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As a maths tutor, when I set tests (past papers in particular), if a student does poorly (~50/60% or below), obviously some topics need to be retaught. But should I make them do the exact same test - closed book again? I think this generally is a good idea in these situations because then they will revise harder on the questions they got wrong and will learn from those mistakes. I do this myself if I did badly in a test and it definitely helps. I guess we should go through the questions they got wrong first before setting the test again.

The student might see this as punishment though. What are your thoughts?

If they get $70$% or above then we just go through the few questions they got wrong, and those people are generally smart enough to improve on some of the questions they got wrong. Maybe I should get these students to gen up on/revise these questions and then set timed tests - but the test consists only of questions they got wrong - later on as homework?

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    $\begingroup$ It seems to me that this strategy would lead the student to become very good at the problems you put on that particular examination, but not necessarily very good at other problems. This seems like a bad idea to me. $\endgroup$
    – Xander Henderson ♦
    Commented Oct 3, 2022 at 12:43
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    $\begingroup$ Timed tests are problematic. $\endgroup$
    – Sue VanHattum ♦
    Commented Oct 3, 2022 at 15:38
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    $\begingroup$ @SueVanHattum "Timed tests are problematic". But the students have to prepare for their GCSE's/ A Levels. Preparing at first without a time limit is fine, but at some point it has to be introduced otherwise they will have no feel for their time limit in their exams. $\endgroup$
    – Adam Rubinson
    Commented Oct 3, 2022 at 16:04

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I advise to go for it with a small tweak. Instead of doing 100% the same, make it equivalent problems (VERY SIMILAR), but slightly different numbers, formulas. It's worth doing if they 100% missed a basic concept.

The one experience like this I had was in AP Chem where entire class got crushed on a unit in descriptive chemistry (sources of the elements), since all the students were primed for the heavily algebraic problems in stoichiometry, equilibrium, etc. and basically just didn't grok that they needed to memorize some things and answer essay questions (e.g. describe the Bessemer process). When we did the retake, teach said it would be very similar (was), but she varied all the questions except one. But the fundamental thing was a corrective aspect for a major part of the course and even for a mindset about "what we have to learn".

Let students keep the higher of the two tests. (If they crush it, roll with it and let them have a bone.)

And I would not make this an every time type thing. Just with a real trainwreck where you think the vast majority, didn't get a basic important module. Maybe every 3 years or so. Not twice in a class. [You should at least be able to advise next years classes to "watch out".]

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Either that or changing some questions slightly (for example question A has "x=5 and y=3x" then change it to something else). Because, personally, the way you said might just turn them instead a bit "lazy" when facing hard questions since they can always just go back and solve them.

*Although this means more work for you, so...

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