Do you have any ideas like “the divisibility rules” (TES Teacher, November 8, 2002)?

A) I carried out the following with a lower-set Year 10 class as part of their GCSE coursework. It could easily be adapted for older or younger students, and it will be just as good with a large or a small group.

Part of the data-handling strand of the national curriculum requires pupils to carry out an investigation. In our case, pupils designed an experiment based on my Perfect Times multiplication tables game, during which they collected their reaction times. A free online version is available for the 9 and the 24 times tables, together with reaction times at www.perfect- times.co.uk (pupils can use pseudonyms, but are advised to note their login details in their planners). We are not alone in doing this: in the AQA (modular) maths specification B, a statistics coursework task of module 2 (2004) is based on reaction times and is accessible to all candidates regardless of tier of entry.

Before collecting the data, students played the game themselves. This gave them a “feel” for the game and helped them decide on questions and how to analyse the data.

To help generate questions, start with this statement written on a piece of card: “People are faster at their nine times table than their nine divides table.” Next, ask pupils what other statements they might make concerning the game. These might include: reaction times are faster without music playing than with it playing; reaction times with large multiples are slower than reaction times with the numbers 1-12; reaction times of people aged between 10 and 20 are faster than those of people aged between 20 and 30. By the end of the discussion you should have plenty of ideas.

Then they need to design the experiment. They must decide on a hypothesis to test. This could be different for different pupils. They also need to decide on who will make up the sample population, how large the sample should be and how much data they need to collect. And they need to be aware of any time restrictions due to other commitments.

They should also consider any special conditions they must set. For example, if they choose to investigate differences between music playingno music playing conditions, a set of ear defenders should be used to block out other sounds.

They should consider how to analyse and display the data. For example, which average to use - mean, median or mode? Or the type of graph that best illustrates the data: line graphs, box-whisker plots, percentage of data above below certain times and so on?

I normally get them to write up the main points from these discussions before collecting any data as I find it helps them focus on what they plan to do. It also provides a focus for the final report, which needs to contain their conclusions. In this they should not only report on their findings, but also discuss any faults with their experiment, what points they would change and what they would like to find out next.

If they have used the website to collect their data, they can turn to the results page and see if their data have been replicated with a much larger dataset.

Q) We are currently revising transformations. Can you suggest any interesting approaches?

A) One of the mistakes that pupils make when constructing their own reflections is that they don’t make their lines for the construction of the image of reflection at right angles to the mirror and at the same distance from it. Your class might find it interesting to begin the lesson by discussing my poem “Reflection on transformation”. In particular use it as a way to draw out the rules for creating a correct image. The poem is also available for you to photocopy on www.mathagonyaunt.co.uk in “TES Teacher articles”.

Wendy Fortescue-Hubbard is a teacher and game inventor. She has been awarded a three-year fellowship by the National Endowment for Science, Technology and the Arts (NESTA) to spread maths to the masses.

www.nesta.org.ukEmail questions to Mathagony Aunt at teacher@tes.co.ukOr write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX