I am still quite stunned by the difference it made to my children helping them with maths at home. My children are currently aged 12, 10 and 7. I began when my eldest daughter was in Year 1. Having seen the rather dramatic difference it made offering regular and systematic help I began to also work with my younger children at home. Whatever your child’s ‘natural’ ability in maths it is perfectly possible for them to excel when compared to standard expectations. People often ask me for advice about helping their own children so I thought I would share my experiences of teaching my son from age 2.
When he was two I bought my son a few nice picture books to teach recognition of numbers. Robert Crowther does a number book as well as an alphabet one.
There was a marked difference in the speed with which my children learnt numbers but it is best not to introduce too many at once. I just focused on numbers 1-3, then 1-5 and finally, after quite some time, 1-10 until my son recognised those with real confidence. Some children will remember numbers from a bit of incidental chat as it occurs each day but not my children. To build memory it was crucial to look at the numbers most evenings. When my son was only two I would simply trace my finger around the number shape and say its name ‘two’ and then count out the ‘two’ items illustrated on the page. It took a minute or so every evening and initially I didn’t expect my son to join in.
Meanwhile… I did lots of counting with my son. I remember thinking my eldest was ‘not good at maths’ because all her pre-school friends could count to 10 and she couldn’t. I now realise it was silly waiting for something to happen ‘naturally’ that was clearly a taught skill. We should have just counted more regularly with her than we did. Therefore, with my son I always counted up to 10 before turning off the light at night and ensured I counted with him numerous times every day. I’m stating the obvious but it wasn’t obvious to me with my first child. It is really important that as well as learning the numbers by rote you count items out. You want to isolate the relationship you are trying to present so use different items. This helped my son realise the numbers represent quantity of any item. We counted up the stairs, we counted out plates, at tea time etc etc. What was crucial was that we did so everyday, numerous times a day. When he was counting a number of items reliably I began asking him to count out a number which I specified in advance. This meant remembering the number which tells you when to stop.
Once my son recognised numbers 1-5 I put those numbers onto cards and started getting him to put the cards in order as he counted. We did this after tea every day – for about a year (it seemed that long anyway!) We gradually worked up to 30 and would line them up in tens. He didn’t always want to and I did make up stories in which he was a super-hero and would save the world only if he could get the numbers in order! I did insist my son did his number work but realised that generally if my child was becoming very resistant to working it was probably because I had made it too hard and I needed to go back a few stages and ensure most of what he did was easy.
The really crucial concept for my son to understand was ‘one more’. It seems obvious but it SO isn’t for a young kid. You can ask for one more shoe or for them to pass you one more spoon. I used the cards once my son had laid them out each evening. I would point to the number 2 and ask ‘what comes after two?’ Once he was quite confident with this I would start with 9 and work backwards asking what comes after nine? Then what comes after 8? I would ask the same questions with lego bricks, placing another brick down each time we counted ‘one more’. After a while (you have to be very patient and try and appreciate how new these ideas are for a young child) he got the idea that when counting, ‘one more’ means ‘the next number’. Once he had got this idea really sorted (and not before) I explained simple sums to him on paper e.g. 2+1 etc. I again used blocks and other household items to show what the sum represented. We soon worked up to having sums asking what one more was for all the numbers up to 20. I stopped using the cards in order every evening and would do those sums instead. By that time he was really confident counting to twenty (and then thirty) and so at night I started counting backwards from ten to one every night before turning the light out. (ready to help kick off the idea of ‘one less’.) I was never in a hurry, I was content for it to take many weeks or months for him to learn the next thing.
I had twin goals. I wanted my son to understand how numbers work and I also wanted him to become fluent in using numbers. Understanding isn’t all or nothing and often developed after fluency, proficiency allowing my son to appreciate a pattern as he was not overwhelmed simply calculating. I both wanted my son to understand how to work out a calculation but also to begin to know those ‘sums’ without thought, automatically. Therefore I would give my son the same calculations to do everyday so that he reached the stage where he could have done them in his sleep, he was so automatic! I then began to introduce calculations of ‘two more’ and then ‘one less’.
The next big hurdle was ‘counting on’. If presented with 3+2 a child will initially count up to three and then count two more to reach the answer. A child needs to learn to start at the number 3 and simply count two more (probably on their fingers/lego to begin with). Teaching this took enormous patience and lots of modelling. Simultaneously I was now beginning to work on ‘number bonds’ with my child. He needed to know, without having to calculate, the different ways of making ten, 10+0, 9+1, 8+2 etc. I taught him to be able to fill in any one of the three numbers in the sum if it was missing . Once I started to teach him number bonds he did some practice everyday, to build up memory and then continued to practice number bonds long, long after they were apparently known. I taught doubles and moved onto adding 3 and 4. My goal was that anything committed to memory had to be known in the same way a child knows their own name, entirely effortlessly and with no risk they will forget.
This is the first page of an early exercise book. (BTW in case you are wondering the purple pictures are aeroplanes, there was a long aeroplane drawing phase!)The same calculations were done every day – gradually adding in more. By the end of this exercise book my son was doing about 50 calculations a day but hadn’t dropped any of these.
This investment in the early stages I have outlined is invaluable. The next big step, ‘place value’ (this means understanding that the value a digit has depends on whether it is in the place for ones, tens, hundreds etc) is fascinatingly to teach. A child can appear to understand that 13 is one ten and three ones but not apply that knowledge in any other context. If you are interested in where to go next with you child look at the National Curriculum which sets out clearly what needs to be taught at each stage.
All that I have described is well known to any primary teacher and so it is worth explaining why it led to my children becoming advanced in their maths. My son went to school with rock solid foundations in place, he was not reliant on the teaching in his school. In schools the focus on understanding is too frequently at the expense of fluency. The focus in my son’s reception class was on learning in authentic environments. The intention was good but elaborate learning contexts or responding to the maths as it arises through play makes it hard to build learning systematically given that maths is relentlessly hierarchical. Such contexts can mean the child is distracted from the key learning intention of the activity and they get little practice for fluency as each activity is very time consuming. My son might do a handful of calculations a day at school. He would come home and do fifty, by year one he was quickly managing over 100 calculations at home . The extra focus on fluency and automaticity gave my son firm foundations as all subsiduary steps could be done without thought, leaving my son free to focus on the one new thing being learnt.
The real secret to all of this is very regular practice or the child forgets. I’d be one of those annoying smug type of people if I try and pretend my kids always wanted to do this work. I have been very dogged but it has really paid off. People assume requiring children to do work at home will put them off maths when it had the opposite effect. It actually made my children enjoy school maths because it was easy. Maths is tough when you don’t have the fluency and automaticity. Try long division or multiplying fractions when you are not fluent in your tables! I could have left my children to discover maths was ‘hard’ at school, like it had been for me. Instead I made it easy for them.
I have already outlined some useful general tips and in my next post I will talk about how I taught reading.