Posted by
Charles Lewis on Wednesday, December 26, 2007 11:37:21 AM
by Charles Lewis
Since 1987, when I left a teaching position at a very good Washington, DC private school, I have taught and tutored (mostly in math) government school students from all over America. The difference between the quality of (legitimately rigorous, I must stipulate) private schools and the state-run variety was driven home my very first year as a government "classroom manager."
You see, I happened to have in my new homeroom a young man who had been in that same private school with me the year before (his only year at that private school after attending government schools up to that point). He had been a high school freshman at the private school, having been a freshman the year before that in his government school (a "repeat" year having been always required of the tiny percentage of government school veterans who qualified for private school admission under any circumstances).
This individual, whom we'll call, "Bubba," had failed out of the private school, having achieved 2 D's and 2 F's in his four major classes, along with a reputation for academic laziness. One would have expected him to have repeated his freshman year once again or, perhaps (considering he was back in government "school") advanced to the sophomore level, or, just maybe, been a junior, as he was slated to be had he never matriculated at the private school in the first place.
But no, Bubba was in my homeroom, which was for seniors only. And, as a senior, he made the honor role.
On one occasion, I chatted with Bubba about his apparent metamorphosis. I posited that he'd turned over a new leaf, and had become a very diligent scholar. No, he responded, his work habits actually had become even more slovenly.
Then how on earth did he make the senior class honor role? He replied that what he had recalled of what he had learned in that one (freshman) year at the private school (which amounted to next to nothing by the standards of that school) had been enough to carry him to the top of the heap among government school seniors.
And that was 20 years ago. I can vouch for the fact that things in government schools - especially in mathematics - are much worse now.
When I start tutoring a student (generally in pre-calculus or calculus) nowadays, I always ask him a series of questions that a beginning pre-algebra should be able to answer correctly - with no hesitation (and which anyone who has completed the very first section of my elementary pre-algebra text has mastered). These questions involve only the most rudimentary understanding of whole numbers and fractions - nothing as challenging, for instance, as converting or reducing fractions, or even the simplest operations on them.
The vast majority of these "upper level" math students have not been able to correctly answer any of these questions - even with much hesitation. This always suggests to me that all of the "knowledge" these students have gained in the 4-7 supposedly more advanced courses they've passed has been purely rote, and ephemeral. And subsequent tutoring has generally born this out vividly.
You see, "math" instruction these days is typically enveloped in two very non-rigorous teaching methodologies that lead to such phenomena. On the macro level, there is "indisciplinary instruction", which presents the math within a virtual tossed salad of other disciplines, from which it must be somehow extracted and discerned. Even where the title is not explicitly mentioned, the interdisciplinary philosphy is omnipresent, in the form of an emphasis on "problem solving" and/or "issues orientation" that subsumes the pure math content.
"Integrated math" - also pervasive, even in courses that eschew the term itself - does, within the given math, what interdisciplinary studies do within the whole curricular system. "Algebra," "geometry," "probability," and "statistics" (or, really, incredibly watered down versions of the same) are introduced far earlier in the progression of topics (as in the early elementary grades) than those points at which the pupils can comprehend such concepts, and within no particular developmental framework. Arithmetic - the "queen" of the math courses, the lifeblood of all "higher" courses - has been all but jettisoned to make way for the resulting chaos.
The stated idea - in both cases - is to establish, on the one hand, the interconnectedness of the courses within a curriculum, and, on the other hand, the connections within the various branches of math. As a teacher, I used to point out that school is where lines of reasoning should broken down to their atomic parts, analyzed, and mastered before - in ever higher level courses - the connections in question are established, and, yes, emphasized. What good is a welder's torch if the parts being welded are, themselves, all thoroughly defective?
Such objections fall on deaf ears in the education establishment, whose goal at this point is not a knowledgeable, coherently reasoning populace, to say the least. And the fruits are as one would expect.
American government high school math students (and I hasten to point out that a huge proportion of private and even Christian schools follow the same curricula, use the same or similar textbooks, and administer the same bogus standardized tests) find themselves, in general, lost in a sea of symbolism, merely manipulating, completely at a loss as to the meaning of the processes they perfunctorily perform, and unable to retain more than a tiny portion over time. Even with cal and pre-cal students, I always have to revert to my pre-algebra text, and, often, even my basic arithmetic text, in order to remedy the deficiencies in comprehension.
Since the mish-mash math books entail a complete de-emphasis on proving, demonstrating, or even even explaining each new concept, students nowadays are at a total loss as to why - or even that - any concept being applied is correct (and, alarmingly, I frequently find that, at least from a strict mathematical standpoint, they aren't).
This results in math students who:
(1) are utterly dependent on academic authority for their "facts," and who are thoroughly programmed to accept such authority. and
(2) have no propensity - or experience base - toward the belief in objective truth.
When questioned, students often express the impression that math was invented, rather than discovered. If something as (potentially, at least) self-evident as math is taught in such a way that it appears arbitrary, what is immune from the appearance of capricious subjectivity?
Both of the above "student outcomes" are worthy goals if one is attempting to acclimate youth to a coming totalitarian secular dictatorship. Apart from this, their educational utility would appear nil.