Gaming is Good for Students

Before you recoil in horror at the deliberately provocative title of this post, please be reassured that I am not referring to Call of Duty, Grand Theft Auto, FIFA, Angry Birds, Candy Crush or any addictive computer game that, like sugar, is obviously not good for students but they consume in vast quantities anyway. In fact, when a recent study by Dr Kirsten Corder of Cambridge University concluded that students who spend an extra hour a day studying, rather than engaging with a computer/TV/iThing, get better exam results, I was gobsmacked that this was sufficiently newsworthy to appear as a story in The Telegraph.

No, the sort of gaming I am referring to are those wonderful mathematical strategy games, such as John Conway's Sprouts, that are simple enough to introduce and play in one lesson but sufficiently rich to provoke mathematical discussions for many afterwards.

I don't play these games enough with students because I keep on forgetting the rules and never seem to manage to find the time to refresh my memory. This is why I was ecstatic to find the following book in Blackwells this summer:

It contains details of over fifty games that are based on pure mental skill; no chance involved at any stage. Extraordinarily, a significant proportion of the games have been invented in the last couple of decades as advances in computing have allowed creators to share new games in internet forums. The online community tries them en masse and quickly dismisses those that lack drama and depth.

On Saturday I introduced one called Semaphore to my eager Year 10 students (I can't recommend teaching on a Saturday but boarding schools will be boarding schools). There are very few of my lessons that I would class as an unqualified success but this was certainly one.

Semaphore is a game for two players. It was invented by Alan Parr in 1998.

The game is played on a 3x4 rectangular grid and requires a pile of yellow, green, and red counters.

Equipment for Semaphore.

During a turn, a player must do one of the following:

1) Place a green counter on an empty square.

2) Replace a green counter with a yellow counter.

3) Replace a yellow counter with a red counter.

Players take turns until someone makes a line consisting of three counters of the same colour. This player is the winner.

The rules are simple, the game-play is swift but, unlike noughts and crosses from which it evolved, there seems to be no clear strategy. It is exciting and frustrating in equal measure; a player might be certain that he is one move from winning but, in setting a trap, has allowed his opponent a chink in his armour.

It is Player 1's turn. Can he avoid defeat?

The wonderful thing from my perspective as a teacher is that it immediately provoked a wide variety of investigative questions from the students.

Some were easy to answer:

Can the game end in a draw?

Some seemed impossible:

Does the person going first have an advantage?

Some students noticed interesting opening gambits:

Can the next player place a green counter?

Some students suggested extensions:

How does the game change if we add a fourth colour or change the size of the grid?

One pair of students successfully provided a winning strategy for a game on a 3x3 grid. Then they had to think about how this was affected by a fourth colour.

Here's another question that might fool a student into providing a mathematically watertight proof: Is it possible to tell, just by looking at the board, whose turn it is? The argument required isn't sophisticated but that doesn't matter. This is supposed to be fun after all.

However crammed your scheme of work, you must find time for a game or two of Semaphore sometime this year.

from matheminutes http://ift.tt/1Nqryrm