My paper - An Introduction to Number Theory with Talented Youth - was accepted for publication in a special edition of the
School Science and Mathematics Journal
(U.S.A.) on gifted and talented mathematics and science students. The paper was published in the Volume 99, Number 6, October 1999, edition of School Science and Mathematics (pages 348-353).
That paper was a much abbreviated version of a substantial document (54 pages; there's a link further down) with the same title, which describes some of the work that I did with a group of sixteen students in July 1993 in the
Irish Centre for Talented Youth
at
Dublin City University (D.C.U.) in its first year of operation.
How did I - not an employee of D.C.U. - get involved with this project? First, before I was invited to become involved, I had never even heard that D.C.U. was intending offering a mathematics programme for Talented Youth. D.C.U. took its cue from the John Hopkins University (J.H.U.)
TCY program (one that started in 1979); the prime mover for introducing a similar programme in D.C.U. was its then progressive first President Dr. Danny O'Hare.
Now, I don't know how/why this happened, but early in June 1993 I was phoned by someone (X, who will remain nameless) from D.C.U. asking if I would involve myself with its Talented Youth mathematics programme, one based on the (then) John Hopkins model (I hope very much that it's since changed). I asked what the J.H.U. approach was, and I was informed that it involved using a text book - one with material at a higher level than the corresponding high school one - and just teach the contents to the identified talented students...
I wondered what the point of doing that might be, as it seemed to me that the students would just return to their regular high schools and... , and while they would know more than they previously did, they wouldn't have benefited one little bit. What, X asked me, would I do if I was given charge of the D.C.U.-identified 'talented' students? Well, I would give them something to think about... nothing so simple that they would be bored/offended, nothing so difficult that they would be crushed, rather something in between... Like what? Well, I certainly didn't expect that X would be able to cope with anything I might offer him/her, and I could only start to ask questions when I actually saw some live students in front of me...
This was all just too much for X (understandable perhaps), and I got the thumbs down (to my relief at the time)... but then, a few weeks later, X approached me again (D.C.U. was evidently stuck/desperate). and I got the go ahead...
This is roughly what I did. My entire emphasis was on trying to get students to think about serious mathematical questions. I believe I succeeded ... . See for yourself, and let me know what you think (Over the years I have heard from only one person: Dr. Charalampos Toumasis, Director of the Patras State Department of Education (Greece); as Gauss said in another context: few, but great).
The entire test of the original 54-page document (which has my now out-of-date email address, and old web site address) is now
available here
in pfd format. Anyone who wishes to write to me about this document should use my email address at the foot of this page.
I greatly value Paul Halmos' opinion
of the above document.
The following year I was invited to teach for a second time on the programme, and I happily accepted. On that occasion, having just decided to teach a new course (Number Theory and Cryptography) to my undergraduate students, I thought it an ideal opportunity to test out the basic ideas of my course with my young students... A bit of a risk, yes, but it worked. They learned a lot of new Number Theory, quite different from what they had encountered the previous year (several came for a second time).
When I was about mid-way through what I intended doing I was approached by the (then) head of the Mathematics Department
Alistair Wood (oh dear, not much there...) who asked if I would mind if some invited observers from the USA could sit in on one of my sessions with my stars. Yes, of course, any time. I told my young students to expect a visit sometime, to simply ignore them, that they wouldn't have a clue what we were doing. Eventually a large group entered, sat at the back, looked suitably bemused, and left after a full hour. Later Alistair Wood - with some visiting observer from London - informed me excitedly that some of the U.S.A. observers had pledged (on the basis of what they had seen me do with my stars) half-a-million dollars to D.C.U. Wasn't that great? Well, yes, it was...
Besides myself teaching one group, there was a wonderful high-school teacher (Martin Hilliard) taking a second group; Martin and I got on wonderfully well (and we still do!) and we had many a happy mathematical discussion at lunch times.
Coming to the end of the three weeks we heard that the big-wigs were taking themselves off to a dinner in some fancy restaurant, but that none of us (the worker bees) were being asked to join them. I hope they left a big tip out of the half million dollars... That ended my days at D.C.U.
P.S. The day will inevitably come when D.C.U. takes down the above weblink for Alastair Wood, but it will always be preserved at the
Internet Archive.
