Martin Gardner And Recreational Maths
It’s not easy to pin down what Recreational Maths actually is, but generally the idea is doing maths for fun, with no real aim of passing an exam, making money or publishing in any kind of scientific journal. Recreational Maths is full of things like games, puzzles and mathematical magic, often set in a playful context. Problem solving for pleasure is the order of the day, and Recreational Maths continues to grow in popularity with YouTube channels like Numberphile.
You don’t normally need much formal maths knowledge to get involved in Recreational Maths, making it perfect to use with lots of different types of classes. It also ticks a lot of other pedagogical boxes, as it is fun, challenging and focused on problem solving. There are Recreational Maths Problems which are so simple that you could share them with every pupil in the school, and there are others so deep and complex that they could keep your highest achievers busy for months. Some of the best Recreational Maths topics start off simple, are understood by everyone, but lead down a rabbit warren of complexity to satisfy the keenest mathematician out there.
It is certainly an irony that many so called ‘serious’ mathematicians get hooked on Recreational Maths, and lots of important mathematical discoveries have subsequently been made by amateurs and professionals alike. Recreational does not mean unimportant.
Martin Gardner (1914-2010)
If there was a Hall of Fame of Recreational Mathematics then Martin Gardner would be up there at the top, as the most famous Recreational Mathematician of all time. Martin Gardner became legendary for writing a Mathematical Games column in Scientific American for 25 years and for authoring over 100 books. When many people think of mathematical puzzles they think of Martin Gardner - there is even a convention to celebrate his work called Gathering4Gardner which happens every two years in the United States.
Why is it worth introducing Martin Gardner to your pupils? First of all, his puzzles and other writings are so good that they deserve to be shared with the next generation, but secondly, he is a major part of the mathematical culture of the last 100 years, and should be talked about just like an English teacher might introduce their pupils to famous 20th Century authors.
It is of course important to tell your pupils about a wide range of contemporary and historical mathematicians, but the great thing about Martin Gardner is that you can directly engage with his mathematics, whereas you are unlikely to be able to understand the papers of a Fields Medallist.
Quotes about Martin Gardner
"A good puzzle lasts for thousands of years. Martin had very good taste, and hoovered up much of the best material. So, his work is a treasure trove of really neat ideas." Ian Stewart, mathematician and author.
“many would say that he is the most famous modern writer of mathematical puzzles in the world.” MacTutor History of Mathematics, University of St Andrews
How do I introduce the work of Martin Gardner to my pupils?
A good first step will be to pick up some Martin Gardner Books. Martin Gardner was not a YouTuber – he lived in a different era and lots of his good stuff is to be found in print and not online. Luckily it is easy to pick-up second-hand Martin Gardner books relatively cheaply, such as The Colossal Book of Short Puzzles and Problems.
At this point it is worth thinking about your older students and whether you might want to lend out or recommend titles for pupils to read themselves. This could be a good approach for Sixth Formers who are keen on going deeper with mathematics.
For the majority of your pupils who are unlikely to read Martin Gardner’s books directly, it is then worth thinking how you could find an opportunity to introduce some of the material into your normal lessons or into a maths club.
You may choose to start with a classic short puzzle of which there are many:
The coloured socks (Puzzle Source)
Ten red socks and ten blue socks are all mixed up in a dresser drawer. The 20 socks are exactly alike except for their colour. The room is in pitch darkness and you want two matching socks. What is the smallest number of socks you must take out of the drawer in order to be certain that you have a pair that match?
Hexaflexagons
A good way to showcase Martin Gardner is to build some Hexaflexagons. While Martin Gardner didn’t invent Hexaflexagons, he certainly shot them to fame, and they were the subject of his first ever column in Scientific American.
Here is a Hexaflexagon worksheet to download from the Think Maths website
You could also make a Flexagon Christmas card with your classes
The original Martin Gardner work on Hexaflexagons is found here.
If you want to buy a practical Flexagon workbook:
The Magic of Flexagons: Paper Curiosities to Cut Out & Make, By David Mitchell is available to buy from Tarquin Group.
Tackling Martin Gardner with your pupils
If you are feeling daunted by some of Martin Gardner’s more complex or challenging ideas then take some time to read the article ‘Cultivating Creativity’ on the NRICH website. This makes the argument that it is good to model being stuck with your pupils, as it shows that it is completely normal to battle with mathematical ideas.
If any Scholars or Alumni try out the following approach it would be great to hear how you got on, so please do let us know!
What is important is that at any point of being STUCK we acknowledge that we are stuck, and share our thought processes as we start putting our creative juices to work (Mason, Burton et al. 1982). At these points we should not be afraid to experiment and try ideas out - this is a common strategy we can all use. Perhaps a good way to try this out is to walk into the classroom with a problem we have found in an old text book or mathematical activity book, such as books by Martin Gardner, and say "Let's look at this together" - and then spend time thinking out loud. I am not denying that this feels threatening, but we need to show the students that this is a fairly normal state of affairs by sharing such an experience with them from time to time. Allowing students to watch us struggle whilst describing what we are doing as problem solvers is a powerful model.
What next?
Martin Gardner’s legacy is vast, but hopefully you have been inspired to order a few of his books and introduce your pupils to a Recreational Maths Legend. Some people become fascinated by a single aspect of Gardner’s work, such as by Hexaflexagons or by his mathematical magic or just enjoy generally reading his books for fun - let us know how you get on!
Further Information
Three Dice Trick on Numberphile
Dissect Puzzle
Explanation of the Game Of Sprouts
Search the PlusMaths website for articles related to Martin Gardner
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