Re: the calculus wars
Timothy Koschmann (tkoschmann who-is-at acm.org)
Fri, 21 May 1999 17:06:41 -0500
>Tim wrote, on Graham's (& Jay's) complaint that the academic context of a
>high school, and other social contexts like factories and offices, are
>distant universes often with little connection each with the other:
>
>>This is not to say that the way that we currently teach things like
>>trigometry and calculus is optimal. Having students do endless drill work
>>on de-contextualized problems and memorizing formulas only to forget them
>>immediately after testing seems pretty useless. Maybe if we engaged
>>students in things like designing roof trusses in school, they would have
>>an easier time seeing learning trig as an empowering skill. ---Tim
>
>As a practical educator in an Ontario (Canada) high school, I see only two
>ways to bridge the solitudes. Either we teach kids to adapt these
>mathematical tools (including other knowledge forms) to different activity
>systems, an approach which used to be known in connection with
>"metacognitive awareness" (my preferred approach). Or else we create
>different "categories" of discipline instruction which at least approximate
>these different external activity systems.
>
>In Ontario, our radically right-wing government seems to have opted for
>this latter course of action, although not likely for reasons which are
>based on good educational practice, or predicated on the practicalities of
>available resources. As a result, we are contemplating three kinds of
>"streaming" in the high school system: (1) the "academic" stream for the
>university bound, (2) the "applied" stream for those bound for technical
>training in community colleges, and (3) the "applied" stream for those
>going directly into the "work force".
>
>It remains to be seen whether this multiple stream approach will actually
>provide an easier bridge between high school and other activity systems, or
>even be doable. I admit I am sceptical, since it will still be missing the
>element of metacognitive awareness, but Tim and Graham, and even Jay, might
>find the concept behind this attempt interesting.
>
>Comments gentlemen?
>
You bet.
Glenn, I hope you didn't read my original rant as an attack on high school
teachers, because that was not the spirit in which it was intended.
Though I wasn't necessarily pitching a particular solution for how we might
better introduce students to the usefulness of trignometry, I guess what I
had in the back of my mind would be something more like Problem-Based
Learning, where the students are gently guided into a Deweyean problematic
situation and then allowed to "discover" that it might be useful to learn
about trig (or why you get a fever when you have an infection or how you
ask for directions to the restroom in French or how a short story is
constructed). It's kind of the obverse of how we usually do education,
namely tell 'em what they need to know and then give them a problem to try
to get them to contextualize the imparted abstract knowledge.
To answer your query more directly, I don't see any possible benefit to
increasing tracking in high school (and I suspect you are of a similar
view) unless your ultimate objective is to create more alienated kids.
Enjoy your weekend. ---Tim