Tuesday 28 June 2011

Happy Tau Day

Happy Tau Day!

Happy what day? Tau is a mathematical constant, whose value is 6.28... . Is that ringing any bells? Correct:

OK, so tau being 6.28 explains why 28th June is Tau Day (blame the Americans - they write their dates backwards). But why do we need a new mathematical constant, especially one that is simply double another one?

Some maths teachers and academics have been in favour of using tau instead of pi in maths teaching, particularly in early years. It's because 2 pi seems to crop up a lot, probably more often than a single pi, particularly in geometry and trigonometry. For example, the circumference of a circle is given by:

If tau were widely adopted, this would be replaced by:

Personally, I'm not convinced. Tau would certainly be useful in a number of formulae and mathematical solutions. But I think students would end up using a half of tau just as often as they currently use 2 pi.

And if we went to a system where both constants were in use, would this not just add to the confusion, rather than alleviate it?

Finally there are thousands of years of pi tradition. The ancient Greeks obsessed over pi, just as much as modern mathematicians do.

What do you think of tau?

Thursday 9 June 2011

Exam Standards Are Slipping (That's The Papers, Not the Candidates)

You may be used to the idea of going into exams to find questions you find impossible to answer.

If you sat the OCR Decision Maths 1 exam on 26th May you will certainly have found yourself in this situation; one of the questions had no solution.

This embarrassing slip-up was the first of five errors on AS exam papers this summer. The other mistakes came to light on:

  • an AQA Business Studies paper, in which there was not enough information to answer the question;
  • an Edexcel Biology multiple choice exam, in which none of the answers given were correct;
  • an AQA Geography paper, in which the flow of a river was incorrectly labelled at one point;
  • an AQA Computing AS Level paper, in which an arrow was shorter than it should have been.

Reports are also circulating of mistakes on a CCEA business studies GCSE and one more, undisclosed paper.

Jim Sinclair, Director of the Joint Council for Qualifications, said that procedures were in place to cope with these errors.

In the case of the Decision Maths, the question was worth 8 marks out of 72, or 11% of the total marks awarded for the paper. The exam board OCR have decided not to discount the question from the paper, since it was worth such a large percentage of the marks. Instead, they will award marks for correct working, which will reward pupils who spent some of their time attempting to answer the question.

But many students are unhappy with this proposal. Facebook groups have been formed to demand a complete rerun of the exam. Some students think the time they wasted will jeopardise their chances of them getting the grades required for their university applications.

More details about the impossible D1 question are here.

Our advice to examination candidates has always been: if you can't do a question on the paper, leave it and come back to it if you have time at the end. It may be time to modify this advice: leave it; it may not be possible anyway.