Tuesday, November 17, 2009

The Usual Crisis of Faith

Several things happened all at once. Or several questions came up, I suppose I should say. One was on the matter of giftedness and its meaning. The next was concerned with the learning of mathematics. The last was about laziness. All of these issues are interconnected in the heart of the unschooling parent, or anarcho-parent, as I am calling myself these days.

Giftedness is but a label, used to distinguish between the varying needs of children/people in institutional environments so as to formulate proper instruction. In the mind of the anarcho idealist/cynic, all that amounts to in the long run is the continued servitude to the system itself. The only reason the labels are necessary is to provide the specialized instruction. With instruction in itself debatable in value, methodology can hardly be determined as appropriate. Right?

Then the matter of learning mathematics and the possibility of never needing them (or at least, higher math) came up. Someone said they felt as though learning higher math was absolutely helpful and necessary so as to understand relevant tasks in life like how to create a budget, create one's own sewing patterns or understand the patterns of others. In this sense, the formal training of higher mathematics was claimed to have empowered one's creativity. Having watched my children build with Lego, K'Nex, and having created my own insane bits of cloth and whatnot without using formal written articulations of geometry, I argued that really the opposite is true: that creativity can empower an understanding of higher mathematics.

I've been handed similar arguments before - that learning basic mathematics and some higher math (algebra, geometry, trigonometry) by rote eventually enables us to understand some of the beauty of advanced mathematics. I thought of an article - which I admittedly never got all the way through - discussing the sorry approach of traditional math education and how it robs us of a deep understanding of the beauty of higher math.

At this point, I lost sight of my argument altogether. Then I read this article illustrating the concept of "by the time you need it, it's too late." And here the crisis set in.

What if we do need to understand how to articulate mathematics? What if I - oh! I mean they of course! - miss the opportunity to discover that naturally (despite Aleks' continued demonstration of his ability to readily understand and use at least basic math concepts)? What if my children count on their fingers or feel ill at ease with numbers or refuse to do their own taxes? What will that mean?

In the midst of this crisis, I confront what I fear is my own laziness - my own desire to do as little as possible, to find easy ways out. I hear other parents comment on the laziness of their children. I see them mentioning fearing the state of their future adult children - the sorry state of their apartments, their inability to finish college or find a spouse. Surely I must be exactly what they fear: the gifted child highly skilled in getting around doing anything nasty or unpleasant, dependent on a man, college dropout...

My husband made a joke the other day about how I'd better not divorce him as I bring so many demands to the table: I don't work (at a paid job), I like sleeping in, I don't cook, and I like to go out a lot. I of course rolled my eyes and said, "yeah, I bring nothing but demands!"

If I take all these simultaneous concerns together and seek out their underlying basis, the question becomes, what is laziness? What constitutes laziness? What do we really need to be doing? What do human children actually, fundamentally require for successful adulthood? What is my definition of my children's success? What the hell am I doing here?

Here is where I struggle to reconcile what I feel to be true, what evidence supports, and the culture that provides my constant context. I struggle even to articulate these matters simply and succinctly. I could babble on for days or weeks - or years if you've ever read my blogs! - trying to determine what this even is, let alone what to do about any of it.

That said, I think that laziness is a perception. That the idea of it comes from a culture of over-work, of under-pay, of implied (forcibly, subversively) scarcity, - a culture where we lock up the food and work people to the bone, devaluing and undermining the invisible labor of raising future workers and creating instead systems that teach but do not nurture, which spend 99% of their effort on maintaining control in a transparent attempt to sustain the institution itself in an everlasting vicious cycle.

I sense this to be true in every turn that I take. The more I learn, the more I loathe the web I feel ever-trapped in. The urge then is to reject it all and run far away. But there's a catch: I am a product of this culture. I cannot divorce myself from this context. I am in some ways merely the sum of my experiences, all of which have been of this culture, this insane capitalist concoction, born of dominance and endless thirst. I too thirst. I am incapable of wholly rejecting every inch of it.

