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I am marking tests and a student wrote down 64 instead of -64 for one of the questions. This obviously changed the entire question and they would have gotten full marks otherwise, (i.e. all their steps are correct). They also did really well on the rest of the test. I do not know how much I should penalize them since full marks on this question would give them 87%, and anything lower would be an <85% mark. Even half marks would drop their mark to as low as 60%. How many marks would you penalize them?

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    Where does the 64 value come from? Was it a constant to be memorized? In the question? A result? Jan 14, 2021 at 18:37
  • @AzorAhai-him- The value -64 was written down incorrectly as 64, which was the remainder. It was a constant given in the question and to be used in the steps to get the correct answer. Jan 14, 2021 at 18:45
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    An anecdote (perhaps not much help for you): Andy [Gleason] was the reader for my undergraduate thesis on [math]. In those days (perhaps still) each senior was set a special exam on the thesis topic. One question on mine asked me to apply my theorems to [mathe]. But my answer seemed not to need [what happened at x=1]. When I asked Andy later about that, he gently pointed out how he’d carefully constructed the question so that [what happened at x=1 mattered]. I missed that, because when finding the critical points I calculated 2×3=12. He graciously said only that I’d spoiled a good problem. Jan 14, 2021 at 18:53
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    I often wrote something like "below the radar" and gave full credit if the error was something entirely unrelated to what was being tested and the error provided no essential simplification of the task. Jan 14, 2021 at 19:48
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Marks are a measurement of how well the student knows the subject. So it depends on how much of a lack of knowledge that mistake represents:

  • in most cases, if all steps are correct and only a number was copied wrongly, then obviously the knowledge of the subject is very good, and most of the question was done correctly, so "almost full marks" are deserved

  • if the mistake shows lack of knowledge (for example, if that "-64" is a value of power, which can only be positive, or if it leads to an obviously unphysical result that the student should have noticed), then one might remove more marks.

  • a tricky case is if the mistake leads to the problem being much easier to solve (e. g. "Write the last 10 digits of 2^(64+x)"), and it is correctly solved. In this case, it would be unfair to give full marks, as the student did not show much knowledge of the subject. Unfortunately, this should probably result in no marks.

It seems like your case falls in the first category, so I would see no reason to give anything less than "the highest mark that is not a full mark".

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    Marks are not just about knowledge. They are also a measure of the mastery of the tools used. Correctly keeping track of numbers is one of the key skills in some areas and may thus be part of the grading considerations. Jan 14, 2021 at 23:47
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    @user2705196: Correctly keeping track of numbers is one of the key skills in some areas – It is much less so nowadays, where you usually deal with so many numbers that you need computers to take care of them anyway. Also, consider that the skill you would be actually measuring is keeping track of numbers under stress and time pressure, which is quite different from what is relevant for almost any practical application.
    – Wrzlprmft
    Jan 15, 2021 at 6:39
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    @user2705196 keeping track of numbers can of course be part of the grading considerations. But if keeping track of numbers under time pressure is worth 25% of the exam's score (as the question suggests), then that course does not seem to have any interesting content.
    – wimi
    Jan 15, 2021 at 8:31
  • Yes, of course what you write makes sense and thus requires some trade-off as you suggest and is appropriate for your learning objectives. My comment was in response to the blanket statement "Marks are a measurement of how well the student knows the subject." which I don't believe is true. Jan 15, 2021 at 12:18
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Whatever it says in your pre-written markscheme. If you don't have one, the UK GCSE one is a fairly reasonable starting point:

Misread or miscopy

Students often copy values from a question incorrectly. If the examiner thinks that the student has made a genuine misread, then only the accuracy marks (A or B marks), up to a maximum of 2 marks are penalised. The method marks can still be awarded.

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The short answer is, unless the rubric clearly lays out which kinds of errors merit which level of deduction, it is up to you. I would strongly encourage you to discuss this with whoever is supervising you in this role, as they may have expectations which have not been communicated clearly to you.

Grading, especially without a clear rubric, eventually relies on the judgment of the person doing it to decide "how important is this to the course? Did they miss anything important because of the minor calculation error?" In many of the courses I took as an undergraduate, the rubric was a simple 5-point scale (though you could choose to use 7, 3, 29, or whatever number you like). Roughly speaking, they marked:

5- Perfect or with minimal errors which have at most cosmetic impact on the problem. For instance, if a student mis-copied a matrix or used the wrong value in a calculation, a generous grader might still award 4.5 or 5 points. 4- Minor computational errors. Some graders will use this to remind students to pay attention by docking a small proportion of points. Others will only use it if there is course-relevant content involved but might not dock points for a student misreading their own handwriting. 3- Major computational errors. If a student made multiple computation mistakes or a severe enough error to make their answer one which a reasonable person could have known was wrong (and did not indicate this) then they might only earn 3/5. 2- Partial conceptual failure. If a student got part of the question right but couldn't finish the job due to a mistake which demonstrated some kind of misapprehension of the course content or misapplication of techniques, but still did meaningful work towards a solution, 2 points. 1- Minimal progress. If a student made a small amount of progress towards a solution but then went into the weeds, they might earn a point. 0- No progress towards a workable solution.

The fairness-based reason that you might knock off 20-25% of the score for that question (or whatever the minimum relevant unit might be) is that if a student makes that type of error on every problem then they do not deserve the same level of credit as a student who meticulously checks their work. If it was possible for the student to verify their answer and they chose not to do so or if they should have known that their copying had failed them, I might mark off an additional point for that reason (because that serves a valid pedagogical purpose: if you could have checked your work but didn't, you missed an opportunity to make up the points).

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