Watching someone attempting the same task again and again without success is heartbreaking. Yet, that is what we have ended up doing with many young people by forcing them repeatedly sit GCSE maths, despite a vanishingly small chance they will ever “pass”.

Many in education feel certain the endless re-testing of students is wrong, but most also acknowledge having functional numeracy (and literacy) is important if young people are to succeed in life.

This tension is at the heart of the debate over the government’s change to apprenticeship standards whereby functional maths (and English) are now not required for adult apprentices.

It’s a bold step and one that, with the Francis Curriculum Review underway too, suggests the time is right to think again about maths assessment more broadly.

The challenge of following procedure

Currently, I would argue maths in school is often just procedural: do this, now this, then you get the answer.

But I think we must question what it is we want from a numerate population. I believe they need the confidence to “look up” how to do something, know what to ask in the process, and have the ability to follow the process to calculate an answer.

They also need a sense of what numbers mean and the size of numbers, like knowing what “100 times bigger” means. This reflex will allow them to know when the numbers do not support an argument, allowing them to avoid being misled by statistics.

A numerate society should be able to decide if apparent patterns are real patterns or simply coincidence.

Remove memory recall

As such, we should remove as much memory recall as possible from assessments.

Recalling facts from memory can make life easier, but in terms of the resit policy, there are currently people who have not picked this up in ten years of schooling. Is memorisation what we want them to focus on now? Especially if, in the real world, they can just look up an answer?

Indeed, almost everyone, even the most mathematically oriented, will use a calculator or a spreadsheet if they need to undertake a complex calculation.

This, then, is the first thing I would focus on in an assessment: helping young people find their own way to a correct solution without forcing them to do it in a particular way.

Towards more authentic assessment

Secondly, part of the answer to transcending numeracy-learning challenges lies in the type of questions we ask, but also in the style of assessments we choose to administer.

Students who resit have already shown they find memorising mathematics particularly difficult so why not consider an “open book” approach within exams - whereby a table linking common percentages, fractions and decimals would be available?

They can access such a thing in real life, so why not let them have it in the exam?

Thirdly, any new assessments must demonstrate that students can follow a mathematical process and not just reproduce it.

To achieve this, we could, for example, demonstrate how to convert currency and ask students to extend that example to a different situation. This is more reflective of real-life scenarios than simply asking them to memorise a process to reach a conclusion.

This change to mirror real-world problem solving may be the most challenging part of our new imagined assessment for many students, but it is also what they need most to succeed after graduation.

Furthermore, perhaps the most important function of using numbers in life is spotting when an error has been made, intentionally or otherwise. In an exam, then, we could, rather than asking students to calculate an “average”, give them an example and ask them to spot an error.

More time

Finally, exam stress is often a key barrier for students, especially in assessments they have failed before.

There is no reason why an exam that we expect students to take in an hour could not last much longer if needed.

Students can and should be permitted the time they need to problem solve on examinations (obviously not literally unlimited, but, say, two and a half hours), to further develop and practice their understanding of mathematical processes.

Time to rethink

Ultimately, the failure of a policy that has seen young people caught in an endless cycle of “resitting” should make us question what we are trying to achieve.

Do we want a society that is numerate and confident with maths throughout their lives - or one where people can do arithmetic processes from memory?

We need to stop forcing students to repeatedly demonstrate they find traditional maths difficult, and instead think about and assess what the numbers really mean.

Matthew Glanville is director of assessment at the International Baccalaureate

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