Well, they aren't. But the French have a reputation for being snobs, and it is said that they have little patience for outsiders speaking their language badly.
So there is a parallel. Most math students learn to expect a certain degree of impatience from even the most jovial of math teachers. And within the ranks of mathematicians, there seems to be a fierce pecking order that rewards the highest achievements, such as the Field Medal, with fawning obsequity, while bumbling performance in, say, factoring a third-order equation would insure scorn for the hapless exponent-juggler.
I am finally okay with this stratification after most of a life spent in envy of math. I didn't get any good math as a kid. But I wanted it. I would press my face against the glass store front of trigonometry and look at the shiny sines and cosines inside the way other kids hungered after candy or toys.
Now that I have decided to learn Calculus at the ripe old age of 56, however, I have made some observations about the teaching of this subject in college that I am forced, by my conscience and modesty, to share with everyone.
I am on the other end of the stick, as it were, struggling through some marvelously bad teaching in Calculus. The weird thing is that the teacher is "good" in almost every respect. He has a sense of humor and self deprecation, and when he is on, he is extremely fluent in the dialect of math called Calculus, without being overbearing.
The problem, I believe, is structural. Teaching calculus in American Universities is a culture that we inherit partly from the European model and partly from the United States home-grown methods devised to ramp up to a war in the last century. There is an odd mix of Imperial theory and Royal protocols associated with an equally rough and ready, rolled-up sleeves practicum which knocks the dainty and the insecure on their ass. I find it a particularly ugly hybrid. The upshot of the mass of skills and information they try to cram into short, crowded class sessions is too much emphasis on the student teaching themself in lengthy, arduous homework sessions. To further muddle the mix, the instructor doesn't establish any real working relationship with the class. You get a perfunctory "Well, any questions?" tossed to the glaze-eyed cohort before he proceeds to erase the brambles of equations and start a new forced march into Symbolville.
Then the test is administered, and it is sadistic. Instead of providing a foundation set of questions to assess the student's basic grasp of the main principles, every single one of the questions pivots on extremely difficult, obscure, multiple encrustrations of operators operating on operators with similar but different effects. In a class of 30,3 people finished half an hour before the 2 hour session was up, and over half were still writing and erasing when the class was over.
I understand the ideas behind this kind of presentation. It seems like an efficient way to cover the sheer quantity of material that needs to be presented. In the whole semester we barely cover the substance of 4 chapters in a book with some 20 chapters, while touching on high points of about 3 others.
But does it really cover the material? And is there really that much material?
It doesn't "cover the material" if 80% of the class gets 70% or less of the material, with 30% of the class getting 40% or less of the material. Only one or two individuals achieve true mastery, and they usually come into this with some background or skills lacking in the other students, something like a parent who teaches or practices in the field, or a great high school experience.
In the military, this might be okay, with each class only needing to provide the engineers with a few highly competent individuals while the rest are diverted into more maintenance and support roles.
If I was a business owner paying to have my staff skills upgraded, I would fire the company that used this teaching method and sue them for fraud.
There is no reason that 100% of the students can't master 100% of the fundamentals, and 100% of the main ideas in the subject.
It would require a major overhaul of the class structure, but it could be done with the available personel and scheduling.
My proposal is as follows:
The first two weeks is exclusively devoted to assessment and drill in fundamentals. No one should go to the first rung of calculus without a complete grasp of logarithm, exponenst, functions, trigonometry, etc. Anyone who can't get up to speed in two weeks of the class should be diverted to the appropriate pre-calculus, or algebra class no matter what their transcript says.
From two weeks on, the class should be arranged so that every student has a drill partnership responsible for their mastering each theorem, law, rule, principle, basic equation, etc with flash cards. Drill partners would have the option of changing their partners the first week to accomodate major personality clashes, etc.
Every class period would have a time for drill/warm up, a time for lecture demonstration, and a time for student demonstration. The drill/warmups could be given the first 15 minutes while papers were handed out and business was taken care of by the instructor. Student demonstrations would involve rotating teams demonstrating homework problems on the board alternating with challenge questions from the instructor that were designed to stimulate, not humiliate, the students. The last half of the class could be lectures.
There should be homework which applies to the lectures done before the lecture, and turned in at the beginning of the next class period. This would make sure the questions, pace and focus of the lectures met the needs of the class, and it would ensure the class did the appropriate amount of work in a timely fashion...with the chance to correct and expand on problem areas in a non-punitive manner.
If people were unable or unwilling to perform to this degree of support, they should be excused from further involvement without penalty.
As it is, you are suckered into a semester of unknown difficulty, with all tuition due whether you drop the class or not, before the first test is given. You are dragged behind an unresponsive vehicle of instruction whose pace and capacity is set by the curriculum committee, not the actual capacity of the students themselves. And in doing this, the committees who are so absent from the classroom almost guarentee the emnity of the real students in the classroom. Or a substantial fraction of the them.
My plan elimnates some of the logjams and disconnects between understanding, demonstration, and performance. Ultimately math, like a language, is a matter of performance, not of simple matching or recognition skills. And like language, it is best learned speaking among natives in a congenial setting, with a fair sense of cause and effect, action and consequence.
The mystique of Royal Academy snobbishness and the crude efficacy of G.I. training clash in our classrooms of higher math. In the meantime, there is a dramatic need for an informed citizenship who can tackle the increasing demands of a technical culture with some confidence and math skills.
My plan addresses this need.
Vote for me.
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