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Emailing professors: Guidelines on choosing papers
Barry Rountree, Computer Scientist, LLNL of Quora claims 80% hit rate for the following e-mail template: (I emphasize a phrase in bold.)

Here’s your email: Dear Dr. Q, I would like to schedule a meeting with you to discuss PhD opportunities, in particular extending your work described in your papers X and Y. I will be in town on the 25th of next month but could also meet late on the 24th or early on the 26th. My CV is attached. What would be a good time for us to meet? Sincerely, You

About the "your papers X and Y", I would like some guidelines please, such as which to include/exclude, how many to choose, the sort order and the formatting. I have a feeling this post may be voted to be closed as too broad, but I wouldn't know the specifics of the broadness until I actually I post.

Which papers should I include/exclude?

Can I include the papers of topics that interest me and exclude the papers of topics that don't?
Should I choose at least paper in each significant portion of research?
Some professors sort their publications by category rather than by date. Should I choose at least paper in each category?

Should I exclude/include a professor's papers on research topics that are not listed as a research interest in the university website, are listed in the selected publications but are not listed in the past 10 years of selected publications?
How many papers should I include?

Of course the answer doesn't have to be (only) quantitative. Could be qualitative for instance "Should be a good enough sample of all the professor's work (or "of the parts of the professor's work that interests you"): Enough to show you have read the professor's work but not too much as to make the professor think you just copied and pasted".

How should I sort the papers?

Descending order of my preference? Descending order of my familiarity with the topics involved? Dictionary order?
Most professors' papers are sorted by date, but one categorizes research into 5 topics and has selected publications for each. How could this reflect how I sort the papers?

Formatting question: How should I list them?

Can I just put the title with a link? Should I put a full citation? This is what I had in mind: (for the listing of the papers and not necessarily for the other parts)

Dear Dr. Q:
I would like to schedule a meeting with you to discuss PhD opportunities, in particular extending your work described in the following papers:

Mathematical finance paper
A paper on stochastic partial differential equations, a topic usually found in applied math, but is surprisingly super pure
On pure math with no hint of applied math

I will be in town on the 25th of next month but could also meet late on the 24th or early on the 26th. My CV is attached. What would be a good time for us to meet?
Sincerely, You

You can answer the above questions in general or my specific context as follows. In case the following makes my post too specific to my context or too broad, I am perfectly fine with removing the following. Anyway, I know stackexchange doesn't really provide career advice on very specific situations that wouldn't benefit others. I'm providing the following context, just in case.

I'm an expat applying to local pure math PhD programs with a master's and bachelor's in applied math. My top choices are probability/stochastics, differential equations and then analysis.
On pure math: I don't have any problems with topology, geometry, abstract algebra or number theory. I have self-studied some of them, like them, but I have never learned them in my classes.
On applied math: I have slight problems with applied math but can tolerate having to do some applied math such as in cases of scientific/numerical computation of PDEs. I'm not that interested in interdisciplinary research. I have very little interest in statistics and finance.
I wouldn't have this problem if I had a master's in pure math, but here we are.
This is my second round of local PhD applications. This time I'm also applying for a master's in pure math, based on the one professor who actually agreed to meet with me despite my stupid template to emailing professors (All of this is moot in the unlikely event that this professor actually finds my self-study sufficient enough that the professor would be willing to take me on as a PhD student)

For Q1:

My fear isn't something like the professor researches in complex analysis and topology, and then I don't like topology (which I do). Instead, my fear is that the professor's research is mainly pure or a significant portion is pure, but then also, a significant portion is applied.
Note the "significant" in the above paragraph. Obviously, I'm not worried about a professor who lists research interests as "main interest in functional analysis, complex differential equations, with a side interest in mathematical chemistry". Here, I have no problems leaving out the (1 or 2) mathematical chemistry papers.
This is particularly the case for those whose research is in probability/stochastics or differential equations, topics which I was told by a coursemate and confirm on Wikipedia, are apparently more for applied research.
Luckily, there are some professors in my area who research on differential equations in a pure way.
There's ONE who does probability/stochastics in a pure way, and the publications (not just the selected ones) reflect this: Less than 1/5 are about statistics or finance while the rest are on probability/stochastics and are the purest I could find in my area. The publications are sorted by date and not by category, but I'm still worried there might be some risk in leaving out the statistics or finance papers.

