“Is my child learning enough math?”

October 18, 2010

It’s a question that bothers many parents, especially homeschooling parents. After all, being responsible for a child’s math education is a heavy load to carry.

There are two major things that can go wrong in math education:

  1. Students can be pressured, over-drilled, and forced to do a lot of symbol manipulation that doesn’t have much meaning to them. They grow to dislike math, and all the practice doesn’t seem to help them actually understand anything anyway. They become bitter towards math as adults, and describe at length the sadistic teachers and parents who ruined the field for them with their insistence on repetitive, empty exercises.
  2. Student get away with avoiding math and never really learn anything at all. (This is a particular risk in unschooling!) Having no real skills, they continue to avoid it as they get older, since, having no experience with the basics, they’re unable even to get started on thinking about more complicated problems. They end up being terrible at it, and describe at length the well-meaning but deluded teachers and parents who ruined the field for them by never insisting that they learn anything.

We have our Scylla and Charybdis in math education, and we run real risks if we over-pressure or under-insist. What to do?

To this question, there is an elegant solution: do math with your child every day, but don’t worry too much about exactly what kind of math you’re doing. Follow your child’s lead, and don’t sweat it if your child isn’t “where they’re supposed to be”; in fact, your main job is to find the kind of math that will be most stimulating and engaging for your child, and do that. If you do math every day and make it fun, you’re ahead of the game. Way ahead.

To do this successfully, we need to expand our notion of what mathematics is to include more than arithmetic. (This is a fringe benefit, and needs doing anyway.) Games, cooking, puzzles, measurement, patterns in art and nature; all these things touch on mathematics, sometimes quite deeply. Moreover, children tend to love mathematics naturally. It’s their nature, and ours, to make order out of our world, to seek patterns, to determine structure. It’s common for children to count for fun, to compare and classify different objects as a kind of game, and to seek mastery in mathematical thought from a very young age.

Think how wonderful this is! We’ve got young children already interested in math! Our primary goal is just to avoid ruining it for them! And how can we do math without destroying the joy of it? Play games, do crafts, cook, garden, role-play as salespeople, build with blocks, take stuff apart, ask big questions and let them ask big questions. And feel free to do arithmetic too–just don’t stress it. Let the child lead the way, and while you can gently nudge them in the direction you want them to go, be aware if they tell you it isn’t the right thing for them.

But Doesn’t My Child Need to Know X by the time they’re age Y?

An excellent question, and here’s the answer: if your child is doing math regularly and enjoying it, you almost certainly don’t need to worry. Now, if your child isn’t really doing anything mathematical at all, and watches TV all day, then you may have a problem. But if they’re engaged, you don’t have to sweat it if they don’t have all the formalities in place.

I’d like to quote from a summary of some studies on this topic.

In these studies formal arithmetic instruction was withheld in one group and administered as usual in another group. At the end of the experimental period, the comparative achievements of the two groups were measured. In each case the experimenter recommended the postponement of “formal” arithmetic…

On the basis of these and other studies the plan of eliminating formal arithmetic instruction from grades one and two, sometimes also grade three, has been adopted by a considerable number of school systems. In some systems there is not even an approved plan of informal or incidental arithmetic. Such a procedure fails to recognize certain very important facts about the studies referred to above. A careful reading of the reports of these four experiments shows that while formal practice on computational processes was postponed in the experimental groups, there was a great deal of use made in these classes of various kinds of activities, games, projects, and social situations through which the child was brought into contact with numbers and given the opportunity to use them informally in meaningful ways.

We have here, of course, the classic way that schools take a good idea and mess it up in the implementation. If you remove mathematics altogether, you end up with kids who can’t do mathematics. But if you postpone formal arithmetic until kids are ready for it (and hungry for it!), you can focus on the more foundational mathematics that they’re ready for and that lays the groundwork for real success in math.

So don’t worry about technicalities, but make sure they’re working with numbers, shapes, games, etc. “informally in meaningful ways.”

Should I use a curriculum if I’m homeschooling?

Sure, as long as it passes the acid test that the child is excited to work from it. If you hear them saying that they hate math, then you need to change things up.

What do we really want here?

That’s a question for you. What do you really want your child’s relationship with math to be? And what it is now?

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