[seqfan] Re: Sequences K-12 project

Mon Apr 28 12:40:11 CEST 2014

Dear Neil, 

I really like this idea. In the UK I have been involved with running and leading Mathematics Masterclasses in Kent, which are supported by the Royal Institution of Great Britain. This is a national scheme, offering classes on Saturdays for bright kids picked by teachers from local schools, and we have been running them at the University of Kent in Canterbury since 2009, with Year 9 (aged 13/14) and Year 12 (17/18). However, I have also been doing workshops with schools, and with mixed ability groups, for over 10 years. 

I can nominate three sequences right away (the 3rd one is a personal favourite which may not be to everyone's taste): 

1) A000079 Powers of 2: This is great for introducing exponential growth, and can be introduced in connection with population growth, starting with bacteria and moving on to people. For younger pupils, it can be the chance to introduce exponent notation for the first time. It can laso lead into radioactive decay afterwards. Several times I have had the comment "Wow, I didn't know that maths had anything to 
do with biology!" 

2) A000045 Old chestnut: This naturally leads on from number 1 in a discussion of population biology, by telling the story of Leonardo of Pisa's Liber Abaci, the introduction of Indo-Arabic numerals into Europe, and then the rabbit-breeding problem. This works really well as a workshop where the students don't know the sequence already, and have to derive the recurrence from first principles (about an hour is needed in that case); even when some of the students have seen the sequence before, they may not see how it is connected to the rabbit problem, and then they are surprised when they spot it. Usually I give them the first three terms or so, and then it is fun for people to guess the answer to the rabbit problem. 

For more advanced pupils, the growth of the sequence leads to thinking about limits and convergence. It can also be used to introduce modular arithmetic, by considering the divisors of the terms (it is a divisibility sequence), and proof by induction. Plotting pairs of points (F_n,F_{n+1}) can be used to think about conic sections (the points lie alternately on one of two hyperbolae) and curve sketching. 

3) A006720 Somos-4: This is a truly nonlinear sequence, and grows much faster than numbers 1 & 2. Going on from modular arithmetic, divisibility and conic sections from number 2, one can look at elliptic divisibility sequences and elliptic curves, starting from this sequence. It is a good thing to motivate really bright pupils and show them where maths can lead beyond school (Fermat's last theorem, elliptic curve cryptography,...).  

Another one I have used successfully in workshops with schools is A005130 (ASMs). Again this is for more advanced pupils: but the story of the ASM conjecture and its resolution is really inspiring, and one can have a lot of fun with combinatorics, trying to get them to work out the lowest terms by hand (3x3, 4x4 probably the limit); one can go via factorials and Stirling's approximation along the way.

I'm not sure if you are only going to focus on education in the US. In any case, I thought I'd give you some of my experience from across the pond. 

All the best
Andy 

________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Tanya Khovanova [mathoflove-seqfan at yahoo.com]
Sent: 25 April 2014 22:03
To: Sequence Fanatics Discussion list
Cc: Gordon Hamilton
Subject: [seqfan] Re: Sequences K-12 project

I teach a class of Olympiad Training at Advanced Math and Sciences Charter School in MA. From time to time I give a class about sequences.

As a homework I give them the MIT Mystery Hunt puzzle called Functions:
http://web.mit.edu/puzzle/www/2008/functions/

which is based on some sequences.

________________________________
 From: Neil Sloane <njasloane at gmail.com>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu>
Cc: Gordon Hamilton <gord at mathpickle.com>
Sent: Friday, April 25, 2014 3:59 PM
Subject: [seqfan] Sequences K-12 project

Dear Sequences Fans,
Gordon Hamilton and I have been talking about the idea of getting some
integer sequences into the K-12 (Kindergarten-Grade 12) curriculum. Gord
has made some really excellent videos about sequences in the OEIS, one of
which is mentioned in the attachment. There are also links to them from
entries in the OEIS.

The idea is to have a 2-day conference in Banff, Canada, next year, with a
dozen
math teachers, and a dozen sequence people,
with the goal of picking out 13 sequences that
could be used by math teachers (one sequence
for each of the 13 years).

There might also be a virtual conference, run on a web site where people
could sign up and contribute. For people who are unable to travel to Banff.

We would like to hear from OEIS folks who would be interested in this
project. Particularly people who are involved with teaching mathematics.  I
know we have contributors from many different worlds - but I don't know
which of you are math teachers. Please let me or Gord know if you are
interested in helping, or if you know of people who might be.

But we would also like to hear from non-teachers who like the idea, and
would be willing to work on picking out sequences that would appeal to
students. This seems to be a good way to enliven math teaching both in the
USA and in Canada - and of course in other countries.

Here's a link to Gord's video about the Recaman sequence. I think
it is really excellent: http://youtu.be/mQdNaofLqVc

Attached is a rough draft of our proposal for the conference.

Suggestions, comments, etc., will be welcomed.

Neil

--
Dear Friends, I have now retired from AT&T. New coordinates:

Neil J. A. Sloane, President, OEIS Foundation
11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
Phone: 732 828 6098; home page: http://NeilSloane.com
Email: njasloane at gmail.com

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