Rebecca Turvill (Brunel University)
As I sat in my kitchen re-editing an article about ‘number sense’ in young children I heard the news that Michael Gove had been shuffled out of his role as Schools Minister. Having been hoping for this for some time, I was surprised to have that uneasy feeling of anti-climax, like you get after a wedding. When the fun and build up is over and you’re left with a slightly dodgy tummy and a lot of hairspray to comb out.
I have not been a big fan of the changes introduced by Michael Gove, and as a primary school teacher with a particular interest in mathematics I’ve been quite troubled by his actions. Moving on six weeks before primary schools everywhere (except those who became/were made academies) come to terms with a brand new curriculum is pretty nifty. He doesn’t have to take account of the impact of his changes.
Mathematics receives much attention in part because people tend to love it or hate it and, more importantly, those with higher levels of mathematical attainment generally earn higher salaries. I am particularly interested in a concept called ‘number sense’. There isn’t an easy way to define it, but it can be thought of as a ‘feel for number’. That sense you have when you look in your wallet and realise that you will have to choose between the bread and the milk as you don’t have enough for both. Or, when you top up your Oyster card with £20 because that should cover the travelling you expect to do this week. It is about knowing how numbers work, their relationships and having an approximate way to calculate with them and it has been a big part of the primary mathematics curriculum.
Essentially, number sense was a core function of the national numeracy strategy (NNS) (DfEE, 1999), the previous government’s vehicle for improving primary school mathematics. It aimed to place mental calculation back on the primary mathematics agenda and implemented a ‘rigid’ 10-minute mental calculation starter to every mathematics lesson. The importance of mental calculation evolved over the lifetime of the strategies, but at one point it recommended that children were not taught formal calculation strategies until they could manipulate two 2-digit numbers mentally (QCA, 1999). Not surprisingly, such restrictive recommendations were fought against, as each child learns differently and needs different opportunities. However, in general, it was aiming in the right direction. Research suggests that children need experience of concrete manipulation of quantities before they move to the more abstract representations that mathematics introduces.
At the time, there was a lot of debate around the research-based claims of the numeracy strategy (Brown et al. 1998) and continued criticism of the specific methods and stages it required children pass through. Despite this it was well received by practitioners, which, it is believed, was due to the clear structure it gave non-specialists in the teaching of mathematics.
So, to the new National Curriculum planned for September 2014. In summary, it has brought content earlier, which makes things harder. The expectations are that children accomplish specific aspects of number – and wider mathematics – sooner than they used to (e.g. multiplication tables). Alongside this, and less well discussed, is the idea that you don’t push children beyond these expectations. Once a year group’s curriculum is set, rather than rush children on to the next year’s work if they are accomplishing what is expected of them, they are encouraged to broaden their experiences – solve problems, explore mathematics and apply the skills they have been developing. That is not to say they cannot be taught later skills, but there is no longer the constant drive to cover more content, without a breadth and depth of understanding.
This is welcomed by maths teachers. The work of authors such as Jo Boaler (Boaler, Altendorff, & Kent, 2011) demonstrates the power and importance of a rich, purposeful mathematics curriculum in removing barriers to learning mathematics. Children who learn maths like this see it as more relevant. For me, this is a positive turn. The idea that we will now be immersing children in rich relevant mathematical experiences that enables them to foster a love for the subject is truly exciting.
I do however have some concerns and don’t see a utopian primary maths curriculum emerging quite yet. For the children who were served well under the old curriculum this is likely to continue to be the case, but it is not such children we have ever had to be concerned for. Will it be necessary to get a “gold” on the latest multiplication test before you are allowed to have a go at solving problems? Are we going to reduce mathematics to a list of facts to be recalled? Similarly, recent research shows that parental ability to support ‘high-potential’ children is mediated by economic background (Koshy, Portman Smith, Brown, 2014). What about those children whose parents don’t “print off 50 times tables and have to do them in 6 minutes” as in an example I was told of recently!
The evidence suggests that it is the ability to see connections between mathematics that enables the successful learners to be successful. Subjecting children to endless practise and rehearsal of unrelated skills and facts won’t make these links apparent. If we save the rich and varied problem solving until the facts are mastered, will we prevent some children from ever having this experience? My research is leading me to argue that we use ‘number sense’ in primary school, the facts, rapid recall and simple calculation as a gatekeeper to all the mathematics beyond it. Without mastering this set of ‘core skills’ children are not enabled to glimpse what the beauty of mathematics can be. There are many analogies around, but the image is the same, the way we often teach mathematics – the basics without the bigger picture – is like teaching swimming without getting in the water.
I believe these difficulties are perpetuated by two key sets of thinking in primary schooling. The first is the idea of fixed ability which is slowly being challenged by authors (Marks, 2014) and practitioners, but the reality is that children experience teaching by ability grouping and are fully aware of it. Secondly, this is supported by the strength of cognitive theories which underpin educational practise. The idea of innate cognitive skills such as subitising and estimation, which correlate with later mathematical achievement, are powerful, especially when they offer potential to identify ‘mathematical difficulty’ and remedy it (e.g. Butterworth, 1999)
So, how do we move forwards? If mathematics does act as a gatekeeper to life’s opportunities (Noyes, 2007) how do we ensure equal access to it? Essentially, I am arguing for a broader perspective on primary mathematics. I appreciate that practise and rehearsal are going to feature within the curriculum, but they need to be placed in a curriculum which is relevant and stimulating. We need to find where the mathematical reasoning really falls in children’s lives and teach them the skills for that. In the past week I have seen children sneaking a stop watch into school to time their mates in races and learning advanced yo-yo tricks from pictorial explanations. I have also had the most complex sport/extra-curricular/lunch rota explained to me, with a sense of disbelief on the part of the child when I couldn’t work out what they could do that day. Children are immersed in a mathematical world and number sense is a vital part of accessing it. By viewing their mathematical literacy (Venkat, 2014) from this starting point we are better placed to enable them to access the formal world of mathematics we treasure so highly.
And perhaps Michael Gove has helped us to get here. His curriculum reforms kept problem solving and reasoning as a core aim of the curriculum. After years of following lists of objectives, are we ready to embrace this wider aspect of teaching and learning mathematics. Are we ready to teach children about mathematics, rather than teach mathematical skills to children?
Boaler, J., Altendorff, L., & Kent, G. (2011). Mathematics and science inequalities in the United Kingdom: when elitism, sexism and culture collide. Oxford Review of Education, 37(4).
Brown, M., Askew, M., Baker, D., Denvir H., & Millett, A., (1998) Is the National Numeracy Strategy Research-Based? British Journal of Educational Studies, 46(4).
Butterworth, B. (1999). The Mathematical Brain. London: Macmillan
Noyes, A., 2007. Mathematics Counts…for what? Rethinking the mathematics curriculum in England, Philosophy of Mathematics Education, 21.
Koshy, V., Portman Smith, C., & Brown, J. (2014). Parenting ‘gifted and talented’ children in urban areas: Parents’ voices.
Venkat, H. (2014) Mathematics Literacy. What is it and is it important? In Mendick, H. & Leslie, D., (Eds) Debates in Mathematics Education. London: Routedge.
Rebecca Turvill is a first year PhD student at Brunel University, supported by a bursary from the School of Sport and Education.