Prepared to work

A pile of book and a collection of pencils in a pencil cup on a table, with a blackboard filled with mathematics in the background

Did you take A levels or GCSEs (or equivalent)?

Can you remember the period leading up to the exams?

Were you someone who organised your revision notes assiduously, or did you have a dog-eared binder from which loose leaves fluttered from time to time? Or perhaps you didn’t make written notes at all, but used classmates to quiz one another frantically as the deadline approached? Did you have a neatly colour-coded revision timetable – and did you stick to it? And finally, did you have any issues, illnesses or emergencies that interfered with your exam preparation?

The A level (and GCSE) situation has sparked lots of conversations and opinions about assessment strategy in general, but I was particularly struck by the comments made by a student interviewed on Radio 4. When asked what he thought about the cancellation of exams and therefore being awarded grades through other means, he complained that he was disadvantaged because he was one of those students who always left everything to the last minute and would have done much better in the exams than his work during the previous term might have predicted.

It may be tempting to see this attitude as lazy, to consider that a late sprint involving memorisation to gain an extrinsic reward is not the point of exams, and therefore such students are missing that point. But realistically, as adults, we can probably all look back on our time in education and identify occasions when we did not prepare as gradually or conscientiously as possible for assessment. It is interesting to consider how this might intersect with maths specifically. How much mathematics can you remember from school and how much do you use now? It is often claimed, for example, that maths is worth studying in and of itself as a discipline embodying logical thought, reasoning and solving problems. Respondents would argue that much of the maths curriculum is irrelevant – how often, for example, would one need to use the angle properties of a circle in everyday life? Many of our students see much of maths in that way. This is also related to revision for exams, as studies show that students revise in different ways depending on whether they are expected to show procedural or conceptual understanding.¹

The PISA tests in 2021 are beginning to address this issue of relevance. There are changes to the content, which now includes computational thinking and is promoted as assessing mathematical literacy, defined² as “the capacity to analyse, reason and communicate ideas effectively as they pose, formulate, solve, and interpret mathematical problems.” These problems are real-world problems which require the “ability to apply those skills in a less structured context, where the directions are not so clear and where the student must make decisions about what knowledge may be relevant and how it might be usefully applied.” And since we know that educational policy makers are keen to move up the PISA tables, is there a possibility that notice will be taken of these revised criteria, and curricula world-wide will be adjusted accordingly? And maybe students will be more engaged?

But is this enough? The OECD Future of Education and Skills 2030 Project³ sets out to determine a) what competencies students will need for individual and societal well-being in the future, and b) what curricula and learning environments will be needed. Part of the study involves exploring how work practices have changed over time – the graph here indicates a rise in non-routine tasks, both interpersonal and analytical, and a decline in routine manual and cognitive tasks.

Change since 1960 in prevalence of types of tasks required for work

What does this mean from a mathematical point of view? Various surveys⁴ of industry have identified the importance of addressing particular content including an emphasis on proportional reasoning, risk and uncertainty, algorithmic thinking, estimation and number sense, complexity, interrogation of large data sets, and simulations and modelling. If we are to take this seriously, make the curriculum more relevant to students and begin to incorporate these ideas, some content in our current curriculum would have to go.

Now there’s an interesting question. What would you remove?

References:

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