Friday, January 20, 2012

Algebra Before Breakfast

Anyone who knows me had to know this post was coming.

One of the things I have often heard from people who are afraid of unschooling revolves around something they think kids won't, or can't, learn on their own. With a few notable exceptions, it is nearly always math related. How will they learn algebra? How will they learn calculus?

The underlying theme is that people won't learn these things unless they are forced to, because no person in their right mind would ever be interested in these subjects. They are too hard. Too distasteful. Too complicated. Too... mathy.

We live in a culture that is, for whatever reasons, terrified of math.

If I were to name the One Thing I think schools do the worst job at, the thing I think they harm the most, and/or do the greatest disservice to, it would be math. I don't know whether it makes me more angry, that people are being taught to fear something that is so integral to their daily existence, or whether I am more sad that they are being taught to fear- and avoid- something that is both incredibly useful, and extremely beautiful.

It's simply unfair that this is so.

I hear it all the time, young people (or old people!) who say they "hate math" or they "can't do math."
I don't believe either thing is possible.
I believe those who believe those things, have no idea what math really is.

I saw this fabulous museum exhibit once, years ago. It was a large column, from floor to ceiling, approximately four feet in diameter. It was painted white, except for a small section, on the bottom, that was painted black. That section was about an inch tall.

There was a sign on the column that said "If all of math was contained in this column, all the math taught in schools would be in the first inch."

For people to believe that what is taught in schools is all of mathematics, would be like believing that the alphabet was all there is to every language on earth. Are they connected? Yes. Are they synonymous? No.

The worst thing that schools do to math is separate it out from its purpose. I remember that it wasn't until my third year of college that I suddenly- and I recall the very moment- realized what calculus was FOR. Why didn't they ever tell me that? People struggle to memorize equations without context. Why do that?

One of the most interesting parts of unschooling for us has been the freedom to explore everything in an interconnected way. What this means for math is that as the need came up to be able to figure something out, or predict things, or create things, whatever mathematical concepts were involved became part of that activity. Often, it was all mental math, without writing anything down. Occasionally, it required some sort of method of writing things down, and I absolutely loved watching the kids come up with their own way of conceptualizing and making some sort of written or illustrated representation of their thoughts.

I wish we still had all of those. The pages of prime numbers. The drawing of equally spaced fence posts that led to an exploration of patterns. The charts and graphs. They came and went as they were useful, and then the need for them passed.

The thing is, math is part of everything.
And I do mean everything.
It is about relationships between things.
It is a way to describe things, and those relationships between them.
A way to describe movement.
A way to clearly define things.
A way to predict the future, and to understand the present.
It is a part of everything in nature, and everything that man has created.

Explain to me, how would it be even remotely possible for someone to "hate" all of creation?

I think the biggest difference in how an unschooled person learns these concepts, and in how they are supposedly "taught" in school, is that in school, the method, the written representation, comes first. Understanding, if it comes at all, comes afterwards.

In the real world, the need for the information comes first. The exploration and understanding comes next, and any written method or interpretation comes last, if it is necessary at all.

What good is a calculator, if you don't know what to calculate, or how?
How can you figure out an answer, before you figure out the question?

Learning math by rote makes people able to calculate, when given the information on what to calculate.
It does not help them figure out what they need to know.

I find it much more useful to figure out what it is I need to know.
Look at what information I already have, what I already know, what I can use.
Then use that to figure out the missing piece.
A concept so simple- yet often not specifically taught.

Instead, we have people struggling to apply equations, without knowing how to define the variables.
People who come up with "answers" that logically make no sense, and could not possibly be true, but who don't recognize their errors because they have no idea what the answer is supposed to mean, when they get it.

Crazy making.

I wish there was more of an understanding of the concept of numeracy.
People know what literacy means, and in some places, make an effort to promote it.
Numeracy doesn't get even that.
Instead, it is culturally accepted and popular, for people to claim to hate math. They proudly exclaim this at every opportunity, and it is applauded.

The funniest part is that sometimes, the very people who shout the loudest about hating math, actually use it the most. They are so disconnected from things that they don't recognize what they are doing as being math-related at all.

I'm kind of okay with that part of it.
Sometimes, it's not as important to be able to describe or talk about how to do something, as it is to be able to do it.

The part I dislike is that people are made to have very negative feelings about something they could, instead, find joy in.

So, I say to the people of the world, to the builders, the farmers, the artists and musicians, the hunters and gatherers, to the people who sew clothing, to those who play games, to anyone who walks or drives or rides a bike, to those who run, jump and climb trees, to database organizers and dog groomers, to bakers and waiters, to actors, to writers, to those who make things, and those who make do... whatever your place in the world, do the things you do with a full heart and willing hands.

But don't proclaim that you hate math.
Hate "school math"? Sure. But don't blame math for how it has been profoundly mistreated.

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