# Tag Info

61

The evidence says no What research I'm aware of is all about how giving any overall data about their own performance is actively harmful in promoting further learning. They learn considerably more from instruction about what to do differently in the absence of a grade or numerical score. To repeat; individual scores discourage learning! (Explanations for ...

48

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 into determinant ones is, generally speaking, the point. If the professor had some other solution in mind, then they made a mistake. They should have chosen a ...

43

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 justifies this by differentiating $\sin(x^2)$. In fact, this solution demonstrates deeper understanding of the meaning of these symbols than the variable ...

41

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 if the base were constant the answer would be $x^x\log x$, so she added the two together to get $x^x+x^x\log x$. I was just about to mark the answer as wrong, ...

32

Students are used to other people being the source of truth. Even in an algebra class, they will do something (incorrect, at least in the common context) like this: $(x + 3)^2 = x^2 + 9$ and then ask me if it is correct, or if it actually goes a different way. The implication is that I know the truth and they cannot know it without me. My goal then ...

30

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 not-so-great answers look like?

20

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:

18

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 to students why using the integral of tan, which they happen to know, is off limits, while using other integrals they know is allowed, other than as a detailed ...

16

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 take off points for this student's answer. Just to be clear, this isn't because I'm being somehow lax or generous as a grader. My opinion is that this is a ...

16

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 main objective is just a completion grade (or something fast like an overall plus/check/minus grade), this should be sufficient. I would argue against ever doing ...

15

One technique which is fairly obvious, but (at least for some of us) surprisingly difficult to implement consistently, is to just model for them in class what you expect them to write on their own. When I solve a problem in class, I try to show the same work and write the same explanations that I expect them to show. I also try to talk about it as I do it, ...

15

The part of this question that raises red flags for me is the line: However, many timesit [sic] is good to have a wide spread of grades. Why? This seems backward reasoning to me wherein you know the distribution of grades that you want to give and are figuring out how to design the test to fit that distribution. Your assessment should be criterion ...

14

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 discuss three different kinds of computation errors (i.e. not including logical errors, wrong proofs, etc.). The given error in your image falls in the third ...

13

You wrote: My problem is that I ... end up giving too good of grades at the beginning, and then face the task of either trying to lower their grades by being much tougher or not fulfilling departmental expectations. My advice is that, as a practical matter, things turn out much better when one is tougher in the beginning of a course, easing off if ...

13

Since you remark that your question is "deliberately non-specific," here is a (necessarily) incomplete response: First are two links to documents about assessment that might be of interest, and then two grading schemes that I have encountered in mathematics courses. Documents: As far as the philosophy of creating examinations, early work on this was done ...

13

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-arbitrary, even if clear, rules set down by the teacher, or whether there is an underlying reality, and best-practices, etc. Some of the "rule" nonsense can be ...

12

Make clear that the "make sure the proof is correct" is part of the work to be done in the homework. If it is my proof, or yours, or from <famous textbook> that is wrong, the answer is wrong. (Yes, need to emphasize that even the above cited authorities get it wrong sometimes).

12

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 (a), make a rubric (either in advance or a running one as you go) which lays out the criteria for awarding points. This allows you to be consistent with how ...

12

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 college, certainly -- the one department is, by definition, where all the experts in that subject work. To some degree this actually is done in places, in the ...

11

By recommending some book you implicitly acknowledge all of its contents (unless specified otherwise). In fact it would be similar if the student used a solution you presented, which happens to be wrong, but you only discovered the flaw when grading the exam. What would you do? First, I would not penalize the student for copying the solution from the book, ...

11

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 pettiness of the mistake, and so on.) If the student gets a wrong answer, checks it and sees that it is wrong, and notes this in his answer or work, I do not remove ...

11

For multiple choice questions it is much better to ask in a slightly different way, namely Are the following numbers even? yes no 1.) O O 17 2.) O O 22 3.) O O 33 4.) O O 42 5.) O O 57 6.) O O 61 7.) O O 49 8.) O O 99 9.) O O 13 10.) O O 30 The advantage is, that you explicitly open the ...

11

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 sends a mixed signal, so most of the time small proofs get either zero, one-third, two-third or full credit. Basically I try to give one-third credit when the ...

11

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 is to assess mastery of basic knowledge covered in the course. If one uses a more powerful outside theorem, then the steps that they've skipped likely ...

11

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 the two. So if you aren't expecting proofs written in sentences with all proofs eventually going back to epsilon-delta definitions, then you should accept ...

10

Why do so few professors assign extra credit? In my experience, the attitude towards extra credit is consistent throughout the department. Nearly every professor in the education department at my university puts extra credit questions on the test, but only a few in the math department do. After chatting with other students and professors, this seems to be ...

10

The math classroom standard "show your work" is really just a version of "communicate your reasoning" or "explain yourself", required in any profession. We sometimes do a disservice by implying that math classes have a special show-your-work requirement that is somehow not used in other disciplines. I do model this communication in my own writing in ...

10

This is my interpretation of your question: The student in my above grading example achieved the correct answer, and therefore feels cheated at losing points for the extra (incorrect) simplification. Should we be sympathetic to the student's complaint and give full credit, excusing the extra work done? My Best Argument Against Taking Off a Point If you ...

10

Students tend to only pay attention to feedback that affects their grade. In your example, where the student calculates the height of the door to be 0.0001 inches, showing no sign of realizing that the answer is impossible, I would give a zero on the problem. If the student writes, "Hmm...obviously this is wrong, but I've run out of time to track down the ...

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