I'm not talking here about the stress exams put students under, although I could. I'm talking here about how exams are one of the worst possible ways of testing whether someone is a good mathematician.

Here's the problem: maths exams are tests of a) memory and b) calculation. You can do well in almost any maths exam by getting hold of all of the past papers and working through them. That's what I spend about 80% of my time as a maths tutor doing, because it's the most effective method I know for getting students a good grade in the exam.

It doesn't need to be that way. The most important skills - in my opinion - for a mathematician to have are:

- Persistence
- Looking things up
- Modelling real-life problems
- Discussing ideas with others
- Communicating results clearly

Virtually none of those come up in an exam. The last one, sure; possibly modelling real-life problems (although normally you're spoon-fed the model the examiners want) and possibly persistence (although you're limited by how much time has been arbitrarily allotted to the exam).

However looking things up and talking with your colleagues - two of the most important skills as a mathematician, and two of the most transferable mathematical skills - are considered 'cheating' and will lead to you failing the exam and probably having other qualifications revoked as well.

**Let me say that again: the exam system actively penalises two of the most important skills that can be learned in maths.**

Meanwhile, they encourage things like last-minute cramming, following instructions blindly, and teaching to the test - which I do, because my job is to ensure that little Jimmy gets the grade he needs to get to university. (I'll do my best to foster his curiosity and get him enthusiastic about maths, but if I do that and he still does poorly, it does nobody any good).

Exams are designed for convenience. An examiner can sit down and grade your work (you got 80% of the available marks, so you deserve to get a letter A! have a cookie) and a university can say 'you have the magic letters A, B and B, so you're allowed to come here and study for more exams in much the same vein', or so an employer can differentiate between candidates without having to bother interviewing them.

This isn't just silly, it's actively harmful. We end up with a workforce whose main characteristics are docility, a good short-term memory and the ability to work in silence under pressure.

And I don't think those are the traits we should be emphasising.

## Tammy

As a fellow math tutor and former math teacher, I agree wholeheartedly! Not saying memory and accuracy are not important, but certainly not more important than collaboration and communication.

Seeing as today is the AP Stat exams, and I used to score the free response sections, I can say that they are at least a step up in that half of the exam is free response and communication/explanation of your answer is critical! We gave a LOT of leniency on what we considered \’typos\’ or possible data entry errors in calculator as long as the reasoning and communication was sound!

Of course you are right, those exams are time consuming to administer and to grade, and convenience always seems to win, unfortunately.

## Colin

Thanks, Tammy!

## neilnjae

Yes, exams are a pretty rubbish way of assessing anyone for most disciplines. But what they do give you is a way of authenticating that this person has the skills tested on the exam. Most other forms of assessment allow (or encourage) students to collaborate, which makes is tricky to assign credit to individuals.

## Colin

Personally, I think it just authenticates that a student has memorised an algorithm that works for a particular kind of problem – and I\’m not sure that\’s a useful thing to test for ;o)

I think if you did several group assessments over the course of a year, you\’d be able to do some pretty basic statistics to see which students contributed most.

## Adrian Beckett

Absolutely agree. At primary level, I think the exams are a truer indication of a child\’s ability as a Mathematician. There\’s a lot of problem solving going on. The kind where you do need to persist and approach the problem intuitively not just blindly following a rule. I find those inchworms – the ones that follow procedures – struggle with these problems. Meanwhile, the grasshoppers – the intuitive learners – are more likely to succeed. I\’d be interested to know what kind of assessment – if any – you would propose instead Colin. Cheers mate.

## Colin

Thanks, Adrian!

Certainly at secondary level, I\’d like to see – perhaps – half-term long group projects solving real-life problems assessed by a combination of reports and presentations. (For instance: the corridor outside F4 gets really crowded at certain times. How can that be fixed?) With randomised groups, it\’s easy enough to do the stats and see which students are consistently contributing.

At the very least, I\’d like exams to be open-book.

## Adrian Beckett

That sounds really interesting. I think I would have developed a lot more as a Mathematician. At university level, I really struggled. Maybe this sort of approach would have meant I would have managed much better.

## John Richard Jones

Prior to sitting my A-level Maths exams in 1980 I had always got a grade A in Maths.

I sat both Pure and Applied exams and the Pure Maths was fine but the wording of a question in the Applied Maths led me astray and I used my imagination to solve what I thought was asked.

Doing this I showed understanding beyond the standard of A-level but got no marks for it and it cost me a grade.

This is the only B I got and since then I have lost faith in exams.

When at university I made myself too ill to sit my finals and was awarded an aegrotat degree. In fact if I can avoid exams I will – I would rather not sit them and not have any qualifications as I see exams favour the parrot fashioned but not for those of us with imagination. I didn’t bother going for my cap and gown either.

You will see how a lack of faith in examinations led to me to being treated as subnormal in spite of my qualifications and capabilities whereas if exams had reflected my true image I could have done much better.

I personally don’t care if I am at the bottom as those at the top are often parrot-fashioned. I would like to have put my Maths skills to better use but if I don’t get the recognition I deserve then why should I bother. I don’t put letters after my name either.

A sure waste of talent.

## Colin

Wow, John – thanks for your comment and sorry to hear the system treated you so badly.

I\’d much rather we had a system that tested for that kind of imaginative thinking and, perhaps, took some of the pressure off.

## Thalinda

Hello all!

About this point of view of maths exams, I think exams are not that bad… It is true that in primary and secondary you need to practice and practice and memorise algorithms but then, it gets easier and as the time passes and you go to University. There, you do get to write projects and work in a team, but first you need to know the bases of this science so you can come up with good idea.

## Colin

Sure, I’m not arguing that it’s not important to know about the basis of your subjects, just that exams are a rotten way to demonstrate your capacity. Do you have exams to become a professional footballer? No, you play the game and demonstrate you can do it in realistic (sometimes simplified) situations. You don’t sit in a room and write down “I’d stick my toe out and it’d go in.”

## Thalinda

I think that to be good at football, cooking, maths or anything else it takes talent and hard work 🙂

## Francisco

Hi Colin,

Thank you for this post. It provided much needed comfort after failing to pass not a maths exam, but something similar, if not worse … a timed employment numeracy test. Mind you, I have achieved all A’s in my math classes and math-related courses (ie. Economics) during secondary school and my bachelor degree in business. However, I am awful at taking timed basic maths tests and I don’t know why. I just blank out and cannot think straight when it’s timed. I have never been the quickest at mental math but I know it’s not because I am dumb. I know I can grasp complex mathematics but somehow I crumble when I am faced with simple calculations…when timed and only have a few minutes or seconds to solve basic math problems. I do get the right answer in the end… I just take a longer time. It makes me feel like an idiot that I am apparently too slow to be hired. (It was an application to RBS and the test involved only 12 timed questions of about a minute and a half to solve the most random word problems…at one point I had to decipher a bus schedule…which wasn’t even clear…but obviously I couldn’t clarify anything as it was a timed test! How is this even relevant to being a banker?!)

What do you think of these job numeracy tests? And how can I overcome this slowness when doing basic math?

## Colin

I’m not convinced by numeracy tests in general, either (for what it’s worth, I used to have accounts with RBS and was cheerfully informed by my business account manager that nobody there could do reverse percentages. *Used to*.) I like the idea of people being numerate, but I think there’s a big difference between numeracy and passing numeracy tests.

That doesn’t help if you have to take them, though! Really, speed comes with practice, which is tough with proprietary tests. Find similar things and practise those, I suppose. Good luck!