This post is strictly for educators and parents with children who hate maths. No esoteric stuff this time…
When I was a teacher, for some reason I always used to be given the top set for maths – year after year. (I’m not going to get into the ‘Is streaming children for maths a good idea?’ debate, by the way; just saying that’s the way it was.)
Well I enjoyed working with the school’s brightest and best very much, but then one year, the head teacher told me he’d like me to work with the lowest set. That got me really excited!
I always loved a challenge. I spent most of the summer holidays pouring through the finished maths books of my new group, trying to work out why a bunch of hard-working and well-intentioned 10 and 11 year olds had apparently failed to understand the very basics of number, while their classmates had made such excellent progress.
Finally, I had it. There was one simple step that this group of youngsters had somehow missed – and this was the key that would help them to understand. It goes something like this:
In English, we have 26 letters: a b c d e f g h i j k l m n o p q r s t u v w x y z which we use to make words.
The words can be one or more letters long: a my box daft every garden quickly unlikely difficult…
In maths, we have 9 digits: 1 2 3 4 5 6 7 8 9 and one gap-filler 0 which we use to make numbers.
The numbers can be one or more digits long: 3 27 154 2013 53196 100481…
So how was I to get that message across to a bunch of kids who by now were approaching some kind of number phobia? They were happy to work with numbers up to about 20. From 40 onwards they got somewhat panicky, and if a teacher tried to introduce three- or four-digit numbers, they’d start shaking and ask to go to the toilet.
My solution was to give each child an abacus. The ones in educational catalogues were hugely expensive, coloured to appeal to 3 year olds and far too big to fit on their tables. I paced around the local shopping centre for a while and ended up with a couple of packs of self-hardening clay, a bargain tub of those little fusible plastic beads and a stiff yard broom. The bristles made sturdy but flexible and non-dangerous abacus sticks. I set four of them into a little strip of clay and cut them off at exactly the height of 9 beads. That way, the children would be able to make the numbers 1 to 9 on the ‘unit’ stick, but would be forced to take them off and start again on the ‘tens’ stick when they wanted to show the number 10.
The picture shows how I now make them for individual students, using a loop of wire, with beads safely trapped into the abacus. There are, of course, only 9 beads on each wire.
We spent many days ‘building’ numbers from 1 to 99 on the abacuses and writing down the equivalent number. Suddenly the 4 in 46 was understood as ‘four tens’ and the purpose of the zero in 20 was clear.
I insisted that they were forbidden to use the other two sticks, until they were completely begging me to allow them to make ‘hundreds numbers’.
“Nah,” I grinned. “You don’t like big numbers, remember?”
“We do!” they insisted. “We can manage it, We promise. It’ll be easy!”
“Well, if you’re sure…” I said, looking suitably doubtful and working hard to suppress a triumphant grin.
Within weeks, these children were working confidently with three- and four-digit numbers; not just building and writing them, but using them in calculations.
The next stage was to turn the abacuses round and use them to show decimals. Instead of labelling our four sticks as Thousands, Hundreds, Tens and Units, we now had Units, Tenths, Hundredths and Thousandths. There was a clear decimal point marked between the whole numbers and the decimals and I showed them how, in this looking-glass world, zeros had to be used as gap-markers from the left, not the right. Otherwise, they were in familiar territory.
By the end of term, the class was happily creating numbers to four decimal places, and comments like, “I get maths now!” and even, “Actually, I LIKE maths!” were heard around the room.
Now, to my great delight, I’ve been asked to work with Simeon: 14 years old, great at English, clueless at numbers. Here we go again!