Questions that reveal an explanation

A correct answer leaves several possibilities

A learner answers that one half is larger than one third. The answer may come from understanding equal wholes, remembering a familiar fact, or guessing. Asking why gives more information. Asking whether one half of a small cake exceeds one third of a much larger cake tests whether the equal-whole condition is understood. Good diagnostic questions make different explanations predict different responses.

Begin with an accessible case. Invite the learner to draw, speak, write or manipulate objects, according to the target knowledge and their communication needs. A language barrier or unfamiliar notation can obscure understanding. The aim is to gather evidence about reasoning, not to create extra obstacles that merely reduce the score.

Use a question sequence

A useful sequence moves from an answer to a reason, then to a changed case. Ask what will happen, why it should happen, and what would change the prediction. A comparison question can be especially informative: how are these two situations alike and different in the feature that matters? Asking for the reason behind a choice is often more useful than asking whether the learner is sure.

Avoid embedding the explanation in the question. "Since the denominator counts equal parts, is a third smaller?" supplies the very relationship you wanted to observe. A neutral question such as "Show what each fraction represents" leaves room for the learner’s own model. After diagnosis, teaching prompts can supply support; the purposes should be clear.

Interpret a pattern, not a label

An incorrect answer can result from a missing concept, a calculation slip, misunderstood wording or inattention. Ask the learner to retrace the relevant step. A stable misconception is more plausible when a coherent but incorrect explanation predicts a pattern across cases. One error is insufficient evidence for a deep theory about how the learner thinks.

Record the explanation in specific language. "Treats a larger denominator as a larger fraction when the whole is fixed" guides the next lesson. "Bad at fractions" does not. Use a new case after teaching to see whether reasoning changes. Diagnosis becomes useful when it selects an explanation, representation or practice opportunity that addresses the demonstrated gap.

Worked example

Try it yourself

Think through each question before opening the answer.

1. Rewrite "Do you understand evaporation?" as a diagnostic question.

   Show the answer and reasoning

   Ask, "A wet cloth dries in a closed room without boiling. Where did the water go, and why?" The response requires an explanation rather than a yes or no.

   The wet-cloth question asks for a location and mechanism of water transfer without supplying boiling as a necessary condition. The response exposes reasoning that a yes/no confidence report would leave hidden.

2. A learner gives the wrong numerical result but a sound diagram. What should you inspect?

   Show the answer and reasoning

   Inspect the calculation and how quantities were read before concluding that the concept is missing. Different errors need different support.

   A diagram may preserve the quantity relationship while arithmetic or reading goes wrong. Inspect that step so a calculation slip does not receive an unsupported conceptual diagnosis.

3. Why use a changed case after instruction?

   Show the answer and reasoning

   It tests whether the learner can use the revised relationship when the original answer is unavailable as a memory cue.

   The changed case makes the relationship do new work. Explaining it provides evidence beyond remembering the corrected answer to the original case.

What to carry forward

• Ask for the reason that generates an answer.
• Use multiple cases and accessible response formats before diagnosing.