------Response from Richard Askey (by kind permission)------- From: Richard Askey Message-Id: <9703201741.AA10495@conley.math.wisc.edu> Subject: Opinion 14 (fwd) To: zeilberg@euclid.math.temple.edu (Doron Zeilberger) Date: Thu, 20 Mar 1997 11:41:23 -0600 (CST) Cc: andrews@math.psu.edu (George Andrews), askey@math.wisc.edu (Richard Askey) X-Mailer: ELM [version 2.4 PL25] Mime-Version: 1.0 Content-Type: text/plain; charset=US-ASCII Content-Transfer-Encoding: 7bit Content-Length: 1413 Status: RO Dear Doron, Let me strongly recommend your read the collected mathematical book of M. Anno. "Socrates and the Three Little Pigs" will appeal to the combinatorialist in you. "Anno's Counting Book" starts at the right number, 0. When you teach mathematics right, 0 is a very natural number, and place value makes perfect sense. In TIMSS, Singapore had only 1% of their students in the bottom 25% internationally, and had 74% in the top 25%. They do not use calculators in the first six grades, but teach their students to think. Being able to compute is part of thinking. Here is a problem in the teacher's manual for fourth grade students. Take the numbers from 1 to 9. Use the eight not used in the bottom line to fill in the following patterns. **** **** -**** +**** ----- ----- 1111 9999 How many ways can each of these be done? There is someone who has been pushing writing computer programs as a way of learning mathematics for many years. This is Ed Dubinsky. He used to be at Purdue, but has recently move to Georgia. I can send you his e-mail address if you want to correspond with him about his program. It would be a shame for you to have to go throught the same learning curve that he did. I think you should be able to learn what can be done by this method in a year or so. The results might surprise you. Dick (of Dick and George) askey@math.wisc.edu -------end Askey's response -----------------------------