This has been “the winter of my discontent” (thankfully, we only turn 50 once — if I can survive it this time), and I have brooded much on old failures, stuff years ago, gone by, beyond remedy, irrational stuff, not worth thinking about: not learning to swim, to sing to dance, to ride a bicycle, to play cards, to play a musical instrument, never having a date in all my high school years. None of these were things that I was excluded from by religion or disability; they were things that I simply failed to do while other kids my age got with the program and did them.
But there is one failure that in just the last few weeks has begun to make me angry: the short abortive course of my math career.
We must always examine our motives for feeling as we do. We indulge in sour grapes. We try to rationalize our failures to escape blame for our incompetence. We fool ourselves whenever we allow ourselves to. Most anger is probably no more than that.
You see, I never took any math beyond plane geometry. Algebra I began auspiciously enough — Bs first semester. But in February came factoring which I never grasped, and so began the long, linear, sequential slide of concept failing to build on concept that wasn’t there. By the end of the year, I was struggling to hold onto a D. Geometry was easy enough — it is not really math — but I never signed up for Algebra II. I don’t remember whether I was counseled not to, or whether it simply seemed futile; if I couldn’t handle the simpler course, what chance had I in the harder, more advanced course that built on it. The lack of math haunted me in Physics; everyone else was in Algebra II or beyond, although it was no handicap in Chemistry. I enrolled in the last catalogue at my college that did not require the standard math course for B.A. candidates. If I were one year younger, I probably could not have gotten into Augustana, let alone passed Freshman Math, a stiff course that began where high school math left off.
In retrospect, better I had failed second semester. Then I would have had to re-take it in summer school to redeem the credit. I suppose I could have done that anyway, but no one suggested that I should, nor did it ever occur to me that I should or might. I was simply no good at math, and there it stayed for over thirty years. I really never thought about it much. But this year, I have begun to brood upon it, along with all my other old, irredeemable failures. I have been noticing some of my students, not even the ones I consider sharp, doing Trig. It is hard to accept that these louts can master something I can’t even conceive of. The other day, a couple of department colleagues were in the lunch line ahead of me talking about their math of all things. (One was preparing for the GRE). I couldn’t understand a word. It was like a fist in the solar plexus. It was like being excluded from a social circle. It was like being the class geek with a crush on the Prom Queen. Total despair.
Nothing so absolutely defines intellect as mathematical prowess. Nothing so clearly delineates who is smart and who is dumb.
The other day, I was talking about math to one of the math teachers at my school. Since I have become obsessive about this subject, I bring it up at strange times, I bait people with it, I assume a forced levity about it. I guess I hoped he would tell me there is balm in Gilead. There is a bonehead course for 50 year old pseudointellectual innumerate geeks to redeem themselves. But the best he could offer was “Well, math isn’t for everyone. Some have got what it takes, some haven’t.”
Now I know why many students hate English.
I first suspected more than twenty years ago that perhaps it need not have been thus. Had things been just a little different, I might have mastered enough of Algebra I to have gone on in math. But I never, until this year, felt it as a personal loss. Now it sticks in my craw and clutches in my stomach in the small hours.
I got the idea that things might have been different from watching a math teacher, Herb Grosdidier, and the math program he built in Payette, 1968-74.
Herb was not your garden-variety math teacher. An ordained clergyman, he had feuded long with the Bishop of Oregon who had spent years trying to get him committed to a mental institution and had in the end been committed himself. Herb had taught English in his previous school, and when I left, he took my assignment and taught English again. He was one of the most intense men I have ever known, and perhaps he was a little mad, although in the end it was his wife who experienced a breakdown. Who can I compare him to? Ahab? Allie Fox? Phaedrus?
He ran a math program like no other I had seen before or have seen since. The buzzwords these last few years are “paradigm” and “paradigm shift.” Herb threw all the hallowed paradigms out the window. One of his most passionate causes was to fight “the tyranny of the calendar,” the idea that Algebra, for example, is delineated by a September beginning and a June end. Herb individualized math instruction so completely that you were done with Algebra when you passed the last unit test with an 80% or better score. It might take a day to master a unit, or a month, or if you fought the program, a semester. No one had to wait for slower classmates, but more important, no one had to move on until ready.
