[seqfan] Re: Sequences K-12 project

Mon Apr 28 18:25:36 CEST 2014

Hi Andrew,

Thank you so much for your input... especially sequences #3 & #4 which need
an advocate like yourself.

There will be tensions in choosing the 13 curricular sequences - one for
each year of a child's education - because of different curricula on both
sides of the pond and beyond ;-)

Gord!

On 28 April 2014 04:40, Andrew N W Hone <A.N.W.Hone at kent.ac.uk> wrote:

> 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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-- 
Gordon Hamilton
MMath, PhD

www.MathPickle.com
Put your students in a pickle!