The particular reason calculators are on my mind right now is because we’re in the middle of the examination season. My Grade 10 (Year 11) class did one of their papers on Friday with another tomorrow (Monday). For part of their exam I was teaching another class in a room next door which was a really odd feeling, a good reminder that ultimately teaching is not about me but about my students.
But it’s my A level classes – second part of pure and mechanics – which have had me thinking about calculators. Sometimes people will say things like, “Calculators make everything easy for kids nowadays,” but I suggest to you that this view does not stand up to examination for a number of reasons. In times of yester-year it was possible to set straightforward graph sketching questions. Now that calculators can do this for you, the questions have to be more difficult so that they cannot be solved simply by pressing a few buttons. Also, it is a basic principle of examining (not always followed) that one examines one thing at a time. If you wish to examine long multiplication, fine. If you wish to examine trigonometry, that is fine as well, but not if you are requiring long multiplication skills at the same time. So in times of yester-year, there were all kinds of ways of making the arithmetic simple in conceptually demanding questions. If a complex question yields the answer 3, it is reasonable to suppose that you’ve done things correctly. With calculators readily to hand there is no need to make the arithmetic work out easily which deprives students of that reasonableness check.
It is still the case today that, in A level papers, you can speed things up considerably with a few basic non-calculator techniques. On “Come to school as a book character” day a few weeks ago I went as James Bond complete with water pistol, which I used to indicate wrong or hesitant answers with my Grade 12 / Year 13 / upper sixth class to questions about the sine / cosine / tangent of 0, 30, 45, 60 and 90 degrees. Graduation is coming up shortly, I suspect that they might take revenge on me for this, ah well, a sacrifice I’m happy to make for their learning. Also, knowing the first three Pythagorean triples – 3,4,5; 5,12,13; 7, 24,25 – can again really speed things up with certain kinds of questions. It just feels that the ‘You can do anything on a calculator’ mentality makes students resistant to this kind of approach.
When I worked in teacher training one of the classes I ran was on the use of a calculator in which I took the view that there are three reasons why one might use a calculator in a mathematics classroom: to explicitly teach their use; when needing to do calculations when actually thinking about something else (eg. trigonometry); as a learning tool. In practice what this means is that calculators need to stay in bags unless there is a good reason to have them out. If doing eg. areas of rectangles when the numbers are straightforward, for goodness sake, let’s use it as an opportunity to do some times tables practice. My small Grade 7 (Year 8) class have taken this on board to the point where they don’t bring calculators even when I specifically ask them to do so. “But you said,” yes, you’re quite right, I did. However…..
So, when doing GCSE and A level questions myself, either alone or in front of classes, I only reach for a calculator when I can’t easily do the calculation in my head or quickly by written methods. I have harangued shop assistants in several countries for reaching for calculators to do things which can be done mentally in less time than finding the calculator, let alone working out which buttons to press.
Am I being very old-fashioned / reactionary / fuddy-duddy? I don’t think so but am not in the best position to judge. As always, any thoughts gratefully received. Thank you for reading, I’ll be back again soon!
Geoff Tennant's Blog 