'Mathematics is not just about utility; it nurtures fundamental human characteristics'
Charlie Stripp, director of the National Centre for Excellence in the Teaching of Mathematics (NCETM), writes:
Maths is not just about utility. I believe that, if well taught, it nurtures fundamental human characteristics that contribute to general well-being and happiness. Everyone likes to understand things properly, and everyone likes to solve problems and puzzles – mathematics is the ultimate tool for these activities. For me, the greatest pleasures of teaching maths are seeing those moments in pupils’ faces when the penny drops and they suddenly really understand a mathematical idea, or when they have grappled with a problem and come up with a solution that they are able to explain clearly and justify mathematically.
The basic content of the compulsory maths curriculum is similar throughout the world – there is a broad consensus on what should be taught. This means reviews and changes to the maths curriculum are much more about the timing and emphasis of the curriculum than about its content.
Here in England, the new National Curriculum for Mathematics has three aims. These are that all pupils:
- become fluent in the fundamentals, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately;
- reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language;
- can solve problems by applying their maths to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.
These aims emphasise the underlying purposes of the curriculum, which are to develop a sound understanding of school-level maths, combined with the confidence and competence to use it in everyday life and work.
The aims are also consistent with the ‘Purpose of Study’ section of the new curriculum, which states:
"A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject."
Some have suggested, incorrectly, that the new curriculum emphasises rote learning, or that it is too ambitious, expecting too much, too early from primary pupils. This is a misrepresentation. The NCETM’s experience, gained through working closely with teachers, and through developing extensive support and guidance to help teachers implement the new curriculum, has been very positive, helping to dispel these myths.
Much depends on interpretation. What does ‘fluency’ mean in mathematics? Does it mean learning algorithms by rote so that you can mindlessly do sums and get the answers right without understanding what you are doing? The answer is an emphatic ‘No!’ Rote learning does not support mathematical reasoning and problem solving. The best definition of mathematical fluency I have seen is that it is the ability ‘to use mathematics efficiently, accurately and flexibly’. Rote learning cannot achieve this. To develop mathematical fluency does require ‘practice’, but that does not mean just doing pages of sums; it involves carefully structured teaching and learning to develop conceptual and procedural understanding in parallel, so that they continually reinforce one-another. This leads to the development of true fluency – transferable mathematical skills that are of real life-long value.
The new curriculum is certainly more demanding than the one it replaces. It requires primary school children to grapple with more demanding concepts (including basic algebra) and it also shifts the teaching of some familiar topics, such as fractions and higher times tables, into younger classes than at present. However, a simple shift in when topics are taught is unlikely to achieve the higher expectations set. Teachers will need to think carefully about how to develop the conceptual understanding underlying these topics, so that pupils can access and make sense of them. Effective use of concrete resources and visual representations, together with opportunities to reason and solve problems using the maths, will play a key role in ensuring that learning is deep and sustainable.
The three aims of fluency, reasoning and problem solving are shared by many high-performing countries that have high expectations of what pupils are capable of achieving. We have recently filmed lessons in English classrooms where children are set exactly these high expectations and go on to meet them with impressive flair, and enjoyment.
An important difference between the new National Curriculum and previous versions is that it is largely a list of content. It sets out what should be taught, not how to teach it. I believe this is a great opportunity, giving schools and teachers more freedom to develop their own ways of doing things, rather than being told what to do. Through our website, the NCETM is making available extensive expert advice to teachers about ways to teach the new curriculum, including videos of classroom practice and high-quality teaching and learning resources, but it is down to teachers to choose what use to make of our advice.
The new curriculum is demanding, but I believe we would be letting our children down if we didn’t stretch and challenge them in this way. Let’s use the new National Curriculum as a catalyst to work collaboratively, both within and between schools, to review our teaching of mathematics and consider how we can improve, extending opportunities for young people and increasing their enjoyment of mathematics.