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53 votes
Accepted

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 ...
  • 4,869
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 ...
43 votes
Accepted

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 ...
41 votes

What value is there in requiring students to answer word problems in complete sentences?

Yes, there is mathematical pedagogical value in the usage of complete sentences - but this does not only refer to "answers" and not only to "word problems", but to all parts of the ...
37 votes

What value is there in requiring students to answer word problems in complete sentences?

I do think there is value in expecting students to give answers in correct English. It will certainly help when they start to face longer and less structured questions. However, the example you give ...
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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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 ...
  • 18.7k
30 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 ...
  • 18.7k
23 votes

What value is there in requiring students to answer word problems in complete sentences?

An example of a problem where phrasing the answer as a sentence might prevent mistakes and encourage understanding is: Alice goes to the store with \$2.00. A gumball costs \$0.80. How many gumballs ...
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:      
20 votes

Point Deductions - Exams and Quizzes

I favor an additive grading scheme, where points are earned toward a possible maximum (say 10) instead of deducting points for the myriad possible mistakes one could make. Here, I would try to adopt a ...
  • 8,328
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 ...
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 ...
  • 8,019
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 ...
  • 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'...
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 ...
  • 3,553
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 ...
  • 1,288
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-...
  • 13.8k
13 votes
Accepted

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 ...
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 &...
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 (...
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 ...
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).
  • 3,553
12 votes

When is the best time to return a graded assessment?

Return at the beginning and go over it then. Any in class drill should wait for the finish of q and a on the papers. Avoid parallel processing. You are leading a large group, not an individual. ...
12 votes

What value is there in requiring students to answer word problems in complete sentences?

Jochen's answer is very good. To add to it, here's the reasoning I was given as a student: answering in full sentences makes students think about the answer in different psychological context. This ...
12 votes

Point Deductions - Exams and Quizzes

I advise being less intricate and put less load on the graders. I personally would go with all, half or zero credit for every question. *All is correct answer (and some reasonable explication, not an ...
  • 199
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 ...
  • 2,962
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 ...
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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