Making sense of
 the maths curriculum

The one dominant concern for teachers with any new curriculum is the steps that have to be taken to achieve the revised standards. As a result of this, we have schools across the country, investing a lot of time producing their own primary mathematics framework, and possibly all coming up against the same challenges and making the same errors.
So let’s look at what has changed. The first thing that teachers will notice is the clear drive to raise standards; much of the content that would previously have been positioned in the secondary curriculum, such as long division and an increasingly complex understanding of concepts such as fractions and decimals, now appear in the primary curriculum. Primary teachers therefore are having to revise in order to teach these skill levels that they may not have had to teach for many years, if ever.
The good news is that our new primary maths curriculum is, we are told, not designed to be a straitjacket, but one that provides guidance in the various curriculum areas. However the required change in the structure of learning is quite exact and very different from the way maths has, generally been taught previously. The central feature is the move away from teaching mathematics as distinct disconnected concepts.

What to teach
Connections between mathematical concepts are now stipulated to be crucial and therefore the most important change in the new primary mathematics  curriculum, is the emphasis on bringing them together. Previously we have separated them out into domains; first we teach addition, then subtraction, then division, then fractions followed by percentages, but of course it is vital that our students understand how these segmented concepts are interconnected.
We need to work to develop pre-conceptual understanding with children and not just teaching them how. They have to get underneath what is going on, not just be able to do it. Only by having this understanding can children know which mathematical concepts can be applied to solve each problem.
While there are few that wouldn’t applaud this change, without a framework, teachers are left to re-write their teaching plan. The danger of the way the new curriculum is presented is that these core aims that underpin the learning objectives are at the front of the document only; because they don’t appear in year groups, the danger is that they will be missed.
This core requirement is backed up by the prohibition of calculators in the KS2 SATs exams from 2014. If children are not fluent with various ways of problem solving, in their head or on paper the suggestion is that they haven’t fully understood all the patterns and number connections. Mental fluency is the name of the game.

Number and place value
So when we are looking at the structure and order of learning activities, we must now talk about what the connections between the mathematical concepts are, and how to make them, or as Professor John Mason talks about ‘working through’ and ‘working on’ an interesting distinction.

For example, in the new curriculum there will be a KS1 learning objective of number and place value; being able to compare and place numbers in order. However, this also applies to measurement in the same way; 5cm is longer than 3cm, 1kg is heavier than 20 grams, Bill is 1 metre 3 centimetres, so he is taller than Jane who is just 1 metre in height. Historically we were taught to memorise facts such as the multiplication tables and number bonds. While it is easy to argue the case for memorising the multiplication tables, if a child is taught to really understand the concept rather than just rote learning, this should not be important.
So when teachers are looking at explaining  the concept of number and place value, it’s about drawing strands of each developmental concept together and looking at progressions between each domain and within each domain. A lot of our teachers who have been familiar with the previous numeracy strategy concentrated on teaching sequences and developing ideas in two to three weeks sequencing. The question was, what am I trying to get them to think about? It’s hard to manage all these interlinked concepts when given a new curriculum but it’s all there, it’s just about making sense of it and structuring the learning pathway.
Sadly simply having a new teaching framework won’t meet all the challenges currently facing teachers.

When to teach
Because the Department for Education will not be producing a Primary Mathematics Framework to accompany the new curriculum, we have teamed up with publisher Rising Stars to develop a fully planned framework to help schools in Devon deliver the new curriculum.
In working with Rising Stars to create the framework for the schools in Devon, one thing we identified was an issue with what is statutory at each stage; what is supposed to be understood by the end of KS1 and KS2? It also highlighted the importance of having a primary framework set out for each year group teacher to follow.
The programme of study is set out on a year-by-year basis, however schools have the freedom of when they teach the content within each Key Stage. The new curriculum is presented in a way that means you do not have to teach what is in Year 3 in Year 3, it just has to be done by the end of KS2 for example. While this freedom sounds like good news, it actually presents teachers with a huge problem in structuring the learning themselves to ensure they interlink all the mathematical concepts and achieve all the understanding by the end of the Key Stage.
There is also the expectation that teachers will present what they are going to teach in each year group regardless of the order in which is it presented. So while schools are given this increased level of flexibility, they do have to plan the school’s curriculum for mathematics on a year-by-year basis and record this online. Communicating what is to be taught and recording results has never been more important.
Another question is, when a child moves from year group to year group, or even from school to school, how does the teacher know that each skill has been learned?
Another challenge that schools must be aware of is that if it is followed by the book, divided into year groups, some curriculum areas can disappear. For example in Year 4 geometry, one learning objective is ‘position direction’. It states that the children should be introduced to co-ordinates in the first quadrant but in year 5 co-ordinates are not mentioned. A year 5 teacher could easily look at the Year 5 schemes of work and think that this doesn’t have to be taught. However, as the Year 4 teachers may not have taught it – it is not stipulated that they have to, then in actual fact, Year 5 teachers must look at the whole curriculum at that Key Stage to understand what each child knows and what they have done; something that I am not sure all teachers have recognised.

A framework for Devon
This is why in Devon we worked with publisher Rising Stars to create a framework for the new primary maths curriculum. We used a model of learning mathematics that comes from Haylock and Coburn; a connective model that looks at how young children form an understanding of mathematical concepts, various elements and connections. We looked at the concepts that needed to be taught and created a learning structure that would introduce each connected mathematical concept showing how they work together and relate to every-day activities. What we’ve tried to do is to pull together all the mathematical concepts that fit in different domains and group them under three themes; number sense, additive reasoning, multiplicative reasoning, geometric reasoning. None of these are addressed on their own.
We also worked to ensure we included the use of meaningful and engaging images and models, which are vital in the development of a really robust understanding of the concepts underpinning the required calculation. Children need an understanding of maths in context through images and pictures. Children must understand how language links with symbols because children sometimes understand that there are a whole number of words that they should say when they see a certain symbol but they don’t know how to construct the mathematical words – i.e when adding and using the word ‘more’ – when thinking about a context of I’ve got three ‘more than’ Jane and she’s got 8’ – mathematical images supporting understanding.
Learning the language and symbols and representations of mathematical concepts; it’s no good just having a maths curriculum that is context free, children need to know how to bring their everyday real live experience to the classroom and see how these experience are relevant to maths. So when we ask where else they use these symbols and language they don’t just say “during maths lessons.”
Michael Gove made it clearly that they would just outline the content without telling teachers how to teach it. However what is vital and recognised by the new curriculum is that teachers need to be able to communicate the broader interlinked mathematical concepts- ‘using’ and ‘applying’ are the old ways of saying it.

Assessment and reporting
In terms of assessment and reporting we have been met with the demise of ‘levels’, meaning that schools will have to report internally and to parents on each child’s progress through their own assessment framework. SATs results will be reported to parents using 10 ability bands worked out on a national level.

Exemplification – probing questions to help assess whether children have successfully reached this point.

We hope that our work in Devon has left the new primary maths curriculum with the flexibility that is welcomed by teachers but with an underpinning framework to give our teachers the guidance they need to ensure the objectives are met. It has hopefully saved our schools a huge amount of time in creating their own framework while giving them the peace of mind that all teachers want at this time.

Further information