One of the very earliest, simple strategies children learn when they are beginning to add and subtract is to 'count on and back' from a given number. When they are adding, this is a step on from having to count all of the items in both sets. For subtraction, it is a simple way to begin to move away from always needing the concrete objects in front of them (although I definitely make sure the concrete manipulatives are still there to be used - kids need lots and lots of experience with them in order to internalise what they are actually doing when they add and subtract using numerals).

So - while this is not a substitute for lots of hands on practice with concrete objects that they are adding together and taking away from, I've found that using fist numbers gives children an easily accessible way to solve simple addition and subtraction problems. Use along side of lots of concrete practice, I've found it can help get kids excited about their ability to 'do math'.

Here's what we do: If we are solving the following sum: 5 + 1 = , we would put the number '5' in our fist (i.e., make a fist and say 'five'), then put up 1 finger as we count on to the next number ('six'). Thus, 5 + 1 = 6.

When I'm doing this with Primary 1s, we always start with adding on and taking away 1, referring both to number lines and using concrete manipulatives while we also count on our fist. That way, they have the chance to connect this early computation strategy with the concrete experience of adding and taking away. Once they have mastered adding on 1, we move to adding on 2. So 5 + 2 would be solved by 'putting '5' in our fist' (e.g., making a fist and saying 'five'), then counting on '6, 7' as we raise 1, then 2 fingers.

I always make a big deal about NOT raising any fingers when we say our fist number - that is the number we are starting with, so we haven't added anything yet - so no fingers allowed! The kids always find this quite funny...but they tend to remember.

Check out the JUMP teachers' materials for a fuller explanation (you'll need to register, but registration is free and well worth a few minutes of your time).

I'm currently reading The Myth of Ability, and I'll be posting my thoughts over the next few weeks under 'Books' here on my blog. The first post is already up, so please head over and have a look!

John Mighton, the author of the book, is the founder of the JUMP Math programme in Canada. I've used many of his ideas in the classroom, and I've found that they empower children. They take a problem that might seem unsolvable and they give a child a way to approach it. One of the simplest of his ideas is giving children a structured way to 'count on and back' (including counting in multiples), using their fingers. We call it 'using fist numbers' (I'll write more about it in another post).

Now - this isn't a strategy you'd want your children to be using for the rest of their mathematical career. But it works - it is a reliable  and efficient way to solve simple problems (while we continue to work on automatic fact fluency), as well as a great way 'in' to harder problems. The sense of achievement children get, both when they have a 'tried and true' strategy for solving simple problems and when they can use that strategy to work with 'big' numbers, shouldn't be underestimated. Several of my Primary 1s, for example, were able to use this 'counting on' strategy to accurately add sums like 22 + 15, without having been asked to tackle sums like that before. Again - I'd rather see them move to more efficient strategies (like those suggested in Number Talks) - but you should have seen the smiles of delight and the cries of 'This is easy!' when they managed to solve this difficult sum all by themselves...