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Not so sadistic statistics

Q

My Year 10 students are struggling with the planning aspect of the GCSE statistics coursework. How I can get them to think for themselves?

A

"If Year 10 students are all tackling the same problem, it is difficult to get them to think individually," says Barbara Cullingworth of the Mathematical Association, who has the following advice: "They don't seem to have the confidence to produce coursework on their own, possibly because they know that the result counts towards their final grade.

"I suspect one needs an open class discussion-cum-brainstorm on: what are we hoping to find out?'; how could we do this?; what do we need to collect, and how much?; what resources are available?. Or, making sure that all are involved, split the class into groups of about four with the same sort of questions and get them to discuss it in the group (a fairly noisy activity) and report back. Data collection could even be done within each group so long as every member has a clearly defined target.

"I have never been ashamed to add an element of competition, with a small prize for the group which produces the 'best' plan of action, where 'best'

can mean 'imaginative', 'most attractively produced', or any other criterion which does not automatically mean that the best mathematics in the room win.

"If they are choosing their own area for investigation, they need to produce a plan, answering the same questions in bullet form. This could then be shared or discussed in a small group with the aim that each student helps the others in the group to refine their plan. To overcome difficulties in making a choice I have always encouraged them to think about their interests, even when those are TV soaps, pop music or internet chat."

And here is a poem that might help:

Planning for Research

Remember for research design

Good planning is essential

To increase the potential

That this work is influential

For informing change

Don't begin your experiment

By collecting the data.

That should come later

When you can cater

For its analysis.

Through focused discussion

and reading ingestion

Leads to a suggestion

Of the research question

For your hypothesis

Now you have an hypothesis.

This discovery of treasure

Gives you the pleasure

Of knowing what to measure

To collect the data.

Next decide on your sample.

By choosing your subjects

Knowing which are rejects

To make the projects

Sample representative

Having decided on recording

Begin the data collection

For the perfection

Of the reflection

During analysis.

Now come the results.

This can be done in parts.

Perhaps producing charts,

Statistics that impart

Some feeling for the data

Now in the conclusion ...

Your teacher will go ballistic

Without the right statistic!

Q

I am a teacher with 25 years' experience and am finding it really difficult to allow the children to develop their own personal methods of calculation.

I'm of the old school where I think all the children should be using is a uniform, effective method.

A

Surely an effective method is one which can be done quickly and correctly. At primary school I was taught to use the "borrow one, pay one back" method of subtraction. At teacher training we were told to teach subtraction by decomposition as it taught children why they were borrowing using place value. I always found it cumbersome; many children entered secondary school not able to subtract properly. Most had forgotten why they were using this process, as could be seen when they tried to subtract in hours and minutes. With the new strategy came the delight of knowing that we can openly encourage children to adopt their own efficient methods.

Name that gradient

You asked (TES Teacher, May 17) why "m" is used for gradient in the general equation of a straight line. The important feature in gradient is that the climb, or y-bit, comes first. (The y-bit and x-bit seem to be awfully useful not just for gradient, but for distance formula and vectors as well.)

I also advertise dy over dx, as seen in displays for Scottish Higher (AS level) classes and used by big sisters and brothers. This gives the class a feeling of knowing something before they should.

I do like your cartoon - is that an example of Cat-esian geometry? Speaking of Descartes: his native tongue was French, perhaps he used monter (to climb), hence the initial m.

Walter Burton, Edinburgh

Wendy Fortescue-Hubbard is a teacher, game inventor and member of the London Mathematical Society. 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. Email your questions to Mathagony Aunt at teacher@tes.co.uk Or write to TES Teacher, Admiral House, 66-68 East Smithfield, London E1W 1BX

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