In my experience with supervising maths[1] exams here in the UK (below university level[2]), there are usually two exam papers in a row, in the same session. A "Calculators" one and a "No Calculators" one, in that order.
Even in the Calculator paper, written workings-out are encouraged even if not explicitly requested. Iif you mis-key something and multiply by 6 instead if 3, you can get credit for the bits of the calculation (before
and after) that you got right, as is true with all non-calculator answers as well of course.
Once the time-limit is reached for the first paper (say, one hour, with one further hour for the second paper), the devices are conspicuously placed on the floor. If the first paper is 'finished' prior to this hour, then there's nothing to do but check you got everything 'right' (FCVO...). When you're in the second paper's time, though, any spare time can be used to go over
either paper (although you may not pick up the calculator again).
Ultimately, the first paper is geared more for understanding. Indeed, the calculator is expected to do the calculations themselves (e.g. stuff like Sins and Logs, these days they no longer having "table" booklets to use to refer to) and do the more complex digit-crunching for you, but you are still tested on whether you can apply the methodology.
(And yet
still, there's a fuss at the beginning of each exam as people who have forgotten their calculators are sorted out and usually the teacher who had
specifically informed them that they needed to bring one makes a note so that they know who to have 'words' with after the exam has finished.)
The second paper continues with the theme of testing methodology but now also tests mental (or at least non-automated) arithmetic skills, actual drawing of graphs and other things that a calculator couldn't so easily do[4]. I'm sure that any 'savant' who can work out logs in their head, etc, is not going to have a problem (calculator or no) with this paper and will be capable (assuming not stymied by social incompatibilities and lack of empowerment due to other factors) of rising to a level of education far beyond secondary school level. If they lose marks for not noting things down[3] then they have been failed by their special-needs tutors/whoever not making it clear they need to do something about this, but they'll probably be fast-tracked beyond this level, regardless, in any decent school system that recognises their respective needs and abilities.
I never did actually use slide-rules (beyond playing around with them in my own time), back in
my day, but I think their use/non-use was equally governed, and while only useful for reference for their specific range of functions the Log and trigonometric table booklets that I (at least once) was issued were not given for every mathematically-inclined (i.e including Physics) exam, much as the "booklets of common formulae" that might have featured some times (while in other papers I will have been expected to
know the formulae for solving a quadratic or for calculating time dilation at a given speed, and was thus tested upon that as well).
[1] Math(ematic)s.
[2] I can't even
remember how it went for me when I was going
through the exams, but calculators (albeit primitive by today's examples) weren't outright banned, but may also have been allowed/disallowed in turn. I remember having an early programmable calculator, at one stage, and showing the examiner/an invigilator that I had wiped the memory clean of any pre-existing programs. (Although I also recall knowing that the examiner was pretty much in the dark about my device, in those early days, and I could easily have snuck something through, if I thought it would be worth it and had actually wanted to...)
[3] I'm not sure if perfect answers can be marked down for no workings out. Probably they can where it
says "show your workings out".
[4] Yes, they can often
display graphs, these days, but as you don't get the chance to let them do that and then copy the results onto paper 2 it's rather moot anyway.
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Topic: So ... why are Asians stereotyped as math geniuses? (Read 13433 times)