War on Calculators

[Toby]

Having recently emerged from the secondary education system in the UK, I thought I might give a perspective on the use of calculators in classrooms as I have experienced them.

In the UK (apart from Scotland, which I think has broadly similar qualifications of different names), all people take qualifications called GCSEs when they are 16, after which most people go on to study A-Levels, which they take exams for at age 18 (until last year and still in some subjects until the specifications change, the exams are split such that some are taken at age 17 as well).

All of these exams are conducted under the same rules set by JCQ (the Joint Council for Qualifications)(See here for the full document), which importantly forbid calculators that are designed or adapted to offer symbolic algebra manipulation, symbolic differentiation or integration, or communication with other machines or the internet, or from having retrievable information stored in them.

In my experience, most people use the Casio fx-83GT PLUS (£5) or fx-85GT PLUS (£6) and variations thereof or (especially once they are doing A-Level Further Maths) Casio fx-991ES PLUS (£15.90). These are all non-graphing scientific models with fairly unpleasant mushy keyboards, and especially in the case of the fx-991ES PLUS, quite a few features, almost all of which are separated into separate modes, which can tend to make them a pain to use. (As if algebraic entry wasn't time consuming enough!) Luckily, only the basic scientific functions (trig., exp., etc.) are ever really required. A very few people get graphing calculators such as the TI-84, but these are the exception, and the students tend to have come from education systems in other countries. (I once knew someone from Germany that had a monster of a TI Voyage 200, only to be told it wasn't allowed because of its CAS) Thanks to me, there were a few people walking around with the WP-34s, but the potential for serial communication (which would require someone to go into the exam room with a load of wires and computer etc, while being supervised) and maybe the fact that it was a modified calculator seemed to spook the relevant people, so we were advised against using them for exams.

In my experience of the pure modules of the Further Mathematics and Mathematics courses, curve sketching is generally done by hand, as are computations using matrices, vectors, complex numbers and integration (even definite integration, as they want exact answers). Most of the emphasis is proving things to be true, manually finding series expansions, and giving exact answers, so calculators are rarely required.

We did occasionally use tools such as Desmos, Geogebra and Autograph for demonstrations, and are sometimes advised to use Desmos in particular if we are really stuck. All students in my classes had smartphones. My school also used to have a site licence for Mathematica, but stopped paying because it was deemed too expensive given that only a handful of students used it.

In the statistics and mechanics modules of the Maths and Further Maths Courses, there is more emphasis (at least in my experience) on calculating things and giving inexact answers, however for mechanics problems, we are advised to only use the calculator to give final answers, working symbolically until that point. In statistics modules we are expected to use mathematical tables. This is possibly partly because the calculators we are expected to use do not feature much in the way of statistical distributions, and also because in the exams, use of the provided tables is likely expected.

In general, where more advanced calculator features allow a quick way to get an answer, workings out are awarded marks in the exams, so any such features are relegated to merely being a quick way to check the answers given.

I'm not sure how this compares to other education systems, but I would certainly say that we are taught Mathematics really quite well. For those interested, specifications for the Maths and Further Maths courses from two of the main exam boards can be found at the links below. (The boards award the same level qualification, and I think the Mathematics courses have to meet certain government standards with regards to content, whereas the content of Further Mathematics courses are (from what I have heard) less prescriptively regulated.)
OCR Exam Board Specification
Edexcel Exam Board Specification
Note that these specifications will soon be out of date, as AS exams (taken as part of an A-Level at at age 17) are being phased out, as are (apparently) modular courses, yet I imagine that the content and teaching methods will be similar.