676 is the new 243

Where is the mathematics in the new mathematics curriculum for primary schools in England?

Some of us in mathematics education will remember the significance of the number 243: not just because it is 3 raised to the power 5, although that helped us to remember it! Paragraph 243 in the hugely influential Cockcroft Report (1982) was very significant in defining what constituted a good and balanced mathematical experience for learners. This one paragraph had a great impact on mathematics teaching and learning and was for many years a positive influence on the mathematics curriculum. Do an internet search on 'Cockcroft 243' and you will see what I mean.

However, 243 is a long way back in history now, so instead I would like you to welcome and celebrate with me 676! I will explain.

The new primary mathematics curriculum for England, being introduced later this year, has an excellent statement of the purposes for learning mathematics. It also has a statement of aims that includes aspects that I would recognise as being real mathematics: in particular, the development of the distinctive ways of reasoning in mathematics and solving problems using mathematics (Aims 2 and 3). But these are then followed by pages of specific learning targets in the programmes of study that just do not seem to match the laudable aims and purposes. My fear has been (and still is) that teachers will focus just on the details in these programmes of study and real mathematical experience for our children will be neglected in favour of rote learning of routines, such as long division and calculations with fractions.

In particular, since there is no longer anything comparable to the 'using and applying' strand in the programmes of study and attainment targets for the current curriculum, there seemed a real possibility that the national assessments at the end of Key Stage 2 would focus just on the specific detail in the programmes of study.

The good news is: they won't!  Of the three papers, one (27% of the marks) will focus on context-free calculations, but the other two will contain a genuine focus on reasoning and problem-solving. And to make sure this happens we have paragraph 6.7.6 in the Key Stage 2 Mathematics Test Framework for National Curriculum Tests, published recently by the Standards and Testing Agency. This paragraph defines in detail what is expected of children at the end of Key Stage 2 in terms of mathematical reasoning and problem solving. This is where the real mathematics is in the mathematics curriculum! Maybe not in the programmes of study, but clearly there in the assessment criteria. And the hope is that if all this is going to be assessed it might just be taught!

Section 6.7.6 Solving Problems and Reasoning Mathematically

Children working at the expected standard are able to:

·            develop their own strategies to solve problems by applying their mathematics to a variety of routine and non-routine problems, in a range of contexts (including money and measures, geometry and statistics) using the content described above

·            begin to reason mathematically making simple generalisations, using mathematical language and searching for solutions by trying out ideas of their own

·            use and interpret mathematical symbols and diagrams, and present information and results in a clear and organised way; for example:

·            derive strategies to solve problems with a two or three computational steps using addition, subtraction, multiplication and division and a combination of these

·            solve problems involving numbers with up to two decimal places

·            select appropriate strategies when calculating depending on the numbers involved

·            use rounding and estimation to check their answers and determine, in the context of the problem, appropriate levels of accuracy

·            identify simple patterns and relationships, and make simple generalisations

·            draw their own conclusions and explain their reasoning in simple contexts using mathematical language

·            make simple connections between mathematical ideas

·            solve problems involving data 

So, hail 676, say I! Three cheers for 676! 676 is the new 243! Let's make sure that our primary school teachers are aware of 676. It justifies – and indeed requires – a proper focus in their mathematics teaching on genuine mathematical experiences for our children.

And, to cap it all, 676 is an interesting number, being the product of the squares of two primes (2 and 13)!

The heart of mathematics:

In an interview about the new primary mathematics curriculum, Debbie Morgan, Director of Primary at the National Centre for Excellence in Teaching Mathematics, has stressed that mathematical reasoning and problem-solving are to be at the heart of children's experience of mathematics.

http://www.youtube.com/watch?v=I4aDZEZaF_A&feature=youtu.be

She argues for the prominence of the three aims given at the start of the mathematics section of the document in determining what children learn and how they learn it. These three aims are, in summary, (1) fluency based on conceptual understanding; (2) reasoning mathematically; and (3) problem-solving.

All this would be great, if it were not for the fact that the detail in the subsequent pages and pages of statutory requirements focusses almost entirely on the first of these and contain very little to indicate how precisely the other two are to be developed.

Two factors that will be crucial in this are the end-of-key-stage 2 national tests (the so-called SATs) and Ofsted's approach to inspection.

Over the years those responsible for the national tests have at least identified aspects of 'using and applying mathematics' as defined in the current curriculum that can be assessed in the context of written tests. This has been possible because, for all its deficiencies, the current curriculum does actually  contain specific statutory requirements for children's learning in this respect. I fear that the likelihood is that there will be political pressure on test developers for the 2016 tests onwards – when Gove's new curriculum will start to be assessed – to emphasise disproportionately the assessment of written, formal arithmetic skills and to assess only the detailed statements in the programmes of study. Is there any hope that aims 2 and 3 will be not be overlooked entirely in the national tests? If they are then teachers will overlook them in their classrooms as well. And Debbie Morgan's laudable aspirations will prove to be a fantasy.

And is there any hope at all that Ofsted will give the highest endorsements to those schools who seek to embrace all three of the aims in the experience they provide for children? Will they be checking that children are engaged in genuine mathematical reasoning, following a line of enquiry, conjecturing relationships and generalisations, developing arguments, applying their mathematics to non-routine problems? Or will they just be checking that Year 4 children can multiply a 3-digit number by a single-digit number using the formal layout, that Year 5 children can multiply a mixed number by a whole number and that Year 6 children can divide a fraction by a whole number?