Order, Order! The Importance of Sequencing
Posted 5th February 2020
We’ve had several queries recently asking how we chose the order for the topics in the White Rose Maths curriculum. We touched on this briefly in our 2019 Ofsted Framework blog, and this blog looks in more detail about the sequencing and the decision making involved in both our primary and secondary curricula, and also looks at how this ordering helps pupils to learn and remember.
The basic principles
The fundamental idea behind our curriculum design is to support pupils to be able to perform simpler tasks so they can then move on to perform more complex tasks. For example, we cannot expect pupils to add two numbers together before they understand what each individual number represents.
This thinking gives rise to a typical sequence of ‘blocks’ of mathematics that you will see in most of our year groups.
Within each of these blocks we then have ‘small steps’ which are again sequenced in order of difficulty and dependency. Here are the first seven steps (of 18) in our Year 3 Addition and Subtraction block:
As you can see, nothing is left to chance – each step builds carefully from the previous step, building on pupils’ prior knowledge to develop new skills, with nothing left out. Pupils are ready for this having covered addition with 2-digit numbers in Year 2 and Place Value up to 1,000 in the first block of Year 3.
Similarly, here are first few steps of our Year 8 Fractions and Percentages block:
We start with “review steps”. This is material that will have been covered in KS2 or Year 7. Teachers can use their knowledge of their classes to decide how and when to cover these and then move on to the KS3 material, again building up slowly and ensuring that pupils can become fluent with both calculator and non-calculator methods.
So are “review steps” what the WRM curriculum uses to help pupils to learn and remember?
We only use review steps in our Secondary curriculum, and they are only one part of the story! Our curriculum is designed to use skills that have already been learnt in different contexts (sometimes called ‘interleaving’) whenever we can. This helps pupils to remember and to make connections between different parts of the curriculum.
Taking the Year 3 example, after the Addition and Subtraction block, pupils will revisit and practice these skills again in these blocks later in the year:
- Multiplication and Division
- Money
- Length and Perimeter
- Mass and Capacity
…and then they are built on and extended in Year 4 and beyond.
Likewise in Year 8, fractions and percentages will feature in:
- Standard index form
- Area of trapezia and circles
- The data handling cycle
…before being built on and extend in Year 9 and beyond.
We try to include this revisiting in our example questions, and also in the worksheets that accompany our small steps available with our Premium Resources subscription. The subscription also includes other useful resources to help pupils remember:
- Flashback 4 – a daily starter activity consisting of one question each from a topic covered last lesson, last week, two or three weeks ago and last term or last year
- True of False – a question for each step that can be used whenever the teacher wants to bring that topic back to the front of pupils’ minds
So…is the White Rose curriculum ‘mastery’ or ‘spiral’?
Sometimes educational debate can be very divided into ‘black or white’ positions such as ‘traditional’ or ‘progressive’ teaching, ‘conceptual’ versus ‘procedural’ learning and, of course, ‘mastery’ or ‘spiral’ curricula. Often there are good points to both sides of any argument, and there is need for a more nuanced and balanced approach.
We’ve tried to combine the best of both ‘mastery’ and ‘spiral’ approaches in our curriculum. It certainly follows many of the mastery principles – spending longer on topics to help gain deeper understanding, making connections, keeping the class working together on the same topic and a fundamental belief that, through effort, all pupils are capable of understanding, doing and improving at mathematics. But we also recognise that just spending a good chunk of time on a topic doesn’t mean that all pupils will ‘master’ it the first time they see it, and that they need to see it again and again in different contexts and in different years to help them truly develop their understanding on their journey to mastery, so we’ve built in the revisiting and reinforcing features of spiral curricula too.
And going back to the order, is it all to do with one topic depending on another?
Mainly, but not entirely. For example, it doesn’t really matter whether angles is taught before statistics or the other way round, so for these more ‘stand-alone’ topics (they all have some dependency, e.g. on number, if not on each other) we try to organise these to give as varied a curriculum as possible. We also try to avoid one topic always being at the end of Summer term, or similar, to minimise the chance of something not being covered.
What about the order of fluency, reasoning and problem solving?
These key components of learning mathematics are included in all our small steps. We certainly don’t advocate that all the fluency in a block is done first, then the reasoning and then the problem solving. We believe these should be integrated into classroom practice as much as possible in the order that is appropriate for the step, e.g. the process of division may be introduced by a problem about sharing or grouping for which we need to become fluent at the procedure.
I have more questions!
Don’t worry, we have more blogs! Coming up over the next few weeks will be looking at:
- Supporting SEND pupils
- Reducing teacher workload
If you have any questions about the contents of this blog, or anything else related to our curriculum provision, please email us at support@whiterosemaths.com We cannot promise to answer all questions individually (but we will try!), and the most frequently asked questions will be answered in the upcoming blogs.
