The Impact of Fluency on Maths Planning

As my week on planning continues, I will now confess the biggest mistake I had made when moving over to the new curriculum in 2014: I only read the programmes of study.

The maths curriculum document is relatively large, and as a deputy headteacher I have a range of responsibilities beyond mathematics, so I thought I had become relatively good at skim-reading important documents and pulling out the key information. In maths I thought it was the programmes of study – the actual content of the curriculum. As it turns out, I was wrong.

In a short section at the start of the document, the aims of the curriculum are spelled out:

• become fluent in the fundamentals of mathematics, 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 mathematics 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.

It would have been easy for me to take that in, but I skipped it and as it turned out, so did everyone else in my school.

This year, as we have striven to correct the mistakes of the year before, fluency, reasoning and problem solving have become the language of maths. Whenever we speak about maths lessons, or books, or planning, or CPD, those words always come out. If you did a Word Cloud of our dialogue around maths, those words would by far be the biggest. But what do they really mean? In this post I’m focused on fluency, but I’ll come to other two in the future.

Fluency is three things:

• efficiency – instant recall and speed – having the very best method for solving a given problem
• accuracy – getting things right and knowing you’ve got them right.
• flexibility – being able to use maths in different contexts and domains.

What’s interesting is that if you just take the programmes of study for maths and deliver the content you find there, you will not make the children fluent. For example, in year 5 it says to teach the pupils this:

add and subtract whole numbers with more than 4 digits, including using formal written methods (columnar addition and subtraction).

If you took that statement at face value without the overarching aim of fluency you might consider it perfectly fine to teach the children how to add and subtract using a number line and if they are always accurate with the number line, you might teach them the formal method, but not really expect them to use it because they already have a method that works. You’ve taught rhe children to become accurate, but they are not yet fluent.

If you want the children to become fluent, you need efficiency too. So you have to teach them the formal method and teach it well, because for most 4-digit calculations, the formal method is the most efficient. You would also teach the children when a mental method is more appropriate, as we’ve all seen children do something like 4000-3998 in a formal method, because they are so conditioned to use it blindly.

But fluency is more than this. It is also flexibility. It’s easy to show that a child can add and subtract 4-digit numbers in a lesson about adding and subtracting 4-digit numbers. But what tended to happen in my school was children only being exposed to 4-digit numbers when they had to. When they were learning something else, say measures or coordinates, the numbers would be much smaller. The implication of fluency is clear – children should be able to add and subtract 4-digit numbers in any context and even in lessons when they have not been directly taught it. The teaching of the add and subtract 4-digit numbers objective should have an impact on the children that lasts into every maths lesson.

This has made a huge impact on our planning, some good and some bad:

• Good in that expectations are much higher – when an objective is taught, the expectation is that it will not be dumbed down in future lessons throughout the term. This means when I where my monitoring hat, I am deliberately looking for occasions when the child can use something they have been taught out of the original context. It also means that teachers are now always on the look out for ways to use a taught skill in a different context and are more flexible in their own planning, adjusting lessons to to recap and consolidate key skills when children have not quite learned them.
• Bad because all of our text books and resources don’t work like that, so teachers have had to spend a lot more time preparing activities then they used to.

There’s a another aspect to the impact of fluency on planning. The mental maths skills that underpin the ability to fluently add and subtract 4-digit numbers are not explicit in the programmes of study, but they are explicit when you read each statement with the words in the ‘fluency aim’ bullet point echoing round your brain. For example, when should children be able to double 36? At what point should a child be able to say that 3.4➗2 is 1.7 because half of 34 is 17? When do they get the sense of number that means they don’t blindly use a formal method to do 4000-3998? The reason I’ve put this at the end of the post is that we’ve not solved the mental maths side of things yet. That’s next half term’s work.

• Social Slider