A wrong answer is the most useful thing in the room

When a student gets a question wrong, two things happen. The first is automatic and unhelpful: a small flinch, an apology, a hand moving to cover the page. The second is the one I care about: somewhere in that wrong answer is exactly the misconception holding them back — written down, in their own hand, for free.

Mistakes are sorted, not random

Almost every wrong answer falls into one of three buckets:

1. Arithmetic slip — the method was right, a number went astray. Annoying, low priority. We fix it with neatness and a quick check, not more theory.
2. Method gap — they reached for the wrong tool. This is a teaching signal: the map of "when do I use what" has a hole in it.
3. Concept fault — they believe something untrue about how the world works. This is gold. Find it once and a dozen future questions unlock.

Telling these apart is most of the work. A parent sees "got it wrong." I see which kind of wrong — and that tells me what to do next.

A worked example

A student computes the acceleration of a $2\ \text{kg}$ block pushed with $10\ \text{N}$ and writes $a = 20\ \text{m/s}^2$. The instinct is to say "wrong, try again." Instead:

They multiplied where they should have divided. That's not a physics fault — it's a sign they're pattern-matching on "$F = ma$" without holding onto what each letter does. So we don't re-teach Newton's second law. We slow down on rearranging one equation until the division feels inevitable.

The habit I want them to keep

Don't erase a wrong answer until you know why it was wrong.

That single rule turns a test from a verdict into a study guide. The students who internalise it stop fearing red ink — because every mark is just the next thing to learn, pointed to with an arrow.