Rejection of everything, too, leaves me directionless and with a confused feeling where I grope around for evidence to support the decisions I make and find little in the way of proof. Therefor I rely on a bizarre, unscientific test: If I lived in the woods, with other people, in a hut, writing cuneiform in the dirt or whathaveyou instead of blogs, what would I and my children need? Not written higher mathematics, in all likelihood.

However, regardless of the need (or lack thereof) of higher mathematics articulated in written form, I still find them somewhat useful in this life; in this context; now. Now is where my children live, unfortunately. Thus my own unscientific test fails me. And my confusion and fear dig deeper.

What to do then? Contrive ways in which we might trick the children into learning higher math? Have faith that Lego and Magformers are enough for now? Or do I do as I usually do and rely on the conversation to lead us there, encouraged onward, no doubt, by my fears and worries pressing in on me in years to come? Is this, then, but finding faith in the constancy of uncertainty?


Mel said...

*giggles with a hint of hysteria*

yup. what you just said.

I (surreptitiously) use my fingers to count, am generally uneasy around numbers and pay a lovely man to do my taxes. Does that leave me lacking? Not as far as I can tell...

I'm constantly at odds with the 'am I doing enough?' thing? I felt a bit guilty relying on an Irish mouse to teach my kid to make change...but that's how she learns, that's how she WANTS to learn so that's how our conversation evolves and the solutions we've found to our various and assorted challenges....

YES - to the utter uselessness of labels..I went through school in an *enriched* program which only served to teach me to jump through more elaborate hoops to do as little as possible to achieve the best result....the damage had long been done before they slapped that little tag on me...

if it makes you feel any better whatsoever....I've done the higher math and simply do not see the use for it unless you're a physicist or something, or else just like gadding about with numbers for kicks...*shudder*...

and this has become an essay which could easily drone on for much longer...but I shall end here...


em said...

Math prowess never mattered to me until I needed it and didn't have it. In college I was constantly thwarted by my lack of math skills and it dictated what fields I could enter. I wanted to work in GeoEnvironmental Engineering and didn't have the math chops, which sucked. Now I am a PhD in Environmental Economics and still use calculus everyday and WISH that I had done more math at a younger age. Yes, you can take the classes and learn later, but it is rough.

This is not to say that it is right for everyone, but to me math is the only universal language and the a completely necessary component to many things in life. Can you survive not knowing calculus or linear algebra, absolutely. But can it also can open many doors.

I am not sure exactly wanting to do engineering trickles down to the math that a child has to learn, but for me, the excitement of math and patterns came at a very late age. Now I wish my parents had drilled a bit more into me at a young age and I know that I will make math a very integral part of my daughter's life.

Anonymous said...

It is rather interesting for me to read that blog. Thanx for it. I like such themes and everything that is connected to them. I definitely want to read a bit more on that blog soon.

Rebecca said...

Ah, you've hit my doubt place, too. I'm one of those people who could call themselves an unschooler... except for the math. Ahem.

However... if your child is demonstrating "his ability to readily understand and use at least basic math concepts" at his tender age, he's likely just fine.

I've heard a number of first-hand anecdotal stories from people who did not *make* their children do formal math learning when in the single digit ages... and their kids were fine picking up the basic skills, etc. when they were older. It does come easy to those adolescents (when they want to learn it) if it's done in a way that make sense to them. They can conceptualize complexity much easier than younger children - and it's easier for them to memorize facts, too.

Of course, I still do something semi-formal with my own child. But he likes it and uses it (in playing games, etc.). He's a puzzle-solver anyway so math is a fit for him.

I think that if your boys show interest in math-related things at any point, then it's fine to support that interest. Like this guy's dad did. I love this bit:

"Q. When did you become interested in mathematics?"

"A. It started from playing video games when I was quite young. I asked my dad how people wrote those games, and he said you first have to learn how to write a computer program. He got hold of some books on programming so he could teach me, and soon I was reading the books on my own. After a year or so of that, he said, "If you want to be good at computers, you have to be good at mathematics." So I said, "OK, let's learn some mathematics." I started with a high school algebra text, and things took off from there."

Of course, this guy is a math whiz type... but he was meant to be (it's in the wiring) and he figured it out.

