How many past papers should my child do?

It is one of the most common questions in 11 plus preparation, and one of the few with a genuinely useful answer.

How many past papers should we be doing?

The answer is that the number is not what decides it. Here is the arithmetic that shows why, and you can run it on the last paper sitting on your kitchen table.

Do the sum on your own child's last paper

A typical paper is forty questions.

Say your child scored 80%. That is a good score, and most parents would be pleased with it. It also means:

• Thirty-two questions confirmed something you already knew. Your child could do them. You suspected as much. Now you are certain.
• Eight questions hold every mark that is actually available.

Now do another paper. You will get another thirty-two confirmations and another handful of lost marks — and unless something changed in between, they will tend to be the same kinds of question.

That is the whole problem with counting papers. More papers give you more of the part you already had.

And the better your child is, the worse this gets

This is the part that catches out the families working hardest.

A child scoring 50% is getting a paper that is half useful. A child scoring 90% is getting a paper that is one-tenth useful. The stronger the child, the smaller the share of each paper that tells you anything you did not know before you started.

So the family doing a paper a week with a capable child — the ones being most diligent about it — are the ones getting the least back per paper. Nobody is doing anything wrong. It is just how the arithmetic falls.

The thing a score cannot tell you

Say those eight lost marks were spread over decimals, measurement and a couple of word problems.

The score says 32 out of 40. It does not say which eight, and far more importantly it does not say why — and why is the part that decides whether it happens again.

Because those eight can be eight completely different situations:

• The child has never properly met that content.
• The child can do it perfectly when it is asked plainly, and cannot spot it when it is buried inside a longer question.
• The child can do all of it and was rushing by that point in the paper.
• The child did the maths correctly and answered a slightly different question from the one asked.

Four different causes. Four completely different things to do about them — and every one of them looks identical on the score sheet. They look identical in the mark column too. A cross is a cross.

This is why "he got 32 out of 40, we'll do another one" so often produces 32 out of 40 again. The second paper does not know anything the first one did not, so it asks the same child the same kinds of question and gets the same answer.

So what is a paper actually for?

A paper is for finding. It is very good at that, and there is no substitute for it — you cannot aim at a gap nobody has located.

A paper is not for fixing. Nothing about sitting forty questions teaches anything; it measures. Expecting papers to fix what they find is the single commonest way a whole term of work produces no movement at all.

So the honest answer to "how many past papers?" is:

Enough to find the problem. Then stop counting papers and start working on what you found.

For most families that is far fewer papers than they are currently doing, and considerably more attention paid to each one.

What "working on what you found" looks like

Not another forty questions. Eight questions on the one thing that keeps costing marks — the same mistake, asked several different ways, so it cannot be got right by luck or by remembering the last one.

And then, crucially, asked again later. A mistake put right in October and never revisited is not fixed; it is unobserved. The whole reason it was worth finding is that things fade, and they fade quietly.

That is a short piece of work compared with a paper, and it is the part that actually moves a score.

When another paper is the right call

To be fair to papers, there are two moments when doing one is exactly right:

• At the start, to find out where you actually are rather than where you assume you are.
• After real work has been done on what the last one found, to see whether it held up under exam conditions. That is the only honest test of whether something is fixed, because doing eight questions on a topic you have just been told about is not the same as meeting it cold, in the middle of a paper, against a clock.

What is rarely the right call is a paper because it is Saturday.

The one number worth watching

Not how many papers your child has done.

How many of the mistakes those papers found have actually been dealt with.

A family who has sat three papers and closed most of what they found is in a far stronger position than a family who has sat fifteen and closed none — and the second family has worked considerably harder to get there.

That is the whole of it. Papers find; they do not fix. Count the things you have fixed instead.