Is there a more monotonous exercise for a pupil than calculating some summary statistic of a set of lifeless data lying flat in the pages of a textbook? One of my own school reports mentioned that I thoroughly enjoyed maths "apart from the more mundane parts of statistics". If treated with some imagination, however, the introduction of statistical concepts and measures can provide some entertaining lessons. The trick is to remember why this branch of maths exists in the first place.
We need statistical techniques so we can unlock the stories behind sets of data. I suppose we could introduce the idea of averages by plucking some numbers out of mid-air, writing them on the board and calculating their mean, median and mode. This rather misses the point though; with no backstory and no context these calculations are meaningless algorithmic processes. To bring these ideas to life, all you need to do is get pupils to generate the data themselves. Their generation doesn't remember a time before interaction via social media, now as common a pastime as watching television. Why would they wish to sit passively and explore someone else's data?
You could, for example, get pupils to perform an experiment in class. One activity suggested to me years ago, which I have used several times, involves asking them to stand behind their desks and hold their breath for as long as possible. It is almost inevitable that, after about 10 seconds, one pupil will no longer be able to contain themselves and will start giggling. In turn, a bunch of satellite gigglers will emerge. This is brilliant news, since you will be able to ask why the modal time is much lower than the other two averages. Every link that a pupil can forge between the statistics and their own experience is precious.
A second idea that works well is to use data from sports fixtures in which pupils have played. I show various graphics from cricket matches I have umpired and ask the class what they can deduce about the match's progress, conclusion and star players. They explore the contrasting details they can glean from a Worm (a comparative cumulative frequency diagram) and a Manhattan (a bar chart summarising each over's action). Again, they feel some ownership of the material; the numbers reveal information about something with which they are personally familiar and this reinforces the narrative nature of statistics.
Owen Elton teaches maths at Charterhouse in Surrey and writes a blog about extra curricular maths ideas: www.matheminutes.blogspot.com
Try XPMath's online game, Plinko, for a practical lesson on probability.
Analyse statistics about global issues with real-life data graphs from Nicholas Wilson.
In the forums
In the TES maths forum, teachers are debating the top three things needed to improve UK maths achievement in the next few years.
Find all links and resources at www.tes.co.ukresources036.