For Q2: This could go both ways.

If a pure math professor has significantly researched applied math but not done so in the past 10 years, do I have to include the applied math papers?
If an applied math professor has significantly researched pure math but not done so in the past 10 years do I have to exclude the pure math papers?

An example for Q2:

There's a professor in my area who, based on selected publications, was apparently researching a lot of topology, functional analysis, complex analysis, differential equations (in a pure way) and algebra up to 2008 but then for the past 10 years has researched on mathematical finance.
The university has listed interests to be "PDE, control, applications in stability and quantitative finance", but on the professor's page under "research", the professor declares, in third person, (I paraphrase) to be interested in everything but, because of time and economic constraints, restricts to topics some of which are to be deduced from the list that follows.
Then there's a link to selected publications, arranged by date and of the last 10 papers, 9 are in mathematical finance. The most recent paper is technically applied math but mostly in a pure way and has no finance. My initial thought is to include the 10th paper, include the purest of the 9 mathematical finance papers but to choose the remaining papers from the papers more than 9 years old (the pure math papers).

I've never used this template, and also find the phrasing more fitting for an established researcher than an incoming student. That said, what's your goal here? If it's just to get a meeting, maybe try to pick the two papers that interest the professor the most - which is likely somewhat skewed towards the more recent works. If it's to get a PhD position with an advisor and topic you like, and would enjoy working on for ~5 years, why not pick out papers you're interested in?

@NajibIdrissi (tears of joy and gratitude) I thought my question would be stupid. Thank you so so much for your reply! Do you then disagree with Barry Rountree about the extolling part in this paragraph: "...applicant...spends most of their email extolling their GPA and classes taken..." I have a feeling Barry Rountree would extend this to self-study and research and would advise to not mention GPA, classes, self-study or research and to save those for attached CV or upcoming interview.

@Anyon (tears of joy and gratitude) I thought my question would be stupid. Thank you so so much for your reply! Do you then disagree with Barry Rountree about the extolling part in this paragraph: "...applicant...spends most of their email extolling their GPA and classes taken..." I have a feeling Barry Rountree would extend this to self-study and research and would advise to not mention GPA, classes, self-study or research and to save those for attached CV or upcoming interview.

@Anyon About the non-interested papers (or non-interested areas of research hahaha), I was thinking the professor might think of me as not having looked him or her up well enough.

@corey979 Thanks! Well, it's a just a template. Barry Rountree might say we might do a little personal touch but to still keep it as short. For example, for pure math professors, I just briefly mention that I'm "now looking to pursue research more in pure maths". Actually, isn't mentioning the professor's research papers in itself a personal touch?

I find "What would be a good time for us to meet?" somewhat presumptuous.  It hasn't been established that the professor is even willing to meet yet, and this language makes an "out" tougher to word.

Sorry, I haven't read the whole question, but only up to the subquesitons 1.-5. and here is my answer to 1.-4.:
You should exactly list the papers for which you are keen and have ideas to "extend the work of the professor".
Honestly. The professor will notice, and get bored or even angry when they note that you are not really interested in what you wrote or even do not any idea what the papers are about exactly or how to extend the work.
For subquestion 5.: It doesn't matter much. The title is enough, a link to some obscure website where one can download the paper may not be good.

I'll assume the risk of the professor getting bored or angry is worse than the risk of being seen as not having looked up the professor enough, @Dirk. Thank you!

I don't know, but what I wanted to say way: Do write the email honest and not because you found some template. If you are really interested and have ideas, then go for it. If not, let it be.

Relieved. Follow-up: A professor therefore does not necessarily expect their PhD students to be working on all the research topics listed in the research interests, and it could be that a PhD student will mainly research in only some of the professor's research interests? I mean, of course it depends on the professor, but the point it's possible and therefore, it's okay for potential PhD students to exclude papers in professor's research interests that don't match the research interests of the potential PhD student?

"exactly list the papers" What if I'm genuinely interested in 15 of them?

…**and** have ideas to extend the work….