So I suspect your guys will be okay if you just let them cruise through this stage of childhood without being overly concerned (or beating yourself up with that awful L-Word). If you really can't stand it when they are 10 or so, then talk to them about it and figure it out. Until then, the spatial relationships they are learning about through playing with Lego or K'Nex will provide them with some elegant underpinnings for any math they may want to do later on in life.

And I know it's much easier for me to type this than it is to live it!!

anna kiss said...

Em - the question that comes up for me with what you're talking about is: how far do you take that? Depending upon what any given child wants to "be when they grow up," different skills would be necessary or not. We can't possibly drill for everything and to me, school proves that that methodology really doesn't work so well. Most of the folks I know who felt totally incompetent in math as adults were shamed and punished in their learning as children (and subjected to endless mind-numbing and painful work on it).

The whole idea of unschooling is that when learning is joyful, it is much easier to do. If I look at my son, he does just that. He plays with patterns constantly, works with money, figures his out needs and points in video games, and draws and multiplies and counts and plays all the time. Math has really been the least of our worries. The discovery for Aleks, at least, was spontaneous and fun.

Sometimes for myself, I'll ask him math problems, but it's a bit of game that we play. More often than not, he's coming to me discussing numbers and trying to figure out addition, subtraction, or multiplication. The kid's asked me how much gas was in my tank before, which spawned a discussion of fractions and percentages!

I guess the thing is - if it is true that one should drill for math because there is no other way to learn it, should I also be drilling to make sure he has a good grasp on chemistry or biology or that he can draw? Having not felt confident in my drawing skills was part of what stopped me from going to art school. Chemistry mystifies me and I'll therefor never pursue the hard sciences professionally. Certainly there's more to it than that, but those factors are there.

Then the other thing is, maybe drills aren't the only way to learn this stuff. Maybe we really do get what we need in the way that we need it by following our passions and interests. I've always learned history through art history, for instance. Sitting learning straight history was mind-numbing for me, but learning social history through my interests in other subjects has been fascinating.

It's also been my experience with my children (or child, thus far - Bastian is but four and a different beast altogether) that the basics get covered so deeply and naturally I don't even think about it most of the time. When I get these crises, my mind digs and tries to step back and see what's really happening and learn what they really know. Aleks just gets it. Maybe that's luck. Bastian can't count to ten without help, but his verbal skills are just so different than Aleks'. Everything about him is different and I hardly think that I can predict almost anything at all at four. I guess we'll see. I still don't know what the exact answer is, but these questions have killed me yet!

anna kiss said...

Rebecca - I really don't usually doubt math at all, but this question of drilling as the only way to actually get it was troubling to me. I just don't believe that it's universally true. What worries me is if it's true at all, under any circumstances and providing that it is, if that might mean something.

Rebecca said...


Perhaps somethings do require repetition (is that the same as drilling?) in order to move toward mastery.

I wonder, though, if the learner is engaged and keen and wanting to learn, if it matters?

I don't believe there is a critical period to learning things that are not part of our biological development. That includes math. Music. Art. So many things.

em said...

I guess maybe my comment was not as clear as I would have liked. I don't think that drilling math is necessarily the way to go, I just wish that it has been more of a part of my life in some shape or form at a younger age.

I agree that drilling for any subject that you might potentially be interested in is very silly. It is just that in my experience, math is the key to understand chemistry, physics, economics, statistics, and the algorithms in art and nature.

Though not an unschooler (though I have a 2 year old so I guess up to this point she is unschooled), I agree with child led learning and really embrace a lot of the principals. I personally was just not motivated to embrace math in my life really until college and then it was a monumental hill to climb.

And no, you don't need to teach to a future occupation, but honestly, I feel that knowing math is a critical skill in life that is often overlooked. I have no idea how to work that into a child's life on a daily basis, but it sounds like you have some really great ideas that I might have to poach. Happy Friday.

anna kiss said...

Sorry! I didn't mean to suggest that you thought drills were necessary. It's just that the article said they were and I was trying to tease out what I thought about all of that. Just talking it all through, not necessarily directed straight at you!

I do think there are a lot of great ways to discover math in the world without much formal training.

em said...

Agreed :) Yes math is important, but how do we best instill that knowledge? Have a great weekend, squash in your forecast?!