by Laurent Lafforgue
translated from French by Ralph A. Raimi
Let us take the example of the four operations: addition, subtraction, multiplication and division. Their teaching has been considerably retarded and neglected in recent decades, to where the majority of middle school children do not know the multiplication tables and many high school students are unable to add two fractions. These operations have been neglected because of the emergence of calculators, and the belief that an operation carried out by a machine can be the same thing as an operation carried out by a human spirit. It is the same thing as to result – supposing that one has calculated correctly and not made an error of fingering, and with the reservation that there are, just the same, many occasions where the calculator doesn’t replace a mental calculation: I recently received a letter from a grandfather whose granddaughter had been fired after several hours as a salesgirl in a market because she was unable to make change.
. . But above all, a calculator which one has programmed to perform certain operations knows only those operations for which it has been programmed. Whereas those same operations acquired and mastered by a student becomes nourishment for his spirit, empowers him, is digested by him, is made his own, enlarges and awakens his mathematical faculties and power. A familiarity with numbers, and similarly as to geometric objects, that permits the life that has been given him to enter, little by little, into the world of mathematics.
Are you aware that each year there are written in this world millions of pages of new mathematics? And that they are the result of the direction to the human spirit given by something so simple as the four operations of arithmetic? Do you know that after all these millions of investigations, mathematicians still have not finished with addition and multiplication, that probably they will never be done with them, that the creative power of human beings still finds nourishment in them, and something to transform in the same way that our organism digests food – changing it into bone, flesh, muscles and nerves, then into movements, and so on into the profusion of human actions?
Why the Public Schools?
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I am an adjunct Associate Professor of Mathematics at Rider University, active as a substitute teacher and mentor in high schools, and a retired professor of physics from Rutgers University. I have taken extensive notes from my experiences and given them to my protégés. Recently I collected them into a book. I suggest that your library purchase the book for the benefit of students, parents, and teachers.
I just wrote a book, "Teaching and Helping Students Think and Do Better". This is available on amazon.com, ISBN 978-1-4196-7435-8. May I suggest that you order a copy for the library? The readers will be very pleased!
The reviews are superb. Students, teachers, and professors who have looked at the book give it the highest rating.
Typical comments that I hear are things like this: "Hi, Dr. Aranoff!" said a girl, "I got a 100 on the test! I am so happy! Thank you so much!"
I also wrote a paper in Gifted Education Press Quarterly:
http://www.GiftedEdPress.com/GEPQWINTER2008.pdf
Here are some comments:
"We really enjoyed the latest GEPQ and especially liked the article by Sanford Aranoff. He took a very practical approach on an eyeball to eyeball level. A lot of this really needed saying. He showed a keen awareness of the trends towards anti-scientific education that are out there. We made a hard copy of this article and will send it on to the heads of the science and math departments at Loyola Academy with the intention of their distributing it to department chairs in the Jesuit Secondary Education Association."
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