Nonconformist College Teaching 4: Interrelate Advanced and Elementary

>>From Osher Doctorow mdoctorow@xxxxxxxxxxx

Having taught quite a few elementary college courses in mathematics
including differential and integral calculus for majors and also for
nonmajors, differential equations, statistics, trigonometry, geometry,
elementary and intermediate algebra, etc., I can generally say that I
made it a point almost never to ignore relevant advanced material
including the latest research. To state it as a Principle:

Principle of Non-Introductory Teaching. There is no such thing as an
"introductory concept" which cannot be greatly clarified by relating it
at approximately the time of first teaching it to the latest advanced
research in the field.

I am quite convinced that this holds for physics teaching as well.

For example, I almost never taught an introductory statistics course
without including comparison between Conditional Probability-Statistics
and PI (Probable Influence) Probability-Statistics as examples and
definitions and so on.

I almost never taught an introductory calculus course in either
integral or differential calculus without relating the material to
where calculus goes when it "grows up", including Real Analysis,
Complex Analysis, Functional Analysis, Nonsmooth Analysis,
Probability-Statistics, including some major applications and examples
in each.

As a part-timer for most of my college teachig career, this didn't make
me popular in the departmental bureaucracy. In fact, a few students
would complain in any such course on the grounds that "no other teacher
did this," or "the most senior professor doesn't do this in his
course," with expressions of alarm and at least acted-out "panic"
despite being clearly informed of what I was doing and what was
required in the course which was never dependent on a prior course or a
level of mathematical sophistication not taught in my course in
reference to these advanced concepts.

But how does this help college teachers who may be reading this in
their own decisions? Shouldn't they ignore my suggestions in order to
"advance" in their positions? On the contrary, the bureaucracies will
collapse much faster if more and more college teachers who are really
Creative and innovative will refuse to be pigeonholed into teaching
purely elementary introductory courses without relating them to
advanced work. The departmental bureaucracies will have to eventually
promote the dullest, most conformist bureaucrats and fire the slightest
sign of brains, instead of as they do nowadays using part-timers as
hard-work cannon fodder with the only real inspiration in most of
Academia. I'd even go as far as to make a resume for a teaching job in
one of the top USA universities or European universities or
corporations based on being a Nonconformist who bucked the bureaucracy
with predictable results. While you're waiting for a teaching job, if
it ever comes, you can learn a manual trade or get a sales job - it's
about as much a form of prostitution as Academia is usually nowadays.

Osher Doctorow

.

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