Yes, I’m doing a post on unschooling. Don’t get all wound up or anything; I won’t make a habit of it.
The subject of this post is subjects. What is a subject? What constitutes or limits or defines a subject vs. not-a-subject, more-than-a-subject, an ur-subject, a preter-subject, a super-subject, or real life? As a culture we are so used to the concept of curriculum dividing things into discrete subjects that we don’t stop to question the concept and we fall into that style of thinking pretty much by default. At the recent Good Vibrations Unschooling Conference 2011 in San Diego, a dad who said he’d been unschooling for 13 years stated that he felt the need to teach his 13-year-old daughter algebra and he was getting resistance in his house about it.
There are many unschooling-related posts I could write about that statement but here and now I’m gonna talk about *subjects*. The context of this man’s statement was clearly about sitting her down and doing algebraic formulae and cranking through textbooks/workbooks rather than *algebra* as a component of reality. Why limit algebra to such a dry and uninteresting, and useless, niche when it’s so much more than that?
Go out in the yard and build a shed or treehouse or something and figure out [HINT: There could be formulaic *algebra* involved!] how to cut the roof joists. For big fun, put a hip roof on that sucker. Based on your plan, determine how much of each kind of material you’ll need. Now, that’s algebra. Ya know what else is algebra?
We’ve had the following actual (approximately) conversations in our house.
Algebra, in the generally accepted (limited) sense of that word as a curriculum subject, is a way to discover something that’s unknown by using information which is known. For example, about 200 years B.C., Eratosthenes calculated the circumference of the earth with great accuracy using some very simple measurements and calculating from them to determine the full circumference of the earth. (As an interesting addition, he also calculated the earth’s axial tilt, again, very accurately.) Now, a curriculum maven might put that in the subject of geometry. Fine, be that way. To me, it’s all of a piece and *algebra* includes the *history* (as well as other *subjects* which we’ll get to) of calculating unknowns, which in this case, I find pretty fucking amazing. That’s 2200 years ago. Without Googling it, can you think of a way to calculate the earth’s circumference just by being out and about in the world today? And old Eratosthenes had never even taken a class in algebra, or geometry, or calculus. Poor bastard didn’t even have a slide rule, much less a calculator, much less that wonderful series of tubes known affectionately as the interwebs.
A later conversation about *algebra* and history and Eratosthenes and faith vs. science and a whole bunch of other *subjects*, had us talking about Columbus. About 1700 years after Eratosthenes used straightforward, factual measurements to calculate the circumference of the earth, the religious fanatic Columbus decided against Eratosthenes’ conclusions because his Papally-vetted math used different values, which made the circumference much smaller than Eratosthenes’ original calculations (which were accurate), and his religious texts told him that the earth was 6 parts land to 1 part water. [N.B. As we now know, it’s more like 1 part land to 3 parts water.] Relying on these two incorrect axioms, Columbus concluded that he could reach Asia by sailing West and get there safely using the maritime technology available in his time. Why was Columbus so determined to ignore Eratosthenes’ calculations?
As we know from our study of *algebra* (or history or economics or politics or something), Portugal was the big dog in the Asia trade in those days. They were the guys who knew the sailing routes to Asia going East around the bottom of Africa. It was a long and perilous voyage but the payoff was huge and Portugal was fat and happy. The rest of Europe was jealous. They all wanted to have their own pipeline to the wealth of Asia. Columbus was one of many individuals, and governments, who wanted to cash in on that. Columbus finally got the Spanish monarchy to throw him a few bucks and some old boats. You can readily assume they figured it was a cheap investment. If he sailed into oblivion, no big loss; but if he actually made it, HUGE payoff.
See how interesting *algebra* is?
As we know, Columbus ran headlong into the Bahamas before he could get lost across the actual distance from Spain to China in sea miles if there were no landmass between the two. Columbus was extremely lucky in that the maritime technology of his time would not have gotten him across those distances and our current knowledge of *algebra* (or biology or medicine or something) informs us that they all would have died of scurvy even if their food and water and ships had lasted. Fascinating.
I love algebra!
And while we’re talking about the timeframe of 500ish years ago and sailors finding their way, one of the calculating aspects of algebra for them was limited by the lack of accurate time-keeping when determining longitude. The British government, for one, offered immense cash prizes for the invention of an accurate chronometer which would survive the rigors of a long sea voyage and allow navigators to determine a reasonably accurate value for their longitude. I guess that’s the political or financial part of *algebra*.
It’s probably time to do some algebraic calculations now, students. Problem #1: If the population of the Bahamas before Columbus was 40,000 and the Spanish took them as slaves to work on Hispaniola at the rate of 2,000 per year, how many years did it take before the Bahamas became unpopulated? For extra credit, if the Bahamas remained unpopulated for 130 years after that, when did repopulation with African slaves to work plantations there begin?
The ecology part of our *algebra* also tells us that the early explorers described the Bahamas as lushly forested. They were denuded during the plantation period (Remember the African slave question above?) and remain so to this day. Hmmm, is this the sociopolitical-ethical part of *algebra*?
Shit! Sometimes *algebra* is kinda depressing. No wonder students dislike doing algebra problems. If a train leaves Seattle at noon doing 60 mph and I’m not on it, why the fuck do I care what happens to it? It can crash into the one leaving Chicago at stardate 69.666 doing ludicrous speed, or even plaid, for all I care. If you’re worried about it, send Denzel Washington after that motherfucker. I saw that movie. He can do it. Hell, he has the new Captain Kirk to help him. How can they *not* succeed?
Sorry, I got distracted. We were talking about algebra in all its radiant forms and glory.
I love algebra! Ask anybody who attended the Sunday SSUDs meeting at Good Vibrations, they’ll tell ya. But “subjects,” nah, I’m not so interested in subjects, unless maybe there are verbs and objects to go with ‘em. Of course, the verb might be intransitive, then what's the object? That's ok. It's all algebra.