One item per prerequisite — so a wrong answer names the gap

Asked to build a diagnostic before a lesson, the base model tends to write a general quiz about the topic: ten questions that sample the target skill itself, mix several sub-skills inside each question, vary wildly in difficulty, and hand back a total — "7 out of 10." A total score tells you a student is somewhere below the bar. It does not tell you what to reteach. Two students who both score 4/10 can be missing completely different things, and a score can't distinguish them.

The discipline: a diagnostic pre-test is not a small exam — it is a set of probes, one per prerequisite, each built so that missing exactly that prerequisite is the only thing that can make it wrong. The output is a map of which building blocks are present and which are missing, not a number.

The four moves

1. Work backward to the prerequisite list. Start from the target lesson and ask: what must a

learner already be able to do to succeed at this? List those enabling skills. This is not "topics related to the subject" — it is the specific earlier competencies the new skill is built on. For "add fractions with unlike denominators": find a common denominator, build equivalent fractions, add like fractions, simplify. Each is a separate prerequisite. That list defines the test.

1. One isolating item per prerequisite. Write exactly one question per prerequisite, and strip

each question down so the only thing that can make it wrong is that one prerequisite. If a student gets it wrong, you must be able to say which single skill they lack. Target each item at the threshold of "can they do this or not," not at hard or easy extremes — you're detecting presence, not ranking mastery.

1. No confounded items. An item that requires two prerequisites at once is diagnostically dead: a

wrong answer could come from either, and you can't tell which. Before keeping an item, ask "if a student misses this, is there exactly one skill I'd blame?" If the honest answer is "could be A or B," split it into two items or simplify it until only one skill is in play. Reject any item that also silently requires the target skill you haven't taught yet — that measures the lesson, not readiness for it.

1. Report a gap map, not a score. Score each item as its prerequisite passed or failed, then

report the list of missing prerequisites — the reteaching worklist. "Missing: common denominators and simplifying; has: equivalent fractions and adding like fractions" is the deliverable. A total like "6/8" throws away the one thing the test was built to find.

Worked example

Target lesson: solving two-step linear equations (like 3x + 4 = 19).

Prerequisites, each with one isolating probe:

| Prerequisite | Isolating item | What a wrong answer means | |---|---|---| | Add/subtract integers incl. negatives | 19 − 4 = ? | Can't do signed subtraction | | Multiply/divide integers | 15 ÷ 3 = ? | Can't do the division step | | Inverse operations (undo +/−) | "What undoes add 4?" | Doesn't grasp inverses | | Order of operations | "In 3x + 4, which happens to x first, ×3 or +4?" | Order confusion |

Note what's absent: no item is 3x + 4 = 19 itself. That would need every prerequisite at once — a wrong answer would be uninterpretable, and it tests the lesson you're about to teach. Each probe isolates one skill so the result is a clean gap list, not a blurry score.

Checklist before you hand it over

• ] Prerequisites derived by working backward from the target, not by topic-sampling.
• ] Exactly one item per prerequisite; the test is as short as the prerequisite list.
• ] Each item fails for exactly one identifiable skill — no compound items, none requiring the

untaught target skill.

• ] Output is a per-prerequisite pass/fail gap map (what to reteach), not a total score.