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Topic: Why trig?
Replies: 21   Last Post: Apr 3, 1997 4:17 PM

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Michael Paul Goldenberg

Posts: 7,041
From: Ann Arbor, MI
Registered: 12/3/04
Re: Why trig?
Posted: Mar 31, 1997 4:37 PM
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On Mon, 31 Mar 1997 wrote:

> Why is it that questions from students about different bits of math
> cause so much agitation among teachers?
> I wonder how often English teachers get "why should we study
> Shakespeare?" I don't know about the often, but I suspect their
> answer is that people without passing knowledge of old Will are
> ignorant.
> As for trig, those without passing knowledge of trig are just as
> uninformed as those who wouldn't know Macbeth from
> Macdonalds. Personally, I'd put calculus on the list for everybody
> too, and you can't really make much sense of calculus unless you
> are comfortable with trig.

> * George Yanos *

The problem with George's take on this issue and his analogy with English
teachers and Shakespeare is that no one has the final say on where the
line gets drawn (nothing personal, George). As someone who has taught both
English at the university level and mathematics (mostly at the less
awe-inspiring level of a New York City community college), I'm chary of
arguing to students that any given bit of information on their learning
plate of the day is essential for distinguishing themselves from the ranks
of the ignorant. On that basis, what bit of knowledge ISN'T essential? And
getting E.D. Hirsch to put it in one of his books makes the morsel of
knowledge not one whit more important. Shakespeare, no doubt, is such a
giant that total ignorance of his work impoverishes one in an attempt to
grapple with aspects of the writing of many authors. Yet I'd guess that
I've read much more Shakespeare than most Americans and yet there's much
of his work I've not yet read. So am I Shakespeare-knowledgable or
Shakespeare-ignorant? SHould I include a list of which plays and poems
I've read at least once?

More to the point, any kid who is going to read Shakespeare (even a single
play), is unlikely to do so just because her teacher states or implies
that failing to do so is an indication of being unlearned. And the same
goes for any particular bit of mathematics. How much trig is enough? Will
a student who firmly believes he'll never attend college (or won't take
more than the barest minimum of college math) really buy "You need to know
this for calculus"? I'm skeptical, to say the least.

I've had some success with remedial math students by taking certain topics
in a given course and finding some connection to things in their lives
that are already important to them. After doing that several times, along
with other things that reduce the intimidation factor and help build trust
between teacher and students, I've found them more willing to struggle
with some other piece of mathematics simply because I ask them to look at
it. I prefer, of course, that students get excited about the math on its
own merits, because they find it intellectually engaging, and for a host
of additional reasons. But it doesn't always happen that way. ANd for some
students, I'm not able to find a connection or perspective that works for
them. Having tried sincerely to do so, I feel like I've done my job.

Of course, a completely different slant on the original question in this
thread might be to require that students who wish to be relieved of
responsibility for knowing something have to make a convincing argument as
to why they should be so relieved. They must demonstrate sufficient
'research' to show that they actually know what it is that they "want out
of" and have well-considered reasons for being allowed to skip over it.
Perhaps the process of having to think about what's contained in the
particular area of knowledge will help them see its value. Or maybe
they'll convince the teacher that they should indeed be able to opt out.
But that would be scary, wouldn't it? Maybe we're better off just telling
them that we know best. That argument from parents and teachers always won
the day when I was in K-12, so I'm sure it's just as impressive today.

Michael Paul Goldenberg
University of Michigan 310 E. Cross St.
4002 School of Education Ypsilanti, MI 48198
Ann Arbor, MI 48109-1259 (313) 482-9585
(313) 763-9683 email:


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