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52 votes
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Grading a limit problem

The student changed something which was indeterminate ($\infty-\infty$) into something which was not ($\infty\cdot \infty$). How does that not merit a perfect score? Changing indeterminate expressions ...
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  • 4,771
49 votes

Interesting things you learned while grading?

I once asked students to find the derivative of $x^x$ (with respect to $x$). One student figured that if the exponent were a constant then the answer would be $xx^{x-1}$ which is to say $x^x$, while ...
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43 votes
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Intergration by differentiating will get you $0$ marks - but how to explain why?

Your student should get full marks. In fact, I would say that even a more complicated example, like $$\int 2x\cos(x^2) dx = \sin(x^2) + C$$ should be awarded full points as long as the student ...
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34 votes
Accepted

How should I grade true-or-false questions if the student's writing is unclear?

I read them as TTTFT. But the fourth is very hard to tell, the first somewhat hard to tell, and all show poor writing, perhaps indicating a lack of engagement. You could tell him that such terrible ...
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  • 356
33 votes

Grading a limit problem

If this is calc I, that deserves a 5/5. If this is analysis, it depends on what you taught them. Don't you set up a grading rubric ahead of time? What do the 5 point answers look like? What do other ...
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29 votes

What is the right feedback for incorrect cancellation?

My feedback might be more like this: When you are not 100% sure that a step works, try it with numbers. If x=2, does your expression keep the same value before and after your cancellation? Also, you ...
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21 votes
Accepted

Do you have an efficient way to view student responses to remote assignments allowing them to type math symbols and steps? (Middle + High school)

In a Google doc, one can "Insert/Equation" (marked by $\pi^2$). Then tiny pull-down menus appear in a top bar: Using these menus, I just typed this nonsense:      
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18 votes

Intergration by differentiating will get you $0$ marks - but how to explain why?

I agree with the other post that you should give full credit unless there were clear directions saying what would and wouldn't be acceptable approaches. I think it would be very, very hard to convey ...
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18 votes

Grading a limit problem

Instead of arguing with other people's answers in the comments I thought it might be more productive to present my own point of view. I find myself completely unable to understand why anyone would ...
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  • 7,940
16 votes

Do you have an efficient way to view student responses to remote assignments allowing them to type math symbols and steps? (Middle + High school)

Consider to just review scanned or photographed handwritten homework. Yes, this is not as easy as looking at typed work, but consider: would you require typed work normally? So why now? If your ...
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  • 235
16 votes

Interesting things you learned while grading?

Possibly not what you're looking for, but: the things I've learned while grading are mostly pedagogical, not new mathematical facts (in fact, teaching at a community college as I do, I'm not sure that'...
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16 votes
Accepted

What should I do if students did very poorly in the mid-term exam?

In the past, I've identified the problems on the final exam that review exam 1 material and offered to use them in place of the original exam 1 grade, provided this improves students' grades and they ...
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14 votes
Accepted

How much credit to give a short exam question with one error?

I'll try to make this answer a little more general than just telling how many points I would give for this particular error (if interested: I'd give 5/10 at most, most likely less). For that, let's ...
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  • 1,286
13 votes

Intergration by differentiating will get you $0$ marks - but how to explain why?

A bit too long for a legit comment... I think a very important question in the background here is that of whether we want to teach students that "correct" math involves primarily adherence to somewhat-...
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  • 13.6k
13 votes
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Separating the roles of "teacher" and "assessor"

A question that occurs with a project like this (broader than one department, as you put it) would be: Who is qualified to make those assessments? Probably not any other department at a particular ...
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13 votes

How do you handle the frustration of having to GRADE student exams / homework?

I have found that, for myself, implementing standards based grading has eliminated this frustration entirely. I now find grading to be enjoyable. I have a collection of standards for my course like &...
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12 votes
Accepted

As a TA, how to reduce imprecise notations/statements in students' exams

Let me echo Benjamin's comment that any proactive step that you take should be done with the instructor's permission. At a practical level, I think there are ways to address issues (a) and (b). For (...
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12 votes

Interesting things you learned while grading?

Reading the answer posted by Daniel R Collins reminded me of something else I learned while marking student work. Not exactly something mathematical, more something about constructing math exams. I ...
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12 votes

What is the right feedback for incorrect cancellation?

I tell my students that they can only cancel factors, and tell them to factor the numerator and denominator (to remind them what a factor is).
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  • 2,119
11 votes

A Method to Grade a Multiple Statement or True and False Question

For multiple choice questions it is much better to ask in a slightly different way, namely ...
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  • 2,932
11 votes

How to award points for sense-making at the end of a problem?

In my grading scheme, any answer that is wrong, checkable, and not checked gets $1/4$ off the partial credit. (I give partial credit for work shown, depending on how much knowledge is shown, the ...
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  • 2,504
11 votes
Accepted

How do you assign a grade to a proof?

In France we barely have intro-to-proof courses, but we ask for proofs in other courses. Usually, each proof has little granularity in the grading, and I tend to avoid giving half the points which ...
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11 votes

How should I deal well-known versus the obvious rubric?

Quoted from the first part of my answer on https://academia.stackexchange.com/questions/80898/should-a-student-be-penalized-for-using-a-theorem-outside-of-the-curriculum/: ... the point of an exam ...
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11 votes

Grading a limit problem

Calculus classes are taught at an 18th century standard of rigor, and analysis classes at a 20th century standard of rigor. It doesn't make much sense to try to invent some arbitrary combination of ...
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11 votes

What is the right feedback for incorrect cancellation?

What is the correct student-understandable feedback for the first two errors? [emphasis added] I am not sure there exists a singular answer to this. Ideally, the educational trajectory should have ...
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  • 534
10 votes

Grading homework problems on completion vs. correctness, and overall grading

There's a compromise between "correctness" and "completion" called "Standards-based grading". Here's a few links about it with various people who have tried using it for Calculus: http://blogs.cofc....
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  • 1,960
10 votes

Grading a limit problem

The answer seems ok to me, in that it shows that the student understands what the limiting behavior of $x - \sqrt{x}$ is as $x \to \infty$. If the questioner wants to see a formal justification of ...
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  • 5,113
10 votes

Making solutions to all problems freely available

This is an opinion, but perhaps worth sharing: When I assign that I expect students (particularly lower division students, such as those in calculus or precalculus classes) to do on their own time, I ...
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