At first, I agreed with everyone else. I went through the guidance, the blogs and the articles and I came to the same conclusion: what the new national curriculum for maths meant by “fluency” was being efficient, being accurate and demonstrating flexibility when calculating.
After all, the phrase “ability to recall and apply knowledge rapidly and accurately” suggests a number and calculations focus.
And yet, it never felt quite right. As time moved on, I became increasingly convinced that the definition did not make sense.
So, I went back to the national curriculum aim on fluency and wondered if we could broaden our school approach so that we were looking not only at fluency in terms of number and calculations but also at fluency opportunities within – and across – other mathematical strands.
Since one of the school’s key focus areas is maths, an opportunity to see if this would be possible presented itself this year. I wanted a genuinely whole-school approach and, as part of that plan, my intention was to support teaching staff with the tools they required to develop fluency – in number and calculations, within other mathematical strands and via “cross-strand” application.
First, we restructured our maths displays (known as “working walls”) to make their upkeep easier but more effective. The walls basically became four “windows”: the basics; reasoning and problem-solving; vocabulary/signs; and a “challenges” section.
Next, I provided each year group with a planning support folder, which contained resources and ideas plus a copy of the fluency plan (FP). These plans were compiled by our external consultant and provided a clear pathway through each strand of maths, identifying: the “basics” that the children would need in a logical order; where problem-solving and reasoning fitted; and where “in-strand” and “cross-strand” fluency links could be found.
In one of our September staff meetings, we discussed the folder, explaining what was included and how to use it to support our planning. We spent some time looking at the FPs – their content, how they worked and why they would be a good basis for developing a logical progression through a strand of maths. We also identified examples of “in-strand” and “cross-strand” fluency.
In the past, there was sometimes a tendency to jump from one strand to another, flitting from properties of shapes to fractions to statistics in three weeks. We recognised that this had to change. As a result, we have incorporated greater flexibility in our delivery of the maths curriculum – so, for instance, the early spring term is purely about “measures” – and this has allowed for in-strand fluency.
In Year 4 we are estimating, converting between units, comparing units and calculating. We believe that by teaching the skills required for estimation, conversion and comparison, and applying the calculation approaches that we focused on in the autumn term in, say, length and height, these can be instantly referenced by our Year 4 children when they look at volume/capacity and mass.
Our FPs enable us to make connections across mathematical strands. For example, in key stage 1, staff make links between place value and measures through the “counting in twos, fives and 10s” objective. We incorporate money examples and money number lines as a visual image, so that children can also count in two-, five- and 10-pence pieces.
One key aspect where making links is vital for our children is fractions. The FPs enable us to create a logical pathway through this strand of maths, but we can also reference the fluency links to make connections with other strands. The link between fractions as numbers on a number line and measures is stressed – again, with clear visual images.
We can use the number line to make connections – for example, that the distance from 0 to 1 is double the distance from 0 to ½ or ½ to 1. If I double the distance from 0 to ¼, I get ½. If I treble the distance from 0 to ¼, I get 3 x ¼, which is ¾.
The links to measures in terms of, for example, ¾ of a litre or ½ a kilogram, time (quarter past/to) and sharing money are highlighted. In geometry, we have symmetry and amounts of turn. Then there is the old chestnut of the link between fractions and division – demonstrating to children that ¼ of 96 is the same as 96 ÷ 4, which we can calculate by halving 96 and then halving 48.
Four terms on, teachers have been using the FP, supplemented by other ideas and resources. As a subject leader, I now have:
* A whole-school overview demonstrating coverage of all mathematical strands in a logical progression.
* Key performance indicators identified within the text of the plans.
* Half-termly breakdowns of what we want the children to learn and when.
* References to non-statutory guidance to support the listed objectives.
* A clear glossary of terms with key definitions for each year group.
* Dedicated in-strand and cross-strand fluency links identified.
What difference does this make to the teachers and students? Staff members now have an adaptable planning resource that supports progression across a unit, a half-term, a term and an academic year. Meanwhile, children are demonstrating fluency as they become more adept at using their mathematical knowledge, skills and understanding within – and across – mathematical strands.
Furthermore, our approach is meeting the requirements of the national curriculum in that it is introducing a “basic”, and then applying reasoning and problem-solving opportunities within that area before moving on to the next “basic”.
Also, a recent Ofsted visit identified that there was “better teaching in mathematics” and noted that this was “helping to improve pupils’ outcomes in this subject”.
Katie Bentley is assistant headteacher and maths subject leader at Farfield Primary School in Bradford