"exactly list the papers" What if I'm genuinely interested and have ideas to extend the work in 13 of them? (This is pure math. I'm not too worried. Cameron Williams: "pure mathematics operates at a level that is not very accessible for most undergraduates, even those doing research")

@JackBauer - Don't make a catalog of the papers you're interested in, just cite a couple that you are excited about.  Write a concise email that will pique the person's interest in you.  It should be short but it should let some spark in you shine through.  You want the person to see something that makes him or her want to get to know you further.  A long letter to a stranger will be an annoyance.


text:
Why would a European-style professor want a Ph.D student instead of a research staff? What are the advantages and disadvantages?
Related to my questions:

How much knowledge is expected of a PhD applicant as compared to a postdoc or a research assistant?
For the average pure math US PhD program, what are essential topics after basics topics of complex analysis, abstract algebra and topology?

The question from quora Why would a professor want a Ph.D student instead of a research staff? What are the advantages and disadvantages? is answered mostly by US or US-style professors. I would like to know the European or European-style take on this.
My ultimate goal is to understand Country A (see here or here) which seems European-style. You can go on about how academia varies and how I won't gain much understanding, but please answer the question also.

Well, I'm a German professor in CS - my answer is biased by those facts. Some might be generalized, though. Some answers are based on German employment rules in the public sector and those will most likely be specific to Germany.
Usually, contracts in the public sector are either permanent (hooray!) or temporary positions. We have a law stating (simplified version) that you are not allowed to be employed more than 12 years in temporary contracts (if you want to know more look for the "Wissenschaftszeitvertragsgesetz" - we love those words!)
Another rule is, that for "permanent tasks" you should have a permanent position whilst for temporary / project-style jobs you can hire people in temporary positions.
To make things even more complicated: A university / department usually has both types of positions and can distribute them among researchers and central administration.
If the university does not have enough positions available, you have to acquire third party funding. This is by definition project related and therefore temporary.
This brings me to the following:

In general, I would love to have research staff - but resources are limited and usually you don't have too many available.
If I acquire third party funding, it is just available during the project duration - in good cases this is long enough for a PhD candidate to finish a PhD thesis (in the field of the project).
If the project ends without the PhD candidate being finished, I usually try to apply for a follow-up project which helps funding the candidate. Since I want successful PhDs afterwards, this is a top priority - and induces some stress on professors.
Yes, I could hire someone without intention to do a PhD or even a postdoc, but at least in CS industry is paying that much better, that the possible PhD is the only chance to motivate highly skilled people for this salary (which is ok, but less than in industry).
This brings me to the last point: Motivation! A PhD candidate is not only interested in the project but in his/her PhD as well. So they are usually quite motivated and it is more fun to work with motivated people.

Things are a bit different if you are in a graduate program, but most of what I wrote above still applies.
To add a few words on the comment of Monika:

At least in Germany you cannot fire a PhD student at any time since you are usually having a labour contract.
I agree that there might be strong tensions when a permanent position becomes available and it is open who might get it. But permanent positions in research are quite rare nowadays in Germany so it does not happen that often.

Added after OPs remark:
In fact the situation for postdocs is or less the same: Usually you don't have the funding to support a postdoc for a longer period of time. With this, it is questionable why a postdoc would like to work in such an environment. Doing a habilitation / postdoc-phase and preparing for a full professorship could be a very good motivation as well. The tasks for a postdoc are usually different from the ones for PhD candidates: As postdoc, you want to demonstrate that you are capable of running a group - which involves writing grants, guiding PhD candidates, involvement in teaching, etc. Depending on your field it allows you to do original independent research for the first time (e.g. in medicine in Germany). So if you are looking for such a person in your group, a postdoc is great, but usually most funding schemes are more hands on and so it is difficult to get funding for a postdoc, unless you are having very large funding schemes.

OBu thank you, but I think my question was somehow wrong. I meant to ask why get PhD students instead of seeking those who already have PhDs? This is in hopes to address the issue of motivation in the fourth bullet point.

I added a paragraph on postdocs... Thanks for the clarification!

Ah, so your part of the answer on postdocs is like Alexey B.'s answer except you give the reason why the source of funding may allow? My guess for that was legal obligations. As it turns out, it's to do with the size of the fund?

