A misconception library: the wrong answers you author on purpose

A misconception library is an authored catalogue of the specific wrong ideas learners hold in a subject, stored as records a tutor matches against. Each record names one faulty rule, lists the answers that reveal it, and carries the response that addresses that rule rather than the topic around it. It is content, written by subject teachers, and it lives beside the course material rather than inside a prompt.

The distinction worth building for is between an error and a misconception. An error is one wrong answer. A misconception is a rule the learner applies faithfully, which happens to be wrong, and which keeps recurring.

The same wrong answer, with and without a name for it

A tutor that knows only that an answer is incorrect has two moves: try again, or here is the topic explained. A matched entry gives it a third.

Nothing on the right is cleverer language. It is the same tutor with one extra fact: which wrong rule produced this answer. A model inferring that fresh every turn is less consistent than a record written by somebody who has marked four hundred of them.

A tutor that only knows an answer is wrong can reteach. A tutor that knows which wrong idea produced it can argue with the idea.

One entry, field by field

Triggers decide whether the library is usable in software. "Gets decimals wrong" cannot be matched; "picks the option with the most digits after the point" can, because it names a testable property of the answer. Whether the response leads with a worked line or a question belongs to worked examples or problem practice.

Growing the set from answers you already have

The practice comes from diagnostic questioning: items written so each wrong option corresponds to a known way of thinking rather than random error. The library makes that reusable across the objective.

1. Pull real wrong answers. Every incorrect response on one objective from a term of marking, identifiers stripped first.
2. Cluster by what the learner appears to have done, not by how wrong the answer was. Answers far apart numerically often share a rule.
3. Write the faulty rule before the response. If it will not go into one sentence in the learner's voice, the cluster is a bucket.
4. Have two people tag the same 50 answers independently against the drafts. Disagreement means an ambiguous trigger.
5. Publish ten to fifteen entries, then watch the fire rate weekly. One that never matches is dead weight; one that matches everything is written too loosely.

Step four is the one teams skip and the one carrying most information. In production the question returns harder — whether the tutor's tagging matches what a subject expert would have chosen — and holding that honestly is set out in rater agreement when one rater is software.

What a catalogue of wrong ideas will not fix

It cannot separate a faulty rule from a careless slip, because both arrive as the same wrong answer. A learner who understands place value and mistypes will match a trigger and get a lecture about tenths — worse than the generic response. That check is the working is right and the arithmetic is wrong.

It also says nothing about how much help to give once the diagnosis exists. A tutor answering every match with a full explanation produces dependence that reads as engagement; when to withhold is argued in fading and when a tutor should stop helping. Nor does it supply the graduated prompts that follow, which are a hint ladder.

Built, this is small and content-shaped: a table, a matcher, an authoring screen the subject leads will open, and a weekly fire-rate report — the first slice we scope under MVP and product builds, within AI tutoring and learning support and our education work.

• tutoring
• misconceptions
• content design
• feedback