#
Mathematical

Salad

## Problem-solving for policy

23 March 2018

**Problem-solving for policy
**

I was recently interviewed by Tim Muffet of BBC Breakfast about Maths GCSE resits. Aided by Bobby Seagull of University Challenge fame, Tim and BBC colleagues are going to resit their Maths GCSE this year. At the same time that the BBC presenters are taking theirs, thousands of students across the country will also be sitting GCSE maths, either for the first time, the second time…or the nth. Some will be supremely confident and enjoy the experience, but for very large numbers of them it will only serve to confirm their lack of mathematical understanding and that they are ‘just no good at maths’.

Adrian Smith’s report was commissioned to address two issues - the increasing importance of mathematical and quantitative skills to the future workforce and, by comparison with competitor economies, the low percentage of students in England continuing mathematics post-16. One has to ask if a policy decision to enforce repeated GCSE maths retakes will contribute to solving these two problems. I’d like to look at the facts and suggest an alternative solution.

*Fit for purpose?*

The Director of the NCETM, Charlie Stripp, recently wrote an article in Teachwire about this very issue. He began by stating the purposes of GCSE and the intended outcomes. Whilst I wouldn’t argue with any of these, I would suggest that he has missed one important aspect – that of education for confident and competent citizenship. I don’t equate that with his ‘minimum national expectation of maths competence’ but would rather use the National Numeracy definition of being able to ‘use numbers and data to make good decisions at work and at home’. I don’t believe that following a GCSE maths course adequately prepares students for life, whatever grade you get. In fact, currently one in three adults in England and NI cannot work out the correct change from a shopping trip, and more than half cannot interpret a graph containing basic financial information ^{1}. So, no evidence of long-term learning there then.

*Built-in failure*

Last year, 30% of students sitting GCSE maths failed to achieve a pass (grade C/4). And, in fact, when they were 11 years old, we could pretty well have predicted who they would be -because GCSE grading is mostly norm-referenced, which means performances are judged according to the peer group and only a certain percentage will pass. Now, obviously it makes sense for students who have just ‘missed’ a pass to have another go – but the chances of passing diminish with the number of times a student takes a resit exam. So, on a fourth try you are statistically less likely to pass than on your first attempt.

How can this be a good system for anyone? What are the effects, on individual students, of repeated failure? Is this going to encourage them to a) feel kindly towards maths or b) continue to study maths post-16? I don’t think so.

*Exchange value*

However, if we decide at, say, 11 that a student should follow a path that does *not* lead to GCSE, we radically affect his/her life chances. Grade C/4 has an exchange value for employers and further and higher education, and we know that alternatives such as Functional Skills (the latest iteration of which is a watered-down GCSE) do not carry the same weight. So, it is important that everyone has access to this qualification. Does it follow though that they should be capable of completing the course within the same period of time?

*Summing up*

So, we have three problems – an assessment that does not support life skills, an assessment that is patently not appropriate for a large number of students because they fail and fail again, and an assessment which is certainly here to stay in the medium term and has a high exchange value for future success. Is there a solution that solves all three simultaneously? How can we improve matters?

All students need to be functionally numerate. The mathematics involved in this is not trivial – for example, it involves the application of proportional reasoning in a variety of contexts. Learning this in depth would be a good foundation for the more academic content of the existing GCSE, so let’s link the two together by mapping the ‘essentials of numeracy’ to the GCSE specification so that the second builds on the first. And, students do not all learn at the same pace or with the same ease, so let’s acknowledge this by offering opportunities for assessments at different times.

*A possible solution*

I suggest an assessment of ‘essentials of numeracy’ should be offered to all students. It would be competency based, pass/fail, and offered for the first time at, say, 14. High achieving students would find this easy and study it in parallel with their GCSE course. They achieve both functional and academic mathematics simultaneously. Those requiring more support study for the essentials first, then study the *additional* content needed to take them to the GCSE assessment. Early success at the essentials bodes well for success at GCSE.

Those who require yet more time could focus on the essentials right up to 16. Because the content is mapped to GCSE, they are not prevented from accessing it later.

This would offer:· an assessment that supports life skills for everyone

· an assessment structure that acknowledges different rates of learning and builds in early success rather than late failure

· a structure that allows all to access GCSE

Here at Cambridge Mathematics and working with National Numeracy, we’ve had a go at identifying the essentials, and mapping them against the GCSE, and we think it’s feasible. What do you think?

*1. The financial skills of adults across the world. New estimates from PIAAC *is the latest working paper to be published by the University of Cambridge and the UCL IOE's Department of Quantitative Social Science (QSS). The paper is available from johnjerrim.com