Problem 1 is the 12 year period for postdocs unless you can offer a permanent position, the other is the grant size. So the legal argument is still valid (and can be a major problem, e.g. when you've been in academia until you are close to 50 and you have to look for a job in industry then).

So the rationale for the legal obligation that the funding will go to PhD students is to avoid those kinds of 40-year olds?

Most fund are smaller an there is work to do which is not appropriate for a postdoc. The issue of those 40 year olds is more on the postdoc side. If there are good personal reasons to stay in academia, it's not up to me to influence this decision.

Because a particular source of funding may allow to only get a phd student.

Oh you mean some source will give funding for only PhD students therefore professors can afford and want to get research staff, but they are legally bound by the contract of the funding not to do so? Why exactly would a source do that? Is the source from government or something who hopes to produce more PhDs? I guess that would explain that Country A PhD Fellowship Scheme.

@JackBauer In a way. There are grants and funding schemes that are specifically meant for PhD students. Sometimes, it is the prof or department who "have" the money, but they don't get full control of the money and can only use it to pay stipend and tuition fees (if any) for a student of their choice. And sometimes it is the student who "has" the money, in which case it does not even remotely belong to the prof.

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How to work in a group where the group members need to be taught everything?
Edit: I met with the prof and she agreed that it wasn't my responsibility or place to teach my group mates the foundations they were supposed to have learned.  A direct quote was that "everyone has to fend for themselves."
There are several similar (and very helpful) questions which address some points of this question, but I feel this question is a bit different and thus merits being asked.
(1) How to handle team member who is unable/unwilling to collaborate
(2) How to handle a colleague who hasn't pulled their weight
(3) How to make group work work?
The first two questions do not apply because each of the collaborators wishes to contribute and not just ride the wave so-to-speak.  I attempted to follow some of the suggestions of the third question, but the group thought it was insulting.

add more structure to the group project. This increases the workload
  on your end but it mitigates the most common issues you'll see in
  groups during group projects.
Use and quality based hierarchy, assign the hard-working students as
  group leads.

I am in a group to complete an assignment.  The teammates are very willing to collaborate and work, but the problem is that they did not actually learn the course material when they were supposed to.  Therefore, they cannot actually help out without a significant amount of learning.
The group expects me to sit down with them for many hours (whole days) to teach them and collectively complete the assignment together.  I feel that this is far too much responsibility, effort, and time required on my part, since my teammates lack the skills to contribute because they were unsuccessful in keeping up with the course material.
How should I proceed?

You don't really have many options. As I see them:

You can talk to the instructor, explain the situation, and ask to move to another group
You can talk to the instructor, explain the situation, and ask to do the project individually
You can actually sit down and teach them

As far as which you should do, there are too many variable for us to answer here. However, it seems the best would be start with (1). If that fails, try (2). If that also fails, do (3) and try to find the pleasure in teaching others.

Thank you for this answer.  I did try 3 already, but the group wants several more days (8h/day).  It is not a pleasurable teaching experience because the group tells me how to solve the assignment and then I have to correct their approach, without actually taking any of my input.  Furthermore, I have been told it's my fault and responsibility if the group doesn't complete the assignment.  If I were teaching an actual course, perhaps that would be fair.  But I am just another group member.

Depending upon how far along you are with the schedule, i.e. how much time is left, asking the instructor to move you to another group, including perhaps a group of one, seems to be the only way to avoid the teaching task.

If a professor truly relies on group work, or if it is common or necessary to a field, then it is the professor's responsibility to teach students how to do it. That doesn't help you, of course, if the prof is avoiding this responsibility.
But, it is a common misconception among unskilled students that "group work" means dividing up the work equally (what ever that means) and then combining the parts into a whole. This is both inefficient and ineffective.
In a group, different people can have different "roles". One can be a researcher, another a writer, another a manager. Roles can be shared and can overlap. More than one writer is good if they work together, not independently, sharing ideas. People should have a say in what their role should be, or at least their principle role. But not all jobs are glamorous and still need to get done.
In your case, you might consider taking on the role of manager and calling a lot of meetings and giving a lot of assignments. Assign someone to a task (What does Aristotle mean here, really?) and give someone else a role of assisting.  Have a lot of all hands meetings and some subgroup meetings. Let the work coalesce into a whole.
Imagine the opposite. Two of us want to write the next crime blockbuster novel. I'll write the odd numbered chapters and you write the evens and we'll work in parallel and then just smoosh it together. Or, I'll write the first half and you the last, working simultaneously. Yeah, that should work.
Teams means teamwork. Not all members of a sports team have the same role, of course.
But note that you aren't "teaching" but guiding. Teaching by example, perhaps.

