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Exam technique: is it advisable to use methods beyond the syllabus?
By Sarah Hunak (P2100) on Wednesday, September 13, 2000 - 07:43 pm:

Hiya

I don't quite know how to word this question, but I'll have a go. Sorry if you don't follow!

Say at GCSE level you are taught two different ways of working something out and each way is for its own specific case. But if you know another way to do it which will work out all cases but it is not taught until sort of A-Level-ish then could you use this way in your GCSE exam instead of remembering both of the other 2 ways because you would get the right answer and it is easier for you to remember? Or would you lose marks for not using the way for the specific case on the exam paper that you should have learnt?
If you understand what I'm talking about, then please answer. If you don't, I don't blame you! Sorry!

Sarah

By David Loeffler (P865) on Wednesday, September 13, 2000 - 09:36 pm:

I would recommend that you use whatever technique you find easiest. I don't think you can really be penalised for knowing too much! Remember that the people marking your GCSE papers will probably be teachers who will (one hopes) know the A-level stuff as well.
Also, I have seen a few (A-level) mark schemes and they would seem to suggest that if you quote results at a higher level then you will definitely not lose marks for it, as long as they are correctly used.
(For example: "Anyone quoting the Cayley-Hamilton theorem should recieve full marks for this question" - seen on a Further Maths mark scheme.)

Does anyone know the official line on this one?


David

By Harry Smith (Harry) on Thursday, September 14, 2000 - 09:49 am:

Hi Sarah

In principal, David is right and as long as you understand a more complicated method fully there should be no problem in using it.

However, I would have to recommend that you learn the methods you have been taught by your teacher, and that you use them in the exam. The reasons for this are:

1. You might be asked to use a specific method, or be given a multi-part question that leads you through that method.

2. If you get the answer wrong or make a mistake tapping the numbers into your calculator you are more likely to get the method marks if you have used a standard technique. The person marking your exam will have seen hundreds of scripts and won't spend a long time trying to see whether the method you've used is OK.

I think it is especially important to use the method you've been taught if it is a big difference in approach. e.g. if you have been taught to use trial and improvement to solve an equation like 4x = 21 then you probably shouldn't do it using logs, as trial and improvement tests lots of other skills like data recording.

Another thing to be careful of is if the normal method doesn't need a calculator and your more advanced method does. Because the question could then appear on the non-calculator paper of your exam.

Good luck!

Harry

By Sarah Hunak (P2100) on Thursday, September 14, 2000 - 08:19 pm:

Hi Harry

Thanks for that. All 3 of the methods I am talking about don't require the use of a calculator. The method I know is more basic in principal than than one of the others but I was wondering if you would get marks for using the correct method I should have been taught and remembering the relevant formula for it too?

Sarah

By Pete Capewell (T1368) on Thursday, September 14, 2000 - 11:07 pm:

Dear Sarah,

Please be specific. What problem are you solving, which methods do you dislike and what is the method you prefer? Finally, which exam board is your school using? I have a fair bit of experience teaching for London/Edexcel but you might want to check out the specifications online for other boards.

There are a number of classic problems in GCSE maths that have a number of possible methods: take for instance the multiplication of two whole numbers. You can add repeated values, use 'short' or 'long' written methods, use Napier's methods (also called the Chinese squares method) or even use the Russian Peasant method. All work.

Indeed each of these methods will be awarded marks if you're correct. The issue comes if you are wrong. When you are wrong, method marks become crucial. However, it is often pointed out that half or more of the marks at GCSE are for methods. It's so easy to make a careless error of arithmetic or transcription that even the best candidates should be jealous of their method marks.

Remember your script is a communication between you and your (hassled, underpaid, and not necessarily very awake) examiner. Don't count on them to be creative, inspired or interested in your novel ways of solving a problem. At GCSE (as indeed at higher examinations) there is, sad to say, an element of jumping through hoops. Make life easy on your examiner and he/she will make life easy on you. That means clarity of handwriting, clarity of layout, clarity of method, clarity of symbolism.

It is a useful history lesson to realise that some of the world's greatest mathematicians failed to gain entry into universities and/or to gain the acceptance of their peers by not thinking of their audience. (Evariste Galois effectively told his examiners that their questions were rubbish and dazzled them with innovation to the point that he was rejected - see Simon Singh, Fermat's Last Theorem, 4th Estate, London, 1997. p236)

All this goes some way to explain why many educators deeply distrust the examination as a way of judging candidates' abilities. But we do seem stuck with them for now. So I guess we play the game.

Can I reiterate the point that learning *several* standard methods gives you opportunity to check your calculations. This is essential if, as I guess, you are aiming for a top grade.

Regards
Pete Capewell, teacher of maths, Birchwood School, Bishop's Stortford.

By Marcus Hill (T3280) on Thursday, September 28, 2000 - 12:28 pm:

Quite often, GCSE mark schemes (more so than A levels) are extremely specific and rigorous. If your answer is wrong, the examiner - even if he or she follows your working perfectly and can see that it is elegant, way beyond the level you need for GCSE and that your only mistake was (say) missing out a minus sign in the last line of working - may not be ALLOWED to give you any marks at all.

My advice would be to save showing your sophisticated skills for the investigation tasks where markschemes are much more geared towards allowing any acceptable method.