The New GCSE Mathematics Syllabus: What's Wrong

06/04/2016 11:11 BST | Updated 06/04/2017 10:12 BST

From 2017, the new GCSE Mathematics syllabus will be examined. There's much to admire about the principle - more problem solving, a little more rigour for the strongest candidates, and because of the importance of Maths it will be given extra weighting in school league tables from now on (specifically it is now double weighted in Progress 8). The new system, though, simply exchanges one set of flaws for a different set. It's yet another example of overcompensation; where the 1997-2010 Labour governments went wrong in one direction, the current Conservative government seems intent on going wrong in the opposite direction. Every time, teachers must get used to a massive change in the subject they teach. That's why in my view, small incremental change is better than sudden transformation - but once again, sudden transformation is what we'll have.

So what's wrong with the current changes? To understand the problem, it's first necessary to understand the nature of examination candidates and what our education system should seek to achieve. In my experience from teaching Mathematics, there are three distinct categories:

1. Those students who have the capacity to continue their study to A level and possibly beyond.

I'm referring here broadly to candidates who will obtain an A or A* at GCSE, or possibly those at the top end of a B grade.

For them, a GCSE examination needs to be challenging and intellectually rigorous. It needs a high level of problem-solving and for concepts like mathematical proof to be understood. The purpose of a GCSE syllabus for them is to lay a foundation; it should provide a platform for higher future study. There are a huge number of jobs which will require these skills, particularly given the highly technological nature of our modern economy.

2. Those students who will not have the level of abstract mathematical ability required to consider higher concepts.

I refer here, perhaps, to those who currently are expected to obtain grades E, F or G at GCSE. Their mathematical requirements in later life are likely to be functional in nature. What should we be teaching them?

I want to see them develop their numerical skills. When will they ever use a quadratic equation in later life, or even linear algebra for that matter? Instead, wouldn't it be better for them to be competent with percentages, to come out with an understanding of how interest rates work and the skills needed to know whether you're being offered a good or bad deal by a credit card company? Shouldn't they have a good basic mental arithmetic, particularly given that many will end up doing jobs in the retail sector, and the ability to estimate so that they can broadly spot when an amount is a long way away from what it should be? How about the ability to compare different deals and offers, calculating percentage discounts? Or calculation of areas (imagine a decorator or landscape gardener needing to work out how much carpet or paving to buy in order to quote for a job)? These skills are taught already, but I would rather see a much higher level of competence in these rather than teaching unnecessarily complex algebra which will be of no use to them in later life.

3. Those students who fall somewhere between the two categories above. In my experience somewhere between half and two-thirds of all students are here.

It's important to teach mathematical concepts; I can think of many B or C grade candidates who I've taught who have found need of their mathematical ability in later life. They may have had to work very hard at Maths at school, often asking the question 'when will I ever need to know this after I leave school?'. They may be right of course, but equally they may be wrong. Nor can you ever know which part of the syllabus is important. There's still an importance in focusing on the functional parts of the syllabus, but algebra and trigonometry are also important as part of developing a skill set which could prove to be useful in later life.

Back to the GCSE syllabus, some fifteen years ago it was split into three tiers: Higher, Intermediate and Foundation. It was broadly aimed at the three groups I've identified. The system was flawed, but aimed at the correct people. When the Intermediate tier was abolished, Foundation became more difficult and Higher easier, ensuring that the new examination and syllabus really didn't suit the vast majority of candidates.

Fast-forward to today, and the Gove reforms are coming in. He correctly recognises that more rigour is required to test the top candidates. Maths will now be graded on a 9-point scale with the bottom of a grade 4 being the equivalent of the bottom of a C grade and the bottom of a 7 being the bottom of an A. The Higher tier will become more challenging, as will the Foundation tier - which will have a top grade equivalent to a low B. There is a 'Functional Skills' mathematics course, but its status is being taken away. Schools will try to put everyone through the new GCSE, because it's in their best league table interests to do so. There's even less incentive now for the functional course. That may be indicated by the AQA June 2015 examination entries; just 1974 students attempted the Level 2 examination, with a pass rate of just 38.6% - indicating that nationally, just 762 people gained that qualification with the country's largest examination board. Take away its status, and even fewer people will attempt it. The level 1 course had 2079 entries, for comparison.

The annoying thing is how easy it would be to tweak the new system to meet the needs of all candidates. Keep the new Higher course, relabel the new Foundation as Intermediate. Revamp and soup up the Level 2 certificate in 'Functional Skills' mathematics, add a greater emphasis on percentages and estimation (for example), rebrand it as a new Foundation Level GCSE with a maximum grade D or possibly C in today's grades, and then at least the system would actually reflect what it's supposed to. The various entry-level qualifications (and possibly the Level 1 certificate) could be kept in pretty much their current form for anyone who would struggle to sit any GCSE examination.

With these straightforward amendments, the system would not be perfect - but it would be far better than the system which the government is introducing. There would be an appropriate, challenging examination available for every student. We would have a system which would be robust enough not to require constant structural change, and the residual problems could be dealt with through minor tweaks to the syllabus.