started Kitchen Table Math was to learn from anyone willing to share his or her experience and observations.

That said, one thing we think we are learning is that reactive teaching seems often not to work -- or, at least, not to work as well as we'd like.

This is a bold claim, because reactive teaching is exactly what most parents and, I assume, most tutors do when they work with children on math.

We try to re-teach the material that our children didn't grasp in class. ('Re-teaching' is a formal term in education.)

That was certainly my plan when I set out to re-teach Christopher the Unit 6 material he had failed to learn. I had no intention of launching into an entirely separate, homeschooling-on-the-side venture.

I ended up teaching a separate curriculum here at home (Saxon Math Homeschool Edition) only because I wanted to qualify Christopher for the advanced math track, and to do that I had to find and use a coherent curriculum.

But then things went so well that I began to wonder whether a lot of people ought to be doing this.

This is just my experience, obviously.

But I think it's 'real'; I think the same thing would happen for other parents, working with their own children.

Christopher is thriving. My neighbor, a clinical psychologist, gave me her observations the other day. Her son has always been in 'Phase 4' math, which is the advanced track (until February Christopher had always been in Phase 3) and is a year and a half older than Christopher.

So one afternoon she gave the boys a problem to do that should have been over Christopher's head (and I think was over his head--I'll have to ask her).

She said Christopher approached the problem with confidence. He was assertive. He dived right in, and -- if I'm remembering correctly -- he wasn't deflated when he found out he couldn't do it. He did the parts of the problem he knew how to do, then listened to her explanation of the parts he couldn't.

This is what I'm trying to get at.

Teaching Christopher my own separate curriculum, here at home, hasn't just boosted his grades. It has changed his relationship to mathematics.

It's as if Christopher is in charge of math, where before math was in charge of him.


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Now I think parents should have teach-your-own-curriculum-at-home as an option on the menu.

These are the advantages I think we are experiencing:

1. It's much easier to teach a curriculum that is designed to be taught by a parent in the home than to try to 'co-teach' the curriculum your school is using. This is true even when you own a copy of the school textbook, as I do. I study each Saxon lesson along with Christopher, and I virtually never find myself stumped.

2. I think it's possible that teaching a second curriculum in the home may help a child develop more flexible knowledge of mathematics. Chinese teachers say it's essential to teach math content in more than one way, and when you're working with a separate curriculum, almost by definition you are teaching the same material in more than one way. The school's way, and your way.

3. Few American schools use a coherent mathematics curriculum. I'm not sure such books even exist. It's just not the way the textbook business operates in this country. Thus far I've found at least two coherent textbooks available to the home market: Saxon Math and Singapore Math. (There appear to be several others, as well. I haven't seen them, so can't write about them.)

4. Teaching your own curriculum seems to 'empower' everyone, including your child's teacher. Teachers have a near-impossible task. They must teach math to children without the benefit of coherent textbooks, and without the benefit of release time to work with colleagues in group lesson study. When a parent steps up to the plate, the teacher has a partner. At a minimum, he or she knows that if you've been teaching your child Saxon Math 6 days a week and he still can't find an equivalent fraction (that won't happen!) your first thought isn't going to be, What's the matter with that teacher?

5. Teaching your own curriculum takes you out of the helpless-parent category. You are doing something; you are teaching your child math. And you are succeeding! This has to be good for children; I'm sure of it. Harold Stevenson reports that Asian families see math achievement as the result of hard work, while Americans think math achievement comes from inborn talent and ability. When you teach your own curriculum you make yourself a little bit 'Asian,' and that's a good thing.

MathInTheBlood
ReactiveTeaching
NowThatWereBothHere

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