A mistake is a clue, not shame · البرمجة مع مارتن

A wrong answer shows you exactly where to look. Who rubs a mistake out throws the clue away.

A mistake is a clue. A detective does not rub it out.

A detective finds a clue in the mud. What do they do? Swear and stamp on it? No. They kneel down and read: whose shoe, which way, how old the clue is.

A wrong answer in maths is exactly that kind of clue. It tells you where your method broke. If you rub it out, you throw away the most valuable information you have.

At school a mistake is often treated as shame. Red pen, minus a mark, face in the desk. Not here. Here a mistake is working material.

There is a catch: you can only read a mistake you can see. So we start the first rule of the course: a wrong calculation is not rubbed out. You cross it with one thin line — so it stays readable — and you count again next to it.

Sounds weird? In a few weeks you will have a notebook full of crossed-out calculations. And you will read it like a detective.

Tereza counts 7 + 8 and writes 13. She looks at the answer at the back of the textbook: it should be 15. She reaches for the rubber. “Stop!” Jonáš cuts in. “First look at what happened.”

Tereza looks at her writing: she counted 7 + 8 as 7 + 7, that is 14… but she wrote 13, because she already slipped on the double. And then she forgot to add the extra one. Two clues in one question! “See,” says Jonáš, “the rubber would wipe all of that. Now you know exactly what to train: doubles.”

💡

Cross a wrong calculation with one thin line and count next to it. In this course the rubber is for drawing, not for mistakes.

How to read a mistake: three steps

When you get a wrong answer, first take a breath. Then go by three steps.

Step 1: find the break. Go through your method line by line and at each one ask: does this still hold? Somewhere you hit the first line that does not hold. That is the break. Everything before it is fine — you do not have to count that again.

Step 2: name the kind of mistake. Most mistakes belong in three drawers. Counting mistake — you slipped in the counting itself, like 7 + 7 = 13. نسخing mistake — a number changed on the way, 52 became 25. Method mistake — you used the wrong step, like plus instead of minus.

Step 3: one similar question. Do not recount the same one over and over. Make up or find one similar one and solve it. That checks the mistake is fixed, not just covered up.

In time you will see that your mistakes repeat. That is great news: a repeated mistake is one mistake, not ten. Fix it once and it disappears everywhere.

Example 1: a clue in subtraction

Jonáš counts 52 − 27 and gets 35. The check says the right answer is 25. Where is the clue?

He goes through the method: he counted the ones as 7 − 2 = 5. Aha! He flipped them — he took the bigger digit minus the smaller, even though 7 belongs on the bottom. A classic method mistake.

Right: you cannot take 7 from 2, so he borrows a ten. From 52 he makes 40 and 12. Ones: 12 − 7 = 5. Tens: 40 − 20 = 20. Together 20 + 5 = 25.

Jonáš writes next to the question: “Watch borrowing.” Clue read.

Example 2: a neighbour mistake

Tereza writes 6 × 7 = 36. Right is 42. What happened?

36 is 6 × 6. In her head Tereza reached into the next-door box — she mixed up neighbours in the times table. That is a counting mistake, and a famous one: almost everyone mixes up neighbours.

Fix with a method: 6 × 7 is six sevens. 7 + 7 = 14, that is two. 14 + 14 = 28, that is four. 28 + 14 = 42, that is six. Tereza writes six times seven on a slip — exactly this one link needs extra training, not the whole times table.

⚠️

The worst thing you can do with a mistake is rub it out and write the right answer copied from somewhere else. It looks tidy — and next time you make the same mistake again, because you never read it.

Practice: now you do it 🎲

Now try it for real. You will see all the questions at once, like on paper. البداية with ten. When it goes well, add more.

Count slowly. When you slip, read the clue, do not rub it out.

Practise the questions

On paper: hunt your own clues

You will need an old maths notebook or a marked test. If you have nothing, ask a parent to write you five questions, and count fast on purpose — some clue will show up.

Find one of your old mistakes. Do not fix it yet — first read it: on which line did the method break?
الاسم the drawer: counting mistake, copying mistake, or method mistake? Write it next to it.
Solve one similar question next to it, this time slowly and with a method.
البداية a page at the back of your notebook called “My clues”. Write today’s catch in one sentence, for example: “I flip the ones when I subtract.”

Now you 💪

I can say the three steps of reading a mistake: find the break, name the drawer, solve a similar question.
I cross a wrong calculation with a thin line, I do not rub it out.
I have a My clues page in my notebook and the first note is on it.

✅

Done when: You have read one of your mistakes, named its drawer, and started a My clues page.

What to take from this lesson

A mistake is a clue that says exactly where to look.
Do not rub out — cross with a thin line and count next to it.
Three drawers of mistakes: counting, copying, method mistake.
Check a fixed mistake with one similar question.
A repeated mistake is one mistake. Fix it once, it disappears everywhere.