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How should feedback be given for "silly mistakes" on an exam
I am a TA currently grading a set of 80 midterms for an engineering math course for fourth-year engineer undergrads. The test had four questions, each question had around four parts.
Of course, typically a student can make a wide variety of different types of errors on the exam. But what I have noticed in this exam is that some of these errors are not necessarily conceptual, yet we are basically taking all the points away for these "minor errors" (per instructor's grading scheme).
For instance,

For a question with several parts. A student copied one of his own
(correct) answers from the previous part incorrectly.
A student wrote down all the steps correctly, until the last step
where he had to evaluate the expression at a number and the mistake
was forgetting a negative sign.
After a long derivation, a student substitute formula incorrectly (forgot a square root in the formula, ahem, Gaussian). Everything else completely correct.

There was a litter of other minor errors. Now, these students are in their final year of engineering school, so I think I can give them the benefit of the doubt that they wouldn't make silly mistakes such as writing "0 - 1 = 1" or copy things down wrong in a non-time-constrained setting, which is the situation they will most likely face when they graduate and work in industry.
Is there a way to provide feedback for a student if he or she makes silly mistakes on the exam? I do not think that giving them a zero for writing a minus sign incorrectly is a good way of either providing feedback or preventing the same mistake from happening again in their (long) lives.

This is mainly at the teacher's choice, in practice. Some deduct, say, zero or 5% of the grade for a silly arithmetic mistake (which I recommend); some deduct much more --- to the limit of those who look at the final result only and deduct 100% if it doesn't match the official solution (which I don't recommend).
It may be difficult to give an objective evaluation because in some cases a mistake at the beginning can turn an exercise into a completely different one, much easier or harder. If there is more than one person grading, you should discuss it with the rest of the group.
As a mathematician, an interesting point to consider is that not all silly mistakes are equal. In some cases, a student should realize they have made a mistake with some sanity checks at the end. Examples: if you have shown that a certain event has probability -3.72 to happen, it is clear that there is something wrong. If your symmetric matrix has non-real eigenvalues, you should notice it (if you were taught that it is impossible). More subtly, the eigenvalues you have computed may fail the trace test (sum of eigenvalues = sum of diagonal entries of the matrix); a smart student would make that check at the end as well.
In my view, submitting an answer with mistakes that fail obvious sanity checks deserves a more substantial deduction: maybe student A and student B both flipped a sign, but while student A got a perfectly plausible solution, student B really should have realized that. It's part of their job to check that the solution they find is reasonable. Especially in this age when computers do most of the work in practice, noticing when a computed solution is patently wrong is arguably more important than computing it in the first place.

This is an interesting point, and it leads me to the idea that a well designed exam could include some specific critical thinking problems of the type "What's wrong with this picture?"  I'm actually starting to see that type of problem regularly in the New York State math curriculum ("EngageNY") for middle and high school, where the exam shows "Here's what Hani wrote in response to such-and-so problem; is his reasoning correct or not; explain your point of view."  I like the idea of separating this out for specific problems that focus on this, because (a) it helps students see...

... that critical thinking is important and should be practiced explicitly, and (b) it helps us deal in a positive way with test anxiety.  Test anxiety can lead a smart, capable, skilled student to turn in a certain amount of nonsense, which the next day that same student would see through in a heartbeat.  So when I look over an exam, I try to see the forest as well as the trees.  If a reasonable proportion of the work turned in on the exam shows solid skills and reasoning, I'm basically happy, even if there is an element of kwatsch -- to quote my German spouse.

