Learning and teaching…and learning

When we first started homeschooling our kids, Christe and I generally divided our tasks according to our general areas of relative expertise — she took the more scientific and mathematical subjects, while I dealt with the more humanities-oriented ones, especially those having to do with language. But it didn’t always fall out that way, and sometimes we had occasion to cross those lines.

One of the more surprising and delightful discoveries to emerge from this process was that it offered, on occasion, an opportunity to do right what I hadn’t done terribly well the first time around. My high school math career was not a progress from glory to glory: I did pretty well in geometry, but that experience was sandwiched between twin skirmishes with algebra from which I emerged somewhat bloodied and perhaps prematurely bowed. After algebra/trig, I generally concluded that math was not for me (or that I was not for it) and I set a course that wouldn’t require me to take any more of it. I completely avoided it in college — something that I now rather regret.

But a number of years later, after college and partway through my graduate career, I found myself teaching both geometry and algebra to our kids. It was liberating to have the controlling hand on the algebra, and to realize that once I was able to see the overall rationale behind the subject, it wasn’t so hard. From here it seems painfully obvious that the whole point of algebra is to isolate the key variable for which you are solving, and simplify the expression on the other side of the equal sign as much as possible. This is the invariable task in every algebra problem. Why none of my teachers ever made that clear to me at the time is a mystery to me, though in all honesty, I’m not sure whether my failure to grasp it was their fault or my own. In any case, I’ve actually come to like and appreciate algebra after all these years. Do I use it in my daily work? No, generally not: its intersection with Latin and Greek is fairly slight. But I use it just enough, to solve for all manner of things, that I wouldn’t be without it.

It was not in algebra, however, but in geometry that I encountered my most humbling but exhilarating experiences as a homeschooling dad. We had a copy of the old Jurgensen, Brown, and Jurgensen geometry book — a traditional, solid member of the Dolciani family of texts that many of my generation used in high school. We did not own a teacher’s manual. Most of the problems in the book were reasonably straightforward, once you knew how to tackle geometry in general, and, as I said, I was fairly good at geometrical thinking. A minority of them, however, were considerably less straightforward, and a handful just stopped us — my high-school aged daughter Mary, her mathematically precocious younger brother David, and me — in our tracks. There were a few of them that occupied us for hours over the space of several days, while our progress through the text came to a standstill.

I would be lying if I didn’t admit that I was occasionally afflicted with self-doubt on these occasions. What, I wondered, am I doing to my kids? Don’t they deserve someone with more expertise here? And doubtless in some situations they would have benefited from that expertise. But they did ultimately become very good in geometry anyway, and they learned into the bargain another lesson that I couldn’t have predicted or contrived, but that I wouldn’t trade for anything. We did, I think, eventually come up with a workable solution in each case, but the most important lesson Mary and David got from the experience as a whole was a lesson in gumption. They learned that it was possible to be stuck — not just for them to be stuck, but for us all to be stuck — and still not give up. I wasn’t holding the right answer in a sealed envelope or a crystal box, ready to produce it when I figured they’d evinced enough character or good will. They came to realize that it just wasn’t about them. It was about it — what we were trying to learn and figure out. There was an objective reality out there that was the implacable goal of our efforts. We could get ourselves to the finish line, or we could not; but the finish line wasn’t moving. It wouldn’t come to us, no matter what. It was what it was.

Gumption is a virtue that has largely gone out of fashion of late in educational circles. Concern for self-esteem has in some places eclipsed it, I think, but it’s a bad bargain. Gumption of the sort I’m talking about is rooted in a healthy regard for objective truth, and for the fact that the world as a whole really doesn’t care about our self-esteem. By the same token, real self-esteem comes from measuring oneself up against that objective reality and doing something with it. The value of learning that lesson that cannot be overestimated, and only a genuine appreciation and realization of what it means will turn the passive — perhaps even docile — student into a scholar in the more meaningful sense of the term. I don’t mean a professional academic, necessarily: out of our three kids, only one of them has gone on to pursue formal academics as a career path; many people in professional academics today, moreover, aren’t really scholars in the sense I’m talking about anyway. I mean something else — I’m talking about the cultivation of a bull-terrier mind that won’t take no for an answer or be deterred from finding out. I think all three of our kids got that.

That transformation is not, of course, instantaneous, and in our kids’ case it was not entirely a consequence of wrestling with a few geometry problems. But I think they helped crystallize the process, precisely because it was not a set-up thing, contrived as an object lesson, in which the answer would emerge after one had played the the game for a certain number of hours, or had demonstrated a sufficient degree of effort or frustration. In the real world, the truth is not dispensed, like a treat tossed to a dog who has done a trick. It’s won through struggle. The problems may have been contrived, but our engagement with them was genuine. We realized soon enough that if we didn’t figure the problem out, we wouldn’t get the answer. We worked on these problems together, and we worked on them separately too. In retrospect, I think that the most important thing I was able to do for my kids in homeschooling them was to model my own real response to my own real ignorance.

In a world where there is so much to know, we are surrounded by nothing so much as our own ignorance. It’s with us all the time, and if we don’t confront it honestly, we’re certainly fairly far gone in a pattern of self-delusion. Having a sane attitude toward it, and a way of dealing with it, is essential to overcoming it. The victory over ignorance, however great or small, is never assured: it’s always at stake. Sometimes you just don’t get what you were striving for. There are things we still don’t know, that people have been trying to figure out for a long time. That’s okay. Victory over ignorance is not given as a reward for diligence, but it will seldom be won without hard work. Ultimately the cold fact is that each student must take responsibility for his or her own learning. Nobody else can carry that burden. Nobody — not a parent, not a teacher, not anyone — can learn for you, any more than someone else can eat, sleep, or perform any of the other basic functions of life in your place; neither can you win a race by proxy. The student who grasps that lesson, and is willing to embrace it, despite the lack of assurances, is the one that really stands to make something of education and of life.

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