Addition & subtraction facts, and KIRFs: What's the same, what's different? (November, 2020)

Over the last couple of years, we have heard more schools starting to talk about KIRFs, short for ‘Key Instant Recall Facts’.  In this blog we take a look at KIRFs, and what’s the same and what’s different in comparison to the NSM Number Facts approach.  Generally, KIRFs are laid out through the school, with particular facts that children should know in particular terms and year groups set out clearly for children, families and teachers.

What is the same?

One of the strengths of setting out KIRFs is, in our minds, an acknowledgement that children benefit from having a bank of ‘basics’ that they have learnt to automaticity, and can use in solving other mathematical problems.  When children have quick access to a bank of facts which incur little cost to working memory, they will have more capacity to think about more complex problems that draw on these facts.  In fact one of the main drivers behind us writing NSM Number Facts was frustration at seeing KS2 children counting on their fingers to solve calculations such as 14 – 9 and 6 + 7, and finding how much harder it was to teach more complex maths to children who were still stumbling over the building blocks. 

Secondly we have found that having a clear map of what should be learnt is really helpful in teachers prioritising content.  It moves us from teaching the number of lessons a scheme of work suggests on a concept, to thinking more flexibly about what we teach and how, to make sure all children have the knowledge, understanding and mathematical habits to be able to move onto the maths that will follow.  It gives us permission to flex how we teach maths in order to achieve a really clear goal. 

What is different?

Recall is a problematic word for us in the context of addition and subtraction facts.  We prefer talking about ‘factual fluency’ or ‘facts having been learnt to automaticity’.  We are not against the concept of rote learning – in fact at the school I work in our method for learning times tables to automaticity is entirely based on rote recall of the sound pattern, like reciting a nursery rhyme.  But having spent many hours over many years sifting through the research on how addition and subtraction facts are best learnt, the evidence seems to suggest they are somewhat different.  (At some stage we will do a full blog on ‘what is the same, what is different’ between learning times tables and learning addition and subtraction facts, as that in itself is fascinating.)

The research principles behind NSM Number Facts are here, and our interpretation of the research evidence is that addition and subtraction facts are best learnt to automaticity through a derived fact approach – using what you know to work out what you don’t know.  Yes, children need a bank of some ‘rote learned’ facts (doubles are a good example of this), but after this teaching strategies so that children can derive other facts is the quickest way to learn addition and subtraction facts to automaticity.  It is much easier for a child to learn 3 + 4 = 7 by recognising that it is one more than their known fact of 3 + 3 = 6 than just trying to memorise that 3 + 4 = 7 by saying it over and over again as we might for times tables.  And it is easier for a child to learn that 8 – 6 = 2 by being taught to spot that 8 and 6 are adjacent even numbers, than it is for them just to memorise 8 – 6 = 2.   

Over time, with frequent application of these strategies, some facts (particularly those within 10) become known facts that are truly recalled.  But for other facts this just doesn’t seem to happen – particularly facts which bridge 10.  8 + 9 is a fact that, in training sessions over the years, I have asked probably a couple of thousand teachers to think about how they ‘recall’ it.  In fact, only about 5% of primary teachers find they actually do recall it (in the way they would recall 5 + 5 = 10 by ‘just knowing it’).  The other 95% of teachers find they are very quickly using a strategy: most commonly near doubles, followed by ‘make 10 and then’, followed by adjusting (adding 10 and subtracting 1). (A small minority of teachers also talk about some kind of ‘redistribution’ of one from the 8 to give 7 + 10.)   

So we prefer talking about fluency – yes, sometimes the end game is recall, but sometimes it is fluent application of a strategy, learned to automaticity and applied with limited demands on working memory.

One other thing we think it is important to think about is the distinction between teaching and practice.  If KIRFs become sheets of facts that children are asked to practice little and often (and possibly mainly at home) then many children just won’t become fluent in them.  Yes, children should practice facts regularly – but first we would say that in the case of addition and subtraction facts children need to be taught how they should learn and practice them.  The primary responsibility for this sits (we would say) squarely with us as teachers rather than with families.  Again, we find phonics is a good analogy.  Yes children need to practice a lot, but first they have to learn through clear, direct teaching of approaches that work.

We wrote NSM Number Facts to provide a coherent sequence and approach to teach all children addition and subtraction facts to automaticity.  Every fact is taught at least once through our strategies.  Nothing is left to chance.  The end game is both fluency in addition and subtraction facts, and confidence and flexibility with number, which we hope will provide the basis for a lifelong confidence in, and enjoyment of, mathematics.

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