How good are you at mathematics?

How good are you at mathematics?

Cambridge Mathematics' Lucy Rycroft-Smith discusses the negative effects of grouping students for teaching by their mathematical proficiency and explores some alternatives.

Most people have a strong reaction to this question, although an extraordinary few I have met (including professors of the subject!) answer ‘very’. A high proportion of responses follow the lines of ‘I have always struggled with it’. Some make reference to hating or avoiding maths. Often, people will tell me about their exam grades or which set they were in at secondary school, reducing their mathematical ability (oh, the irony!) to a single number.

I am continually astounded by the myriad ways in which people fail to see their own proficiencies in mathematics. Computer programmers who use complex logic every day; engineers who calculate with astonishing accuracy; mortgage advisors who use formulae with aplomb; pilots and midwives and lawyers and paramedics and scientists who tell me they aren’t much good at maths, but in fact use it competently all the time.

Why? One reason might be the prevailing idea that mathematical ability is easy to measure and, once calculated, is fixed for life. Can you remember being told ‘you are in set two’, or ‘you struggle with algebra’, or getting a low mark on a test - and did you somehow internalise that as an indelible measure of your mathematical worth?

If you grew up in the nineties or noughties, odds are you were put in sets for mathematics – certainly in secondary school, probably in primary school too. If you are a teacher of mathematics now, it probably seems odd to imagine a time when pupils weren’t tested on their maths ability and then grouped for ease of teaching. This practice is widespread in the UK, and happens routinely from age 11 and sometimes as young as 5 or 6 in our schools. But have we stopped to consider its effectiveness, why we are doing it, and what the effects might be on the mindsets of the pupils we are grouping in this way?

I recently wrote an Espresso on attainment grouping in mathematics, and the research surprised me. The evidence clearly says three things:

1) Grouping pupils by mathematical attainment is connected to a fixed mindset – something we have realised seriously obstructs maths learning – and it also has no evidence to support its effectiveness overall.

2) Some of the research points to pupils in all sets finding the practice of being pigeonholed in this way limits the expectations of their mathematical achievement; other findings show the allocation of teachers to sets is predictably unfair, with lower sets getting poorer resources and less qualified teachers.

3) Finally, the strongest and most worrying finding: the most disadvantaged pupils are consistently over-represented in lower sets.

Grouping pupils by attainment in mathematics rests on the idea that one can reliably measure this attainment, and that it is fixed. I can’t help but see a link with this pervasive idea and the responses of all those people I talk to about maths, who downplay their own abilities and lack confidence in their identities as mathematicians.

There are, of course, alternatives – for example the system in some of the Scandinavian countries, where the Cambridge Mathematics team recently completed a research trip, which do not group pupils by attainment at all (and in fact it is illegal to do so). A large study is currently being completed at the Institution of Education at UCL, comparing mixed-attainment grouping with setting; this may be the first step towards a serious reconsideration of setting practices in this country, and their inescapable effects on attitudes towards mathematics.

Lucy Rycroft-Smith
Research and Communications Officer, Cambridge Mathematics