Problems that are too hard

I am self-conscious about homeschooling. It's not something I would have thought to attempt, if it were just me. I believe teaching, like any skill, improves with practice and study; and I have neither practiced nor studied teaching young children. I think most kids learn more when they spend more time studying; and my six-year-old spends a lot less time “at school” than I did at his age—by a factor of five or more. (On the other hand, when he is at school, he is studying.)

But it has been fun noticing things that I can do as a homeschooling parent that wouldn't work at all in an ordinary school.

My favorite is that I am free to pose problems that are too hard.

The kids have school when I'm at work, but I write out a lot of their schoolwork in advance. One of the problems I recently posed for J. is this: I have a box that does some kind of arithmetic. If I put in 7, out comes 3. Similarly 3↦7, 2↦8, and 1↦9. What if I put in 5? (Of course, anything or nothing might come out, but we can learn that lesson another time.) This turned out to be baffling—but that's OK. It will sit in J.'s binder for days, weeks, or months, until one day he cracks it. I don't think he'll crack it by accident but rather because he tries harder or because he develops a better understanding of how addition and subtraction behave. I think it'll be pretty gratifying, and he'll have earned it.

J. likes puzzles. In that regard, at least, his childhood will be a little like mine. Only without the answers.

Homework

Earlier this year I suddenly remembered being taught in school to answer questions of the form “What is the difference between a delta and a wetland?” by copying the definitions of the two terms out of the book and putting the word while between them. Imagine writing this out in cursive on notebook paper:

A delta is a low triangular area of alluvial deposits where a river divides before entering a larger body of water, while wetlands are lands where saturation with water is the dominant factor determining the nature of soil development and the types of plant and animal communities living in the soil and on its surface.

...times twelve or so.

Looking back on it I have to wonder how on earth this happened. The event cries out for an explanation. What would make someone do this to a roomful of kids? Was it a case of perverse incentives? Incompetence? Or straight-up cruelty?

Another obvious question (if you're in my shoes) is if such a thing could possibly ever happen to a home-schooled kid. Sure it could. Parents can be incompetent too. Or cruel.

I try to be humane—I won't be committing this particular atrocity—but there are several things about homeschooling that give me pause. There are no good ways to measure whether things are going well. Finding out what I could be doing better is hard. As far as I can tell by searching the Web, not many people like me are doing this; or else they are all as strapped for time as I am. Most fundamentally, I don't know what I'm doing.