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 :
Here’s juggling melons:
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!