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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 mathwrite
teachers'
organization. I'm beginning to think that the solution is to
ouranything
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
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:Algebraic
Dear Jack,
Thanks for your thoughts about my President's Message on
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
theproblems
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
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 thestand
manipulative algebraic skills and knowledge of function theory
forinvolving
nought. And the student is bewildered by rote exercises
manipulation of letter symbols without any understanding of why
numbers
are not being plugged into calculators. The basic message, which
needsa
constant repition, "let's not just solve one problem, let's solve
whole
class of problems" is missing.
There is a place for functional thinking, but I strenuously doubt
that ityoung
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
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,may
currently in progress. The Introduction and chapters 1,2 and 30
bethere
downloaded from my website at:
http://www.hep.anl.gov/jlu/index.html
under the heading "book". Chapters 3 and 5 are also available
(I amR
currently working on Chapter 14).
Best,
Jack
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