A squash and a squeeze
Chris Brignell, Deputy Director
“Wise old man, won’t you help me, please? My house is a squash and a squeeze”, says the ‘little old lady’ at the start of Julia Donaldson’s book A Squash and A Squeeze. Trying to fit too much into too small a space is a common problem, and one that many think applies to the mathematics curriculum.
It’s a problem facing many university mathematics departments. The current level of tuition fee funding makes it uneconomical to teach modules with small class sizes. So many big departments that currently teach lots of niche modules in their final year are reconsidering whether that is too much of a ‘squash’. The solution is to prune some modules, but every academic thinks their branch of mathematics is the most important and so fights to stop it getting ‘squeezed’ out. Should they keep what’s interesting or what’s useful? Mathematical knowledge or mathematical skills?
Similarly, OCR’s report last year, Striking the Balance, called for a reduction in the size of the GCSE Mathematics curriculum. A couple of weeks ago they issued a follow-up report calling for the GCSE to be split between a new GCSE Short Course Maths qualification in year 10 that focuses on number, algebra, geometry and data handling. This would be followed by the full GCSE in year 11, but they also recommend taking out content on ‘ruler and compass constructions and loci’ (seen as archaic given modern computers), ‘circle theorems’ (irrelevant to real-life) and ‘exact trigonometry values’ (unnecessary memorisation given modern calculators). Their proposal is that the Short Course should be a sufficient pre-requisite for many Level 3 courses and so fewer students will get trapped in the cycle of resitting the full GCSE.
So, is the proposal a good idea? The current system enables students to pass GCSE Mathematics by superficially understanding lots of topics – teachers train lower attaining students to pick-up ‘easy’ marks in order to get the grade 4 but there is little confidence they have mastered fundamental concepts. Putting all the fundamentals in the Short Course would give future employers and teachers more certainty over what they have and haven’t understood. Assessing the Short Course at the end of Year 10 would also reduce the assessment burden for the stronger students taking on the full GCSE in Year 11. The idea of multiple shorter, year-long courses was also alluded to in last year’s Royal Society report for 14-18 pathways.
However, in a digital age where data handling and quantitative literacy are growing increasingly important, is it dangerous signalling to young people that only half a mathematics qualification is necessary to progress in life and work compared to two English GCSEs and two or three Sciences? Around a third of students currently are considered to have ‘failed’ GCSE Mathematics as they don’t attain a grade 4 or above. Should we be focusing on trying new approaches to help them learn? The OCR report also doesn’t consider in detail the knock-on consequences of removing content from GCSE – some of which is pre-requisite material for A levels and vocational qualifications. As ever, holistic thinking is required.
So, while updating the curriculum and assessment in light of current technology is desirable, maybe an alternative solution lies in giving more space in the curriculum for foundational and advanced mathematics and quantitative reasoning as called for by the Royal Society, or a double award in mathematics and statistics as called for by the Royal Statistical Society.
Of course, those struggling to pass GCSE Mathematics disproportionately come from lower socio-economic backgrounds so part of a holistic solution needs to include earlier education phases too. Last week NFER published a study showing that extra-curricular engagement is positively associated with cognitive development but children from disadvantaged backgrounds have less access to these opportunities. They called on the government to provide holistic family support programmes for disadvantaged families and a national extra-curricular bursary scheme.
Of course, who provides extra-curricular activities is an interesting question. The Academy for the Mathematics Sciences published a report last week showing only 5% of undergraduate students are currently involved in outreach work and therefore a cost-effective way to engage more pupils and schools is to incentivise the remaining 95%. There is plenty of opportunity to reach more schools too – on average, each maths department currently engages 14 schools – but they are held back by lack of staff time. Interestingly, there is evidence larger high-tariff maths departments reach no more pupils than smaller lower-tariff departments. Maybe their staff are too busy teaching all the final-year niche modules?
In some ways it would be nice to turn the clock back to 1900. If there was, say, not yet Turing or Ramanujan or Nash or Noether or Ito, then the fields of computational mathematics, number theory, game theory, mathematical physics and stochastic calculus would be much smaller and we might stand a chance of fitting everything in the curriculum. But given the field of mathematics is growing all the time, it inevitably ends up being a squash and a squeeze. The question is what to squash and what to squeeze? Or, like the ‘little old lady’, should we learn to be content with what we have?
Author information
Chris is the Deputy Director of the Observatory and an Associate Professor of Statistics in the School of Mathematical Sciences.
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