Balanced Number Facts Instruction
Have a think about this strange situation.
In primary schools in England, grapheme-phoneme correspondences are taught in a highly systematic way, but very often addition and subtraction facts are not. Every school in England can point to the precise lesson where children are first taught that <ai> represents the phoneme /ae/, but until recently most schools couldn't tell you the precise lesson where children learn that 3 + 6 = 9.
It’s not because GPCs are better suited to systemic teaching. They aren’t. Some graphemes (e.g. <ow>) correspond to more than one phoneme, and likewise phonemes can often be represented by more than one grapheme. It’s much messier than addition and subtraction facts, which are completely regular: 3 + 6 will always equal 9.
It’s not that children acquire facts anyway. They don’t. Many Key Stage 2 children remain stuck on counting for at least some additive facts, and for some children counting in ones is their only strategy. If we teach children to count that is what they do.
Snow and Juel referred to the teaching of GPCs as ‘small unit instruction’, and as number facts are the small units of calculation we were heavily influenced by the features of phonics programmes when we designed our Number Facts Fluency programme:
- We set out in a grid all of the facts children need to know (I always say that trying to teach number facts to fluency without having the grid of the facts children, need to know set out in front of you is like trying to teach phonics without anyone telling you what GPCs you need to teach)
- We identified derived fact strategies to teach (near doubles, five and a bit etc) as an alternative to counting and made sure each fact was is covered by at least one strategy
- We sequenced the strategies, and provided materials to teach each strategy and the associated facts
- We built in regular practice of previously learnt facts alongside intensive practice of the new facts.
So given these parallels between early calculation and early decoding, I was intrigued to hear what the eminent Australian early reading specialist, Dr. Pamela Snow, would say on mathematician Anna Stokke’s podcast ‘Chalk and Talk’. I hoped this reading-maths mash up would provide some interesting prompts for further thought, which it certainly did. The whole thing is well worth a listen, but one part particularly stuck in my thoughts. Dr. Snow talks about balanced literacy, and the introduction of phonics in Australia as ‘a patch on whole language’.
“But what we saw really was a patch on whole language. So there was a reluctant acknowledgement that yes, we'll put decoding in the mix, we'll put phonics instruction in the mix.”
… “We opted instead for the fallacy of the golden mean, that we'll just put everything in the middle and produce a casserole of instruction. And as long as we can take the lid off the pot and see some phonics and see some vocabulary work and see some sentence structure work, then we'll be happy.”
This really got me thinking about our Number Facts Fluency programme. While it is brilliant that schools - which have spent years teaching children to work out number facts through finger counting - are starting to see the benefits of daily sessions focused on structured number facts instruction, this comes with a bit of an uncomfortable truth. The vast majority of schools using our programme (and the NCETM equivalent, Mastering Number) teach them in addition to a main maths lesson. They are a patch. And in those main maths lessons, children are generally taught to add by putting the bigger number in their heads and counting on. Precisely what our programme (taught at a separate time of the day) teaches children NOT to do. Balanced maths. We’ve created the ‘casserole of instruction’ which Dr. Snow is so critical of in early reading.
Dr. Snow also talks about it being the children’s time and us having a duty to use it wisely, and when we start to think in these terms it become even more nonsensical. “I’m going to teach you number facts really well, and then I’m going to spend more time teaching you the same thing not very well and in a way that contradicts the first way and then I will leave you to pick between the two ways yourself (the good way and the less good way) and let’s see where we end up.”
During our pilot year there were schools which took our materials and integrated them all into the main maths lesson, and stopped teaching counting on and back altogether. However these schools were generally relatively far on in their maths thinking, and not representative of all schools. When we launched more widely, we quickly learnt that most schools were reluctant to mess around with established schemes of work, and of course the workload implications of adapting schemes of work in this way are quite significant. At that stage we started to provide guidance about how to teach our programme in a separate 15 minute session, akin to a phonics session, feeling that this was the only way to get structured number fact teaching going in most schools. Now we are in the incredible position whereby this way of teaching has started to take root at scale (well over 50% of schools in the country now use Mastering Number or our Number Facts Fluency programme) and it’s time for the next evolution. The truth is that it simply doesn’t make sense to teach number facts really effectively, and then spend time, at another time of day, diluting this instruction by teaching ineffective and contradictory methods. Snow talks in the podcast about the impact of mixed methods teaching on reading.
"And I think balanced literacy has contributed to a very unfortunate set of circumstances where we've told teachers that they can, you know, as long as they're broadly doing a bit of all of these things that they're teaching is okay and then we're going to have to uncomfortably kind of look the other way and shrug our shoulders when there's a significant proportion of children who don't succeed."
… “it works for some children. Great, but if we go back to thinking at a public health level, it needs to work for the overwhelming majority of children in the same way that road safety policy and laws and principles need to work for the overwhelming majority of road users.”
..."And we've got we need to think probabilistically, I think, Anna, that's probably a concept that works for a mathematician. You know, we need to say on the balance of probabilities, what are the instructional approaches that are going to get the vast majority, 90 to 95 percent of children across the bridge in the first three years of school from doing something that's biologically primary using oral language to something that's biologically secondary.
So if your school has started structured number fact teaching, and you are seeing the impact, here’s a way that you can save time AND make your teaching more effective.
- Simply leave out the lessons in your scheme of work which teach children to add and subtract within 10 and 20 by jumping up and down number lines. The marked number line is an incredibly useful representation for helping children understand the number system, but should not be used as a tool to get an answer to a calculation like 4 + 5.
- Ban the phrase ‘Put the bigger number in your head and count on’ (or count back in the case of subtraction). Never, ever say it again. We don’t want children to end up as finger counters so don’t tell them to finger count. Instead every single time children need prompting with how to get an answer to an addition or subtraction fact, prompt them to use the strategy you have taught in your number facts sessions. In Number Facts Fluency these are all mapped out for you.
There are schools which have created even more time and even more cohesive provision by dramatically slimming down other elements of the Year 1 curriculum as well (fractions, multiplication and division for example) and moving number facts teaching entirely into the main maths lesson. This means there is no need for a separate 15 minute session at all. In my view this is the ideal end point for all schools, so that structured number fact teaching moves from being a patch to a central part of the curriculum particularly in Year 1, and in Year 2 to some extent. At the moment with upcoming curriculum reform I would imagine most schools are not in the market for this kind of work. However I know from speaking to our schools that some are, and for schools which use Number Facts Fluency we have a recorded webinar available in our subscriber coaching section which advises on how to do this. Our materials are flexible enough to be used in this way.
Once we have got to a stage where we have got rid of counting based methods to teaching calculation entirely, and we are teaching one approach with fidelity to make sure all children are fluent in all facts, we will have the basis for mastery in mathematics.
Find out more about our approach to teaching number facts to fluency here