Had I taken Algebra I from Herb, I could not have gone on until I had mastered factoring, however long that took (probably until Easter, me stumping along just as fast as my little 92 I.Q. would carry me). You could not fail Herb’s course; you could only fail — refuse, actually — to complete it. There were a few students who he counselled not to take the next course, feeling they had reached a point of diminishing returns, but they were few indeed. There were malingerers, of course, but never for long. All objects were movable before Herb’s irresistible force. He could wait, he could bully, he could intimidate. I cannot recall a student who did not eventually engage math.
The administration hated Herb’s program, of course. It was not neat. They could not enter credits in a batch at the end of a semester, but they had to do so piecemeal, one at a time, almost every day. The world just doesn’t work that way, does it?
At the same time Herb abolished the calendar, he abolished tracking, and this was his greatest heresy of all. There were no General Math, Algebra, or Geometry classes. There was only math and whatever you were working on at the time. All levels of work went on in the same room, from Helen, a special ed. student (we mainstreamed earlier than any other district in the area) with no number concept, to Kent, who devoured Calculus in a month and demanded whatever came next.
Today, untracking is a new concept, just gaining favor. At NCTE, I discovered in sessions on un-tracking, that the whole nation is still tracked. (Well, a colleague from northern Idaho says that untracking is passe, that his district is re-tracking.) Twenty years ago, Herb untracked math. The bottom line was that more students completed more math than ever before at Payette High School. Our principal, an old math man himself, expressed a fear that Herb was debasing the coinage by making math too accessible.
The curious thing is that math is still the most rigidly tracked of all the disciplines. Its hierarchical structure dictates that it must be so. Math courses are like ever finer sets of screens, sifting, sifting, sifting, until those that pass the last screens are rare stuff indeed. With ever-more complex concepts and fixed windows of time to learn them, all but the brightest and best must sooner or later bobble a step in the sequence — and fall out of the program. The typical math curriculum exists not as a vehicle for teaching as much math as possible to as many kids as possible, but as a machine for sorting kids. It is no coincidence that open-admission universities use math as the flunk-out course to thin the ranks of incoming freshmen.
Herb changed the paradigm. He threw out this most basic assumption on which all math programs are founded, and he made it work. The program died eventually. Some parents saw what it did and loved it, but to others it was not a proper math course. The administration did not love it because it complicated their record-keeping procedures. Some of the other math teachers in the building embraced it, but some resisted it. And it was tremendously labor-intensive. Herb distrusted publisher’s texts and wrote most of his own material. He and his wife were often at school long after midnight, putting together instructional packages. To say nothing of the classroom record-keeping, the need for personal student contact …. it went on and on. When I left Payette in 1976, Herb abandoned what was left of the program and took over my English assignment, which he re-structured just as audaciously. I think that today there is nothing left of it, either. Herb will never revive either one. He eventually left teaching to prospect for gold and died four years ago.
There were things he might have done that he didn’t. I look back and see opportunities for collaborative learning. We mustn’t blame Herb for failing to exploit them, however. In the first place, no one had ever heard of collaborative learning in 1969, at least not in this part of the country. Because he invented one thing, it does not follow that he must also invent something else. He maintained rigid control of the entire process, and perhaps his own will was the mainspring that made the enterprise go. And I know that to him, learning was, like all life, an absolutely solitary pursuit. (I remember the day a hapless first-year teacher invited him and his wife to a faculty party. He whirled about to confront her and face florid, veins standing out on his forehead, he jabbed a punctuating finger millimeters from her eyes and thundered in a voice that must have carried throughout the building, “We! Do! Not! Socialize!”)
Still, he broke down the old structures, swept the hallowed icons from the temple, did math in a new way. And I wonder — if I had spent two more weeks on that factoring unit, I might today be an architect after all, not an innumerate English teacher sitting in this room at this typewriter, divagating over old failures.