How to teach ... subtraction

In the second of our series, Karen Gold talks to three teachers with positive attitudes to a negative concept
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The Independent Online
Ginny Copley,

Reception class teacher (4- to 5-year-olds),

Steeple Morden Primary School,

Hertfordshire

At different times we've created a pavement cafe, a pet shop, a building site, a doctor's surgery. For the surgery we had a notice up saying only five people in the waiting-room at one time, so they had to work out if there were too many, and how many had to go away.

The nurses had a sign up saying they needed two stethoscopes and three bandages, so the children had to keep checking the equipment on the table. And the plasters - the whole class was covered in plasters. The maths we got out of that: how many people, how many plasters ... it was fun and they remember it.

This term our theme is machines and we are making a giant number-crunching machine out of a huge box, which we are going to decorate with dials and slots. The children have to sign in at the work station; then they'll work in pairs with A3 number cards. They'll each choose a number up to 10; then one will choose a sign for adding or subtracting and the other has to find the answer.

To do that they have to know about "more" and "less", which we've been working on a lot. You use the different vocabulary - "less than", "take away", "subtract" - so they get to associate the word with what they do. We'll do it in songs and nursery rhymes, in activities like bead threading, cooking - even taking the register; there are 29 in the class and after the register we'll talk about how many people are away and how many are here.

To introduce the subtraction sign I make a cross with my two pointing fingers - that's addition - and then I take away the one that's pointing to the ceiling. I show them that I've taken away something, and I say the sign that's left means taking away.

From the minute they come in they are doing subtraction without realising it. Some get it on the first go, so you take them to the next stage, perhaps giving them a program on the computer. With others you have to find the right thing, and the penny drops.

A few parents come into consultations and say, "We are concerned that they haven't come home with a page of sums". But I tell them the children are getting the concepts, we are laying the foundations, and they are doing practical taking away all the time.

Jean Willgoose,

Kumon twice-weekly after-school maths instructor (4- to 24-year-olds),

Stapleford Methodist Church Hall,

Nottingham

I taught juniors for 20 years and I always believed in the basics and in repetition, but Kumon has been a revelation. Kumon spends hundreds of worksheets on addition: there are 80 pages of worksheets just practising adding one. It staggered me, but the idea is that if your addition skills are excellent, you can do everything else. And it works. If you know that 17 + 4 = 21, then you don't have any problem taking 4 away from 21.

By the time the students get to subtraction, you can see them doing "decomposition" ("carrying" between columns) without actually writing the figures in. They do subtracting one, subtracting two, and soon get into the swing of it.

After horizontal subtraction they get vertical addition and subtraction, and you can see they suddenly feel as though they're doing real sums. I always worry at that point, because a lot of them come to Kumon because they are having trouble. But they work through it, and the repetition is like water on a stone.

When I give them the first sheet of subtraction I always wait to see if they can do it: I never introduce a subject beforehand, because it's a self-learning system. I'd always set something new for the class and not for homework, though. I'll watch, and as soon as the pencil goes in the mouth or they start struggling I'll be there.

They have to do all their corrections - I'm very strict about that - as soon as each sheet is marked. I have markers now, because I've gone from two students to 54 in 20 months. Their scores and times are recorded so I know exactly what they can do and what is a problem. They are all at different stages, but mostly they'll do about 10 sheets in the 20-30 minutes they're with me, plus some every day at home.

The difficult sums are always the ones with a zero on top, because you can't take away from zero. One of the harder sheets has 503-248 and there's that zero in the middle.

What makes subtraction hard is that philosophically addition is positive and subtraction is negative. You have to see subtraction as reversed addition. If they can do that, and they've got the mental agility that comes from doing a little work every day, then you don't have to teach at all. You just feed them the right sheets.

Enid Edwards,

Year Two class teacher (6- to 7-year olds),

St Chad's Primary School, Leeds

Most days we do maths for about an hour, because they need to keep the rhythm going, especially if they have learnt a new concept. We do a maths scheme and we do work which is linked with our topic.

When we did autumn they had a tree with 20 leaves and they had to work out how many leaves were left if 14 fell off. At Christmas they had to work out how many would be left in a box of 12 crackers if they pulled one every day for 10 days. We'll do sums like that on sheets, or I'll write them on the board. The workbooks do the same kind of things; they might have to do sums on little tickets, for example. It's all to make it interesting .

All Year Two children do subtraction, but if they're finding it difficult, I'll get them to use real things to take away, and the less bright ones only do subtraction of numbers up to 10. The really advanced ones are doing tens and units using decomposition. When I started teaching we borrowed from the bottom, now it's from the top - I think it's easier for the children to see what's happening.

They find it hard at first. I tend to do it with a small group while the others are doing something they can get on with, or when I've got a helper. We'll do it with fixing blocks, so they can see that you can exchange a block of 10 for 10 single ones. You find you do it for one lesson and they say they've got it, and they come back the next day and it's as if you'd never taught it. But after a few days it sinks in.

I wouldn't just give them a page of sums. If I was introducing something new, to check if they'd got it or not, I'd put half a dozen on the board. A whole page would outface them at first. I suppose people could say we are only doing dressed-up sums, but we're trying to motivate children.

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