It reminds me of an exam where we had to calculate the height of some filling in a column. The correct calculation lead to a filling higher than the containing column, meaning that the setup is not possible. Apparently, this was not done by mistake by the teachers - but since all of our practice questions were plausible, everybody was looking for problems in our their calculations...

First, notice that students will typically be able to tell which of their mistakes were silly and which more significant.  So for silly mistakes you don't need to write feedback other than to circle where they went wrong, and indicate the number of points taken off (or granted).
For a more serious mistake you can write more detailed feedback.  Sometimes feedback here isn't necessary, either, other than to write, "see solution."
Second, you can figure out what types of errors and what frequency of errors you want to bring the grade down from A to B, from A to C, etc., and decide how many points to remove based on that.
More importantly: what's a well written exam like?  Example: I'm asking them to solve this eigenvalue-eigenvector problem.  If the student has a vague idea what is being sought, I want him to get one point.  If he sets things up well but doesn't know what to do next, he gets two points.  If he follows through well but for whatever reason didn't quite get to the perfectly correct punch line, he'll get 3 points.  Perfect, complete answer: 4 points. (This is just an example of the point distribution.  You might end up with a different scoring structure.) In short, the scoring should be integral to the exam design from the beginning.
Most importantly: as a TA, you should be getting special guidance from the professor for grading a midterm exam.

I've used a different color ink to distinguish feedback which does not contribute to the grade this time but which might in the future. One of the general problems with an educational system which uses grades punitively as "feedback" is that completely non-punitive feedback is almost always ignored.

I believe I may be more severe in grading than some other instructors. I usually find so-called "silly" mistakes to be indicative of serious underlying issues, and I usually take off around 1/3 of the points for a whole problem. Here are two justifications:
One, this is part of the lesson: you simply can't afford "silly" mistakes. Especially in an engineering discipline, if you switch a sign or move a decimal point and fail to check for that, you'll wind up building a self-destructive and possibly life-threatening mechanism. See many stories of major projects (buildings, spacecraft, etc.) blowing up due to such errors.
Two, there is a question of efficient use of the instructor/grader's time. If there is a long problem and a "silly" mistake occurs near the first line, then it seems egregious to expect the grader to follow through a unique train of logic from faulty initial assumptions, in order to award partial credit. As an instructor, I tend to have a solution sheet and score up to the point where the logic goes off the rails, then stop. (If the other steps are absolutely self-evident, then more grade may be awarded, but this is not assured.) This way I can grade the tests for any one course section within an hour. If this labor is handed off to TA's who don't have authority to set their own protocols, then grading may wind up taking many hours, and this inefficiency may be hidden from the people with responsibility to manage the process.

See many stories of major projects (buildings, spacecraft, etc.) blowing up due to such errors. The life-threatening errors weren't the fault of arithmetic mistakes, which get made all the time. It's a subsequent chain of system failure that ultimately causes a catastrophe. Grade however you like, but please put this ridiculous straw man to rest.

But an exam's environment is very different from what engineers would be in. You're not required to rush as much. If you do, I put the blame on the company for these errors, rather than the individual who do these silly mistakes.

-1 1) I don't think this really answers the question 2) As others mentioned, in real-life there are procedures in place that should catch "silly" mistakes (reviews, tests, etc). If something goes wrong, those procedures should be blamed. 3) You not wanting to spend time grading an exam seems like a very poor reason to reduce points. I agree with Elizabeth, grade how you want (and a third off doesn't seem that unreasonable), but these seem like bad justifications.

@ElizabethHenning: You make a good point, but it seems a bit exaggerated to me.  I don't think review failures can be said to be the cause of the catastrophe to the exclusion of the initial error.  If the initial error is not to be considered as a cause/fault, how could any subsequent error consisting of a failure to detect it then be considered a cause/fault.

I'm surprised at all the downvotes this answer is getting.  It seems pretty irresponsible to me for academics to take the attitude that accuracy doesn't matter because review procedures should catch the errors.

The appropriate feedback on an error depends on how obvious it is to the student and how severe it is to the answer.  It is usual to penalise "silly mistakes" on examinations, both for diagnostic reasons and to create an incentive for students to improve their work.  In cases where there is annotated feedback, the degree of gentleness/harshness is generