11 plus tutoring: finding gaps without re-teaching the topic

You taught ratio in October. It went well — you could see it going in, the questions at the end were right, the homework came back fine.

It is now December. How much of it is still there, and for which student?

Every tutor knows the honest answer is "I find out when it comes up again." And by then it is usually in something else — a percentages question that quietly needs it, or a mock where the marks are gone and there is no time left to ask why.

The divergence starts in the lesson itself

Two students sit the same hour. Both are paying attention. Both understand it.

One walks out completely secure on sharing an amount in a ratio and quietly shaky on working back from one part to the whole. The other has both on the day, and six weeks later has lost one of them.

Neither of those is a failure of teaching, and it is worth saying plainly because the instinct is to take it personally. It is what learning does. Two brains, one explanation, two different sets of hooks — and the divergence widens with every week that passes.

The difficulty is not that it happens. It is that nothing in the ordinary run of a week is designed to notice.

Why the lesson cannot be where you find out

The obvious answer — go back over it — runs into five separate walls, and the fifth is the one that defeats a tutor who is willing to ignore the first four.

There is a curriculum to get through. An hour spent on October is an hour not spent on what is next, and the exam date does not move.

Re-covering a topic to find two gaps is expensive. Most of what you would go over is already secure. You spend an hour to locate ten minutes of problem.

The student resists it. "We've already done this." A student who believes a topic is finished brings less to the second pass than they brought to the first, so the hour is worse as well as redundant.

And the parent notices. If a topic reappears, it is reasonable for them to ask why they are paying for it a second time. That question is not unfair, and having to answer it is corrosive.

And then the fifth: going back over it does not actually reveal the gap. To establish that a student can do one part of a topic and not another, those parts have to be asked separately — and you have to know in advance which ones to ask. That is not teaching. It is measurement, and it wants a different instrument.

What the measurement has to do to be worth anything

A single question tells you almost nothing. Right could be knowledge, a guess, or a half-memory. Wrong could be a gap, a misread, or a rush.

One wrong answer is an incident. The same wrong answer three times is a habit — and only the second one changes what you would teach.

So every skill on one of our topic papers is asked more than once, each time in a different form — the same mathematics in different clothes. Which of them goes wrong is the finding, and it separates three students who score exactly the same:

• One cannot do it yet. That is a teaching job.
• One can do the mathematics but cannot spot when it is wanted. A different lesson entirely, and it is not more practice.
• One knows it perfectly and is rushing. A third thing again.

Those three are indistinguishable on a score, and each wants a different hour from you.

What arrives on your desk

One page, for one topic. What is secure, what has gone, and the specific slip behind each thing that went — not "ratio: 68%" but "takes the fraction of the remainder rather than the original amount, three times out of three."

The lesson then starts at the problem. No warm-up over ground that is fine, no fishing, no re-teaching a topic on the off-chance. It is the difference between an hour of teaching and an hour of diagnosis followed by ten minutes of teaching.

It is also, bluntly, easier to justify. A parent who has seen the page knows exactly what the next lesson is for.

And it asks again later

Finding the gap once is half a job. Whether the fix held is the other half.

A skill that has gone right is quietly re-asked after a week. If it holds, after a month. Then three months, then six — the gap widening each time it survives, because something that has held for a term does not need checking every fortnight.

This is the part almost nothing does. A topic gets taught, gets checked once, gets marked as done. Eight weeks later it has gone, and nothing is watching. It surfaces in a mock the following summer looking like a new weakness rather than an old one that was never really closed.

Yes, the student has to sit something

We would rather say so than pretend otherwise.

To tell you what a student knows and does not know, we need evidence. Anything claiming to find gaps without testing for them is guessing, and you would be right not to trust it.

What we have done is keep it small. One topic, forty-five questions, sat on screen in the student's own time. It comes in three shorter parts so it need not be one long sitting, and it marks itself the moment they finish. Nothing for you or the parent to mark, and no lesson time spent on it at all.

Where this leaves you

Families come to SillyMaths themselves, one child at a time, and the parent sets it up — there is nothing for you to administer and no lesson time spent on it. What reaches you is the page: what is secure, what has gone, and the slip behind each thing that went.

If that is the thing your lessons have been missing, tell us how you work — how many students, which exams, and what would actually be useful on that page. A person reads every note, and it shapes what gets built next.

You teach it. We find what didn't stick.