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 results.
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 College!)
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.