Compare several solutions to the same problem

Copy the problem conditions and identify the required result. Give each approach a separate space and ask its author to mark the first meaningful decision.

Present a problem solvable by drawing a figure or by setting up an equation. Give space in the written record for a correction beyond the final answer. Show the starting point, the change and the part of the original work you still trust. A short labelled correction can prompt better review than a clean page that hides both the earlier difficulty and the reason it was repaired.

Both approaches may describe the same relationship in different forms. Return to the revised material after a short interval and attempt a comparable task without opening the earlier answer. Keep the dates and the conditions of each attempt. A small series of records makes it possible to see whether the change improved recall, understanding or the ability to apply what was learned.

Look for steps that use a special property or require a tedious calculation. Ask whether the method would still work if the starting values changed.

A drawing with reassuring proportions can conceal a boundary case. Write one expected explanation and one common incomplete version before the review begins. This helps you spot when a learner gives a correct short answer without the connection that matters. Ask for one additional sentence that shows how they reached it, then use that sentence to shape the next practice item.

Ask each solver to explain how they would handle a closely related case with a changed value. Keep the first response visible after revising it. Seeing a repair next to the original answer helps locate the point of confusion and gives a second attempt a precise aim. Use a different colour, a side note, or a separate copy if erasing the original would remove that evidence.

Match the decision in one solution with the corresponding step in the other. Attach the feedback to a specific output rather than to a general judgement of performance. Record which part the learner could repair immediately and which part depended on a fresh explanation. The distinction helps you plan practice that addresses a real gap without unnecessarily rehearsing everything around it.

The second activity should feel recognisably related without calling for the same response. Keep the essential concept and replace the example, order or wording. If a method works only with the original arrangement, the new result gives you a direct clue about the understanding still to develop. Let the learner mark the place where they changed course and write one reason for it. Give them time to find their own words before supplying the expected language. A correct final answer is useful, but the explanation helps show whether they can take the same kind of decision in a fresh example under ordinary conditions. Show both worked approaches under identical problem conditions. An alternative method loses value as a comparison if somebody silently solves an easier version. Give the activity a clear output, such as a sentence, a worked step or a marked drawing. That output supplies a record you can compare with the material. A vague feeling of confidence can be hard to assess after a delay, particularly when the subject begins to look familiar through repetition alone.

Choose one changed condition and test two methods on it before closing the session. Give the learner enough context to recognise the type of question without giving away the answer. A prompt that depends on one memorable word in its heading can become too easy to recognise over time. Change the wording once and use the response to see whether the reasoning still connects to the same idea.