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Meaningless problems in algebra texts

I am resending this message because it may not have been transmitted the
first time.
There is one solution that can halp to make more sense out of the
typical algebra texts that are full of mostly "meaningless problems".
Why
not teach algebra together with physics in the junior or senior year of
high school?
It certainly makes sense from a logical view. I suppose that the
major problem in doing so is that the mathematics teachers are generally

unable to teach physics and there are too few physics teachers
available'

Herb


On Fri, 05 Nov 2004 21:05:04 -0600 Jack Uretsky <jlu@HEP.ANL.GOV>
writes:
Following is my exchange with the president of the math
teachers'
organization. I'm beginning to think that the solution is to
write
our
own math texts and teach from them.


On Fri, 5 Nov 2004, John Denker wrote:

Hi --

I know this is off-topic, but I'm stuck and I was hoping some
folks on this list could give me a hand. I've been dealing
with a kid who is taking ninth grade "algebra 1, algebra 2".
By some measures he's doing fine: he's getting high As, verging
on A+. But he complains constantly about the course. He says
he's not learning anything ... and I agree with him, on the
grounds that his knowledge of basic algebra facts is alarminly
thin. (How he can get high As without learning much of
anything
might be the subject for an interesting conversation some day,
but not today, please.)

He also complains about the textbook, saying it is a "tossed
salad of examples" with no explanations ... and I mostly
agree with that, too ... and that forms the main topic of this
note. We're talking about
_Algebra 1_ by Larson, Boswell, and Kanold
I found lots and lots of examples, with astonishingly little
explanation of what the ideas are and how the ideas might be
related to one another, and also very little formalism. By
way of example, there is a section on fitting straight lines
through scattered data, and the only instruction is to find
the "best" line, with no discussion of what might make one
line better than another! (Also there is no mention of the
fact that it might help to use a _transparent_ straightedge.)

I've seen some math books that were justly criticized as
being too "dry", with not enough examples ... but this
book is far too "wet".

I went to amazon.com and sure enough this book got a number
of rotten reviews ... but the other books in the same
category got even worse reviews. Eeek!

So ....

-- Does anybody have any suggestions or recommendations?
What do they use at your school? Are the customers
happy with it?

-- Would anybody care to comment on the Algebra DVD set
from the Standard Deviants? (It gets good reviews, but
I haven't seen it myself.)

-- Are there perhaps _college_ algebra books I should be
looking at, i.e. something that is simultaneously
introductory yet systematic?




_________________________________________________________________________
______
Exchange begins here:
Dear Jack,

Thanks for your thoughts about my President's Message on
Algebraic
Thinking. I
appreciate your perspective on algebra. My discussion of a
functions-based
approach to algebra is consistent with algebra as presented in
Principles
and
Standards for School Mathematics, NCTM's anchor position about
school
mathematics. This position does not exclude other uses of algebra,

but it
does
suggest that more students can learn useful algebra if we approach

the
development of key ideas from the point of view of functional
relationships
among quantities. Obviously, other uses of algebra must also be
included
in a
comprehensive approach to algebra. Solving a wide range of
problems
using
algebraic approaches is an important outcome of algebra.

Sincerely,

Cathy Seeley



******************************************************
Cathy Seeley
President
National Council of Teachers of Mathematics

_______________________________________________________________________
I had written:

Sometime in the last half-century that magic of "let x stand for
the
unknown" seems to have gotten lost from the memory of the American

math
teaching community. But without the use of that magical concept,

all the
manipulative algebraic skills and knowledge of function theory
stand
for
nought. And the student is bewildered by rote exercises
involving
manipulation of letter symbols without any understanding of why
numbers
are not being plugged into calculators. The basic message, which

needs
constant repition, "let's not just solve one problem, let's solve
a
whole
class of problems" is missing.

There is a place for functional thinking, but I strenuously doubt

that it
is at the beginning of a course in algebra. That's because the
notion of
working with symbols, rather than numbers, is so traumatic to
young
minds
that the notion must be given time to settle before being
exploited.

I am making use of some of the ideas discussed here in my Calculus

text,
currently in progress. The Introduction and chapters 1,2 and 30
may
be
downloaded from my website at:
http://www.hep.anl.gov/jlu/index.html
under the heading "book". Chapters 3 and 5 are also available
there
(I am
currently working on Chapter 14).
Best,
Jack





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Herb Gottlieb from New York City
A friendly place to live and visit




Herb Gottlieb from New York City
A friendly place to live and visit