# Concerning multiple choice

So, last night on twitter, there was a bit of a discussion about the use of multiple choice questions (MCQ) following a tweet of Joe Kirby’s excellent blog post — http://bit.ly/1NNKfDh — which if you haven’t read, I suggest you do now.

He makes some really valid points, especially in the contexts he was using as illustrations. Some simple multiple choice questions will really add to the teacher’s toolbox of techniques to use in the classroom. The discussions on twitter that followed also gave some great uses of multiple choice questions. For example, as formative ‘hinge questions’ during a class to let the teacher know who has grasped whatever is being taught.
I imagine the use of small whiteboards, clickers or some such would be useful. Or maybe some of the newer technology available to do such immediate questioning.

I have no problem with MCQ for that purpose. Indeed, in Mathspace, we use a variety of multiple choice questions at times, especially at the start of some topic. You know, “Which of the following are regular?” or “Choose the line with a gradient of -1.5” type of questions.
(We also often have more than one correct answer for the MCQ and this sometimes infuriates students from those countries where MCQ with just a single answer are used a lot, which in itself is an interesting finding)

So, MCQ are not the work of the devil.

BUT (there’s always a BUT!), I do not feel Joe’s second and third points are so valid for mathematics, particularly when pupils are sent away to practice — at home or in the class.

Yes, it is easy for a computer to mark 30 sets of 30 MCQ. After all, one of the main reasons MCQ started to be used was because it was easy to automate the marking and to administer lots of tests at once. But for maths, a side effect is that all the working out or reasoning needed to solve a problem is lost.

For maths, the working out is important. If a student gives the wrong answer, then we need to know as teachers whether they made a mistake or whether they have a misconception. The students need to know where they made a mistake or where they have not understood.
If all we see as teachers is a cross against a box/letter, then we do not know why and the student does not know why the answer is wrong.

We can guess why, if we have used some cleverly constructed questions, but then what is the effect of deliberately putting in wrong answers that look as though they could be right? To make them think?

In fact, could multiple choice (and single answer) computerised testing be the reason we have seen both PISA and TIMMS data indicate a fall in scores, the more computers are used for practicing mathematics? My gut feeling as a maths teacher who likes to see the working out, is that it could be.

To counter this, a tweet mentioned that students may still need to write their working out when answering MCQ. Presumably in a book, and then enter the answer on a computer/device. In which case the sole reason for the MCQ is to reduce teacher workload — which is a laudable aim in itself and one that technology should be able to help with. Doug Lemov wrote on this recently, and I like the idea of helping teachers become more efficient.

Well, one approach would be (is) to ask students to write why they chose that answer. It’s a nice idea but doesn’t it add somewhat to the cognitive demands?
For maths, isn’t it better just to get them to ‘do the maths’? After all, maths is a method of communication itself.

Technology is very powerful and fortunately, it develops.
So there is the possibility now to mark each step of a students work.

Mathspace uses MCQ where appropriate at the start of a topic, but its main aim is to encourage students to write their working getting immediate feedback on their work and support if they need it.

Teachers can see all the marked working — of every step, for every student if necessary — immediately and intervene as necessary. The workload reduction possibilities are huge but are alongside an increased understanding of each pupils work. Teachers get all the information they would have done if they had marked manually each pupil’s work (as in Shanghai), but quicker, and with less work.

So, MCQ are useful. But for maths, they are yesterday’s technology (along with just single answers). We can reduce teacher workload, but we should make sure that what we are doing is more efficient. With new technology, we can reduce workload in the short, and in the long term (maybe fewer weekend revision sessions, 1–2–1 catch up sessions, C/D bordeline intervention classes and so on).

Black and white televisions worked well.
But they removed something from real life.
Isn’t having colour better?