We are already using a Far Eastern influenced approach to maths. Is this just the same thing?
In far Eastern countries, like Singapore and China, children start formal schooling in the equivalent of our Year 2. Children tend to arrive at school already knowing their addition and subtraction facts and so curriculum resources don’t usually focus on systematic teaching and practice of these. If you are using Far Eastern approaches and resources you will notice that there is a lot of focus of understanding the relationships between parts and wholes. Number Sense Maths can supplement this teaching by making sure all children are fluent in the facts they need to use in class.
Are addition and subtraction facts the same thing as number bonds?
Number bonds are pairs of numbers which add to a given total, e.g., 3 and 7 are a number bond pair for 10. Children can use this fact to recognise that 3 + 7 = 10, 7 + 3 = 10, 10 – 3 = 7 and 10 – 7 = 3. Stage 2 of the programme (Making and Breaking Numbers to 10) has a focus on number bonds, taking each number to 10 in turn and looking at the number bonds for it. However learning number bonds one number at a time (e.g. bonds to 5, then 6, then 7 etc.) depends on a high degree of memorisation. In Number Sense Maths we revisit all facts from Stage 2 in Stage 3, and give additional strategies to learn each one. We have found that having a range of strategies is more effective in developing fluency than relying on memorisation of number bonds alone. The other downside to only learning addition and subtraction facts as memorised number bonds is that children miss out on learning about the number relationships that underpin the strategies. Finally, children knowing number bonds isn’t sufficient for them to solve related addition facts. We have seen many children who can confidently say that 7 and 3 are number bonds to 10, yet when presented with 7 + 3 = ___ revert to counting on their fingers to solve it, not recognising that this is simply application of their known number bond.
We do lots of work learning number bonds to 10 and 20, and doubles facts. Do children really need to learn all of these other facts as well?
Yes they do. Number bonds to 10 and doubles are very important and are included in the programme. However, learning number bonds to 10 and doubles facts only covers the two diagonals of the addition facts grid. It is really important that children also know how all of the other numbers to 10 can be made up and broken down. Knowing that 5 can be made up of 3 and 2 supports efficient subtraction (solving 5 – 3 by partitioning rather than counting back). The ‘Make Ten and Then’ strategy also depends on this. To solve 8 + 5 by thinking ‘8 + 2 + 3’, children need to be confident breaking 5 into 2 and 3.
The children are really quick at counting on their fingers to calculate and these approaches are taking them much longer. Can’t I just stick with counting?
These approaches will take longer initially. For small numbers counting is a quick strategy, but it quickly becomes inefficient. Teaching children to calculate using derived fact strategies with these small numbers will make calculating with larger numbers much simpler.
How will I fit in the rest of the maths curriculum if we take so long working on small numbers?
Much of the calculation in the KS1 curriculum draws directly on these number facts. For example, knowing that 9 – 7 = 2 means that children can efficiently calculate related facts like 90 – 70 and 29 – 7 without relying on counting. In fact 19 out of the 25 questions in last year’s KS1 SATs arithmetic paper are just manipulations of the facts learnt in Number Sense Maths. In Shanghai children focus on quantities within 20 up until half way through the equivalent of our Year 2. Their fluency with these calculations, and the understanding of number relationships that they have got from learning them, means they can make rapid progress after that.
Can NSM Number Facts be used as an intervention?
Yes - there may be children in KS2 who have gaps in their number facts and who would benefit from the Number Sense Maths approach. The materials can be used as a small group intervention for children in KS2. Intervention groups should follow the same structured teaching programme, including conferencing of children on entry and exit to identify gaps.