Chronology Current Month Current Thread Current Date
[Year List] [Month List (current year)] [Date Index] [Thread Index] [Thread Prev] [Thread Next] [Date Prev] [Date Next]

Re: [Phys-L] problems with the teaching of algebra



On 10/12/2014 11:16 AM, Philip Keller wrote:
if you believe that it is important that elementary school teachers
can do a little algebra,

I'm not sure about that either way; see below.

putting one or two items on a multiple choice test is not going to
make that happen.

We agree that will never do any good.

You'd be better off requiring that they have one college level course
in a subject that uses algebra, one that they'd be unlikely to pass
without that minimal level you were hoping to see.

That's what we've been doing for eons, and it doesn't work either.


On 10/12/2014 12:37 PM, Robert Cohen wrote:

I've found that students are very good at passing courses without
understanding the underlying math.

An excellent point.

In support of that point, note that on the exams BC cited, you
could pass the test by skipping the one or two questions that
require algebra. The rest of the questions are at the pre-
algebra level ... especially if you are a little bit test-wise
about working backwards from the multiple-guess answers. And I
assume that everybody who is applying for a teaching certificate
is plenty test-wise.

On top of all that, what little these teachers did understand is
soon forgotten.

The typical response I get is:
I'm a second-grade teacher. I took college algebra 17 years ago,
and I have not used it at any time since, in class or in daily life.
Anything I ever knew about it I forgot 16½ years ago.

Why do you ask? And for that matter, why was I required to take
the course in the first place? And why did you wash out of the
program a few million people who would have make excellent teachers
were it not for the algebra requirement?

Why indeed.

Some jurisdictions offer a Pre-K-3 certificate, and if they wanted
to drop the algebra requirement for that, I would have a hard time
coming up with a counterargument. OTOH if somebody has a good
counterargument I would be very interested to hear it.

============

For third grade and up, that's a different question, and I might
have a different answer.

Putting on my physics hat: By third grade, people should be doing
some physics. Start with the unequal-arm teeter-totter. I use
a ladder with a plank on top and a broomstick underneath. I
stand close to the pivot. A small kid stands on the other end,
far from the pivot. It's kinda impressive to see that the kid
can lift me up.

However, the lesson does not end there: There is a tradeoff involved.
The kid had to push down over a long distance to move me up a small
distance. We can quantify this mathematically:
force_1 × distance_1 = force_2 × distance_2

and I would really like the teachers to be able to understand it
at that level, at the algebraic level.

Similarly there are activities such as tug-of-war with pulleys.
It's kinda impressive to see one kid overpower three kids by
using the block-and-tackle the right way.

=============

Nowadays the kids are tested more-or-less incessantly, at every
stage from kindergarten on up.

In some cases, the teacher pays little or no attention to the
test scores. That makes a certain amount of sense, insofar as
a good teacher already knows which students are doing well and
which need help, even before the test is given.

HOWEVER, I conjecture that everybody would be better off if teachers
had the tools -- and the skills -- to make sense of the data. They
could see precisely
-- which students needed more attention, and
-- which topics needed more attention.
There are some schools where this is unheard-of, and others where
it is standard operating procedure. I suspect there is a trend
toward the latter.
http://www.educationworld.com/a_admin/admin/admin366.shtml

There is commercially-available software to help with this. I'm
not talking about full-blown item-response-theory analysis, just
some basic data visualization.

My point is, even this is not strongly dependent on college algebra
in the classical mold. It requires some mathematical sophistication,
including the ability to interpret graphs ... but even so, that is
not synonymous with or predicated on algebra.

I don't pretend to know the right answer, here's a hypothesis to
consider: one could imagine pivoting from an algebra requirement
to a computer data processing requirement. If that caused people
to pick up a useful /subset/ of algebra along the way, that
wouldn't be a bad thing either.

I reckon a small amount of well-motivated useful algebra
is better than a large amount of ill-motivated impractical
unremembered algebra.