Recently, on email@example.com, the issue of whether changes in the standard K-12 curriculum are a natural, reasonable reflection of changes in both society and education, or whether they are yet another harbinger of the coming of the Apocalypse. The debate centered on an opinion piece by Stuart Wachowicz in which he begins,
“Pride in craftsmanship obligates the mathemati-
cians of one generation to dispose of the unfinished
business of their predecessors.”
-E.T. Bell, The Last Problem
The above statement most accurately describes the
legacy of one generation of mathematicians to the next.
However, on might be tempted to ponder whether this
will continue to be possible in North America. The dis-
cipline of mathematics, as we have known it, is clearly
under threat. The threat is a consequence of allowing cur-
riculum writers to change the centuries-old definition of
mathematics and what needs to be learned based on utili-
tarianism, combined with the current practice of allowing
unproven fads to influence pedagogy.
For the full text of Mr. Wachowicz's piece, see "Perils of Modern Math Education"
This led a number of participants to posit that there were certainly things that could be dropped and in fact have been dropped from the curriculum in the past century without any clear-cut harm resulting, but it was difficult to get those who were apparently in agreement with Mr. Wachowicz to stipulate what they feel it has been okay not to teach. Then, in an attempt to turn the tables, Wayne Bishop wrote:
Would you give us a list of a few topics (beyond table look-up and associated interpolation) that would have been appropriate high school preparation for a math-based college major decades ago that are no longer appropriate? Obviously, not every high school student - not every college-bound high school student - has aspirations for a math-based major but we certainly don't want to screw up those who do or who have not yet committed themselves against that long-range goal.
My response, slightly edited for clarity, follows:
Wayne Bishop's theory appears to be, eliminate nothing that, if eliminated, might "screw up" potential math-based majors. Using this logic, we have publishers producing those tree-killing doorstops that both Dom Rosa and Kirby Urner, perhaps for very different reasons, decry, and which seem consonant with the complaint that Wayne and other MC/HOLD flacks echo (when it's convenient) about the mile-wide, inch deep American curriculum, a sin they lay at the feet of those potentially blown-up Schools of Education, especially the reform-oriented progressives who've taken them over.
It's also this logic that has kept topics in SAT, ACT, GRE, GMAT, and LSAT prep books by some publishers that haven't actually appeared on the respective test for years, if not decades. Rather than cut, they simply rewrite and append. After all, it can't HURT to leave in those extra pages, right? The old item types might make a comeback, and fatter book => higher price with not all that much additional cost in production. More trees die, but that's really collateral damage. And anyway, the OTHER guy's books still cover that topic.
There are other problems connected with this philosophy that are more serious for teachers and students.
States suffer from many of the same problems from which individuals and publishers suffer. They are loath to drop a topic if "the other guy" still has it in their curriculum framework. Couple this with the very legitimate push to put some important topics and strands that previously weren't treated until much later (and often in a very cursory manner, if at all, in the high school curriculum, e.g., probability and statistics, transformational geometry, discrete math), and you have a real quandary: in fact, you have state frameworks that, while attempting to go in a reform direction, wind up as . . . yep, a mile wide and an inch deep.
Out there in the real world of struggling inner-city and poverty-stricken districts, high stakes tests and NCLB pressure teachers to get their kids up to snuff not only on the OLD elementary school curriculum with its focus on arithmetic through the rational numbers and maybe integers (in a K-6 school, both would likely be addressed by "graduation" to junior high school), but all this new stuff. But since NOTHING ever gets dropped and new stuff is getting added in, and the approach being used in any given district may not be getting enough kids up to snuff on a host of topics (probably different ones for different kids), the results are predictable: math students enter high school, when and if they do, like a bunch of Swiss cheeses - full of holes in their knowledge and each one with holes in different places.
The teachers are caught between the proverbial Scylla and Charybdis: teach every topic to mastery and understanding for the vast majority of kids and you don't get to a bunch of required topics and risk being fired for insubordination; teach at the usual district or textbook pacing guides and you leave a lot of kids in the dust and you get fired anyway (or your principal does, or the school fails to make AYP and eventually is closed, after it loses funds through various provisions of NCLB). Bummer, dude.
The obvious solution? Fire all the teachers, close the public schools, give vouchers so that the wealthy kids can even more readily afford really nice clothes while attending the ritzy private schools that just happen to be in the neighborhoods where they live (this is, of course, an ENORMOUS coincidence) or off at some exclusive prep school in scenic New England that unfortunately doesn't have much in the way of provisions for the kids in those inner city or rural poverty pockets in their underperforming schools and districts. This is regrettable, of course). The poor kids can attend a local Catholic school, of course, as they are more likely to crop up in ghettos and far-flung areas in rural Idaho.
What we most certainly SHOULDN'T do, of course, is support efforts to repeal or greatly revise a punitive, ineffective law like NCLB, change our assessment focus from using testing to embarrass and discriminate unfairly towards using testing for getting useful information that actually is used intelligently to make things better for those most in need. Nor should we seriously look at any sort of curriculum that actually attempts to address issues for both elementary teachers and students of profound understanding of fundamental mathematics; or that uses any approach or tools other than paper-and-pencil algorithms, generally taught either initially or in the end out of desperation, as "black box" procedures with no understanding whatsoever. The goal becomes passing a test rather than learning and understanding what's actually going on. Student thinking is kept to a minimum to serve the great gods of multiple choice testing.
(For the irony-impaired, proceed with caution following the words "The obvious solution?")