Doing maths for the sake of it

By Mark Dawes (February 2019)

It is often noted that in certain subjects it is common for teachers to use elements of their subject in their personal and leisure activities.  For example, I know English teachers who write poetry, music teachers who regularly perform in concerts and write music, PE teachers who play for teams and drama teachers who also act and direct.  In my school there is a display titled “The Art of the Art Teachers”; all of the members of the art department are practising artists as well as being teachers.

So, what about maths teachers?  What do (or could) we do?

I am not talking about the practical uses of mathematics (when to leave to get to the train station on time, how long it will take to mark a set of tests, how much money to take with me if I decide to run to the shops and don’t want to carry too much, etc), because most people do this (in the same way that writing a shopping list isn’t done exclusively by English teachers), but things that get to the essence of the subject of mathematics.  I can’t keep up with current mathematical research, but I can solve problems and puzzles and can enjoy working on what is referred to as ‘recreational mathematics’.

In May 2005 I had a letter published in The Independent newspaper about their instructions for Sudoku:

Now that you have people hooked on Sudoku to the extent that you include 4 puzzles each day, the time is right for you to rephrase your instructions (“There’s no maths involved. You solve the puzzle with reasoning and logic.”).  This is a golden opportunity for you to point out that reasoning and logic are mathematical skills and that maths does not mean merely ‘doing sums’.  Solving Sudoku without using mathematical skills would be like solving a crossword without reading the clues: possible but very, very difficult.

Aside from different variants of Sudoku and other similar puzzles and problems, what else is there for a mathematics teacher to do?  Mathsjam https://www.mathsjam.com/ , which takes place on the second-to-last Tuesday of each month in a pub in many cities around the world (including in Cambridge) describes itself as follows:

MathsJam is a monthly opportunity for like-minded self-confessed maths enthusiasts to get together in a pub and share stuff they like. Puzzles, games, problems, or just anything they think is cool or interesting.

More recently I have found myself turning to Twitter for puzzles and problems (some of my favourites are posted by Cambridge Maths Hub workgroup leader Catriona Shearer, who posts as @Cshearer41 – if you use Twitter then do follow her!  While you are there you could also follow @CamMathsHub and @mdawesmdawes).

A real pleasure during 2018 was the start of the regular #beingmathematical sessions.  These take place once a fortnight on a Thursday evening and are led by members of the ATM (@ATMMathematics).  A problem is posted a few days before the session for everyone to work on.  Usually this can be accessed in different ways and at different key stages and the task (chosen from an ATM publication) is designed to be approachable.  While it might well be the case that the task could later be used with children (of many different ages) in the classroom, for me the chief reason for doing this is … for the enjoyment of the mathematics.

I thoroughly enjoy being able to think about a task by myself, then having the opportunity to think about how to share my thoughts while also reading others’ ideas.  Very frequently I find myself realising new things during a session, thinking about things in a new way or making connections I hadn’t previously been aware of.  Working with those with very different backgrounds is extremely enriching.  A very early riser often joins us from Australia, there are others from all over the world, people of different ages and those with very different levels of confidence in their mathematical skills.  Seeing a university professor of mathematics trying to work out how a Foundation Stage teacher used Cuisenaire rods to explore a problem is a delight!

So, if you are a maths teacher (at whatever level) and have an interest in working on mathematical problems, do come along to #beingmathematical on a Thursday evening.