Response 1: This is a response to the posting on "Psychologists/New Programs - Boosting Math Scores"
I enjoy reading your comments on the net. You must spend a lot of time replying to and helping people.
I am presently retired but keep active by preparing University of Waterloo contest problems for potential I.M.O contestants. I have just completed two books whose theme is "teaching with computers" - The titles are: Conic Sections and Higher Plane Curves using Sketchpad or Cabri.
The topic that you and others are addressing in the present e-mail leaves me somewhat puzzled. Perhaps if educators realized that mathematics is more than number for children then we might have more success with the subject with youngsters. I did my dissertation at the Ontario Institute for studies in Education. The topic was "Spatial perception and Geometry". If one takes the approach that the real world is a world of motion then transformation geometry can be used as the approach to real world mathematics for children. Using "slides, flips and turns" a program of meaningful geometry (motion geometry) can be developed for children from Kindergarten to Grade 8. I spent 18 years in a large educational jurisdiction as coordinator of mathematics and was able to develop a sound program for elementary schools. I even convinced Donald Coxeter that such an approach was meaningful for children. He tried some of the materials used for "motion geometry" with his grandchildren in Montreal after which he heartily endorsed the approach we were using. - This from a world class geometer! We used the approach in our text books for elementary schools. The program laid the ground work for secondary school geometry. The idea of "motion geometry" in the curriculum for elementary schools is gaining wide acceptance.
If you wish, the article in the 1987 NCTM yearbook on "Spatial Perception and Primary Geometry" will give you an idea of some of my work. The Addenda Series, K - 6, includes material on "Spatial Sense" that addresses the approach, through some of the lessons, we use.
Children in the ghettos and inner city schools are the ones who gain the most from motion geometry. They have a greater spatial sense than children from more affluent homes and readily relate to a "Motion Geometry".
I've had my say. I'd be glad to react to any questions you may have.
Keep up the good work.
John Del Grande Newmarket, Ontario Canada email@example.com
Response 2: Following are a couple responses from Don Cohen to an earlier posting.
(1) Jerry, you should tell your email and other lists of people, about the Japanese translation of my book "Calculus By and For Young People (ages 7, yes 7 and up)", published by Kodansha (18,000 in the first printing), arrived in bookstores throughout Japan on August 20th. It is in their BLUE BACKS series- science and mathematics for young people, which also had Martin Gardner and W.W. Sawyer as authors.
Then, perhaps, more US educators would use the English versions of my materials. I am getting many more homeschooling parents using my stuff now also.
I think I told you Kodansha printed 18,000 copies of the Japanese translation of my book "Calculus By and For Young People (ages 7, yes 7 and up)". These went to many bookstores throughout Japan on Aug. 20. On Sept. 6, I received an email from my publisher, part of which is below:
"And now I have good news to tell you. We are going to print additional 2,000 copies late this month. We can say that your method was accepted to Japanese people as a kind of new text in which they could learn and understand math much more than ever before.
(3) The following are the six items (3 books, a map and 2 videotapes) I have produced, published, and sell:
1. "Calculus By and For Young People (ages 7, yes 7 and up)" by Don Cohen; publisher Don Cohen- The Mathman; Rev. 1989; 179 pp; ISBN 09621674-1-X; $13.95; for grades 1-12. (Reviewed in Scientific American, Dec. '88 + many others.
The Japanese translation of this book, ISBN 4062572249, published by Kodansha (18,000 first printing), is now sold in bookstores throughout Japan. It is also being sold in Kinokuniya bookstores in NY and LA by Sept.30.
2. "Calculus By and For Young People-Worksheets" by Don Cohen; publisher Don Cohen- The Mathman; 1991; 324 pp; ISBN - 09621674-5-2; $22.95; for grades 1-12.
3. Videotape #1: "Infinite Series By and For Young People ages 6 and up"; running time 24 min.; 1990; ISBN 09621674-2-8; Parallels Ch. 1; $42.95; for grades 1-12.
4. Videotape#2: "Iteration to Infinite Sequences with 6 to 11 year-olds"; running time 38 min.; 1990; ISBN 09621674-4-4; Parallels Ch. 8; $42.95; for grades 1-12.
5. "A Map to Calculus" by Don Cohen; publisher Don Cohen- The Mathman; a 15"x18" poster-flowchart, an overview with the chapter nos. and the VT's annotated on the map; $7.95; for grades 1-12.
6. "Changing Shapes With Matrices" by Don Cohen; publisher Don Cohen- The Mathman; 1994; 80pp; ISBN - 09621674-3-6; $9.95; for grades 1-12.
On the internet Amazon.com sells all my materials, as well as The MIT Museum Shop (except for the Map) + other places sell some of my things.