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Topic: algebra for beginners
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Robert B. Davis

Posts: 22
Registered: 12/6/04
algebra for beginners
Posted: Jun 14, 1995 10:37 AM
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I ought to protest that Lucille Peterson is too generous in her remarks about
my work, but I wonUt. A bunch of us - including Kathy Kharas, Beryl
Cochran, Don Cohen, Jerry Glynn, W. W. Sawyer, Katie Hannibal, Irv Vance,
Iris Carl, Marilyn Burns, Edith Biggs, Carolyn Maher, Alice Alston, Gail
Nordmoe, Dorothy Strong, Bob Karplus, Diane Resek, Bob Moses ... and lots
more! - have been working hard on helping young children to develop basic
ideas of algebra, ever since the 1950Us, and to tell the truth I think that
we have come up with some pretty nifty ideas for effective lessons, starting
at least as early as grade 2. Given the time and effort that has gone into
this, maybe it isnUt hopelessly arrogant to be (reasonably) pleased with the

But we DO have a serious problem in finding ways to share this material with
other people. Our most effective (and preferred) way of doing this is
face-to-face, often via workshops or seminars or working together with actual
children. We never seem to be satisfied with our attempts to share this
work via written materials. We DO have some written matierials -- for
example, my book entitled Discovery in Mathematics (available from
Cuisenaire) -- but all of our written materials seem to fall short of the
mark. At a more abstract (or RphilosophicalS) level, we write frequently in
the Journal of Mathematical Behavior (available from Ablex Publishing Corp.,
in Norwood, NJ), but - while we think this provides food for thought - it
probably doesnUt offer much specific help to classroom teachers.

We also have quite a large collection of videotapes showing children as they
work on mathematical tasks, and we hope someday to be able to winnow out from
these some tapes that might be useful to teachers - but at present we regard
the tapes as wonderful tools when one of us comes along with them, to go over
them, discuss them, answer questions, etc. By themselves the tapes might be
confusing - in part because we never tell students how to deal with problems
- inventing ways to deal with problems is, we believe, part of the STUDENTUs
job! (This used to be called Rdiscovery learningS.) So some observers
imagine - incorrectly - that what they are seeing is all review. It isnUt!

Obviously we DO want to share this with as many other people as possible!
But perhaps the best way is still via someone who has worked on these
materials themselves. Our diffusion model might be called an Reach one
teach oneS approach. People who are able to visit us are always welcome,
and we run as many workshops as we can ... but we do recognize the need to
find easier (or cheaper) ways to share these ideas.

Thank you, Lucille, for mentioning this work. Perhaps you are too kind!
(Or too modest - another good idea is to study with the people at Bank Street

Bob Davis
Rutgers University

PS My apologies for the way that our e-mail software has mangled my
original Word document, especially with regard to quotation marks,
apostrophes, etc. I hope you can reconstruct what I had originally written.

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