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New A level Maths: do we approve of calculators in every exam?

New A level Maths: do we approve of calculators in every exam?

After going through the new A level Maths specification for Edexcel with a fine toothed comb  most changes are really positive. Students will be stretched and challenged in healthy ways, actually applying what are routine calculations to ‘wordy’ contexts. It looks like actual ‘on the spot’ thinking will be required -  just knowing the computational basics will not be enough. Based on my experience, I deeply believe that it will produce stronger mathematicians.  

So I am surprised and worried that all exams permit calculators. Is this healthy for A level students?

For the record, I think calculators are useful and serve a great purpose in streamlining the mundane calculations from exams and allowing students to be rewarded for ‘using the numbers’ and not just ‘producing’ them. Having one available all the time however, is like asking a diabetic to work in a sweet shop. Restraint will need to be actively encouraged, not assumed.  

So why do we think the restraint from using a calculator is important? Most of the mistakes made by students on the A/B borderline at A level Maths tend to be silly mistakes and most of those tend to be computational errors. I call it the ‘juggling oranges vs melons’ trap and it is tragic to watch.

This is juggling oranges :

Simple in theory and totally the kind of calculation that is currently being entered into calculators up and down the country by 17 year olds. We are certain that students can do this without, but there is a lost opportunity here to keep the story of common denominators and lowest common multiples alive in their minds. The answer is not important here, it is how we got to it.

Simple in theory and totally the kind of calculation that is currently being entered into calculators up and down the country by 17 year olds. We are certain that students can do this without, but there is a lost opportunity here to keep the story of common denominators and lowest common multiples alive in their minds. The answer is not important here, it is how we got to it.

Here’s juggling melons:

This is in essence a common denominator story with slightly scarier lead characters. Having a calculator is of no use here but a computation of this sort is expected of students. This is where we let students down by not showing them the importance of restraint and how it undermines the long term added value of really knowing the process. Students are more likely to make mistakes because the story of common denominators is not as fresh in their minds.

This is in essence a common denominator story with slightly scarier lead characters. Having a calculator is of no use here but a computation of this sort is expected of students. This is where we let students down by not showing them the importance of restraint and how it undermines the long term added value of really knowing the process. Students are more likely to make mistakes because the story of common denominators is not as fresh in their minds.

So yes, the exam boards say that students are permitted calculators, but the skills expected are heavier and more daunting versions of basic algebra. These are so often under-practiced or totally avoided by over-use of calculators in students hands. Instead, students need to be educated on restraint.  

How can we sell restraint to students? We can’t just say ‘try it without a calculator’, as if we are inflicting unnecessary pain. We need to give them the rational reasoning behind it. Once they see it is not about getting to the answers, it is about practicing the story in the method, the numerical answers and the speed with which they get to them become less important. So when faced with scary looking algebra in the exam, they will see that oranges and melons are just different in weight; the techniques are identical and they have known them all along!

New Maths A Level & the focus on problem solving

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