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Sunday, 13 February, 2000, 00:24 GMT
Back to school for parents

Some parents have been worried that the way maths is now taught in England is different to the way they were taught it - so they might "get it wrong" and confuse their children when trying to help with homework.

Loudwater Combined School in Buckinghamshire arranged an evening to explain the current thinking. BBC News Online's education editor, Gary Eason, found it useful - and fun.

Did you know that in the nine times table, the two digits making up all the numbers involved add up to nine?

9 18 27 36 45 54 63 72 81 90. Remember that, and you'll know immediately that 9 x 7, for instance, could not be, say, 64.

But I'll come to back times tables and (my favourite) "chunking". We started with addition and OK I'll admit it: I got the first sum wrong.

A simple bit of mental arithmetic: 23 + 24. Easy, I thought, jotting down the answer - 45.

Well, I'm sure she said 23 + 22. Anyway that's what I saw in my mind's eye - and that was the point of the exercise - not to find out how daft we were but how we had approached the problem.

A quick check of the few dozen parents present soon revealed four or five different mental strategies for doing even such a simple sum.

Expanding

The strategy children are most likely to be taught for simple two-digit addition is the so-called "expanded method" - break the sum down.

 Maths Year 2000 aims to improve everyone's maths
So 27 + 58 becomes 7 + 8 = 15 and 20 + 50 = 70. Add up the two results and you have the total, 85.

It works for bigger numbers, obviously, and has the advantage that there will be no "carrying forward" of numbers greater than 10 between each stage of the calculation - as there is in the final stage or "standard method" we were all familiar with.

This was novel for many of us but straightforward. More brain-hurting was the method of subtracting by adding up - known as "counting on".

To find out 43 - 19, start with the 19 and add 1 to make 20 - jot that down. Then add 20 to make 40. Note that. Then add 3 to make the 43. Total counted on = 24, which is the difference you were looking for.

To begin with this is done horizontally, using a "number line" with the 19 at one end and the 43 at the other, and drawing jumps from one stage to the next along a line.

Next is a vertical version of the same, with the numbers in columns.

Decomposing

The final stage is again the standard method - but using "decomposition", which is what they call it when you move a number from one column to the column on its right because the number there was not big enough to be taken away from.

It is what most of us used to call "borrowing". That is now a banned word. Instead you "exchange" say one 10 for 10 units - preserving the value of the numbers.

Multiplication. The country numeracy adviser brought in for the session, Clare Tope, began wielding a big stick. Literally. One way to get the children to concentrate...

The stick in various forms is a popular tool in the new strategy. It is marked off into typically 10 equal segments and the teacher sticks on numbers written on card for whatever times table is on the agenda.

The halfway point is a very important reference mark - and we learned that children throughout their maths work are taught to think about halves and doubles of numbers, as a quick way of getting around, as it were.

But: 10 segments? Times tables went up to 12 at least in my day. Nobody bothers much now. No point, with metrication and decimal currency...

This was where we played around with the number 9 and I suddenly had a glimpse of the simple fun that could be had with numbers. Getting that across to children is important.

Baffling

I confess I found the next bit hard - it is difficult to deconstruct a method you have been using for many years, to try to see through the eyes of someone for whom all this numbers business is initially baffling.

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Hence: grids for multiplication. To multiply 67 x 3, for example, you make a grid that multiplies 60 by 3 then 7 by 3 and add up the two results.

Again it works for bigger numbers, too.

And so to "chunking".

If we had 100 Smarties - we did - and seven plates - there they are on the front table - we could work out equal divisions by putting one on each plate in turn, rather like dealing cards.

It works! But it's very tedious... So a better strategy is to put, say, 10 at a time on each plate and see how we get on.

This is chunking. If you write it down, you get division done by subtraction.

For example, 256 / 7. Guess by taking away 20 sevens to begin with, or 140 - easy to do. That leaves 116. Next try another 10 of them: 70, so there's 46 left.

If the children are up on their tables, they'll know that 6 x 7 is 42. Add up the 20, the 10 and the 6 ... 36.

So 256 / 7 is 36 with 4 left over - "remainder 4".

Decimals and fractions

Ahah: remainders! I had completely forgotten that they existed. In fact they don't, of course: the innocently convenient world of remainders is short-lived, and decimals and fractions soon cloud the scene.

At the end of the session I think we all felt we realised where we might mislead our children or - worse - confuse them.

The headteacher, Kathryn Spring, still recalls having a blazing row with her father (also a teacher) saying: "I'm a mathematician and this is the way you do it!" as she protested: "It's not the way we do it at school!"

Reviewing my worksheet from the evening, I find some of it hard to grasp - the grids more complicated than just doing the long multiplication, for instance.

But the aim is to make the maths transparent to the children. Not just drill it into them that 'this is how you do it' but demonstrate why it is that the arithmetic works.

As Ms Tope put it: "Lights have been dawning all over the county."

To which one mother at the end of the row added: "Can I just say, as someone who hated maths at school, lights have been coming on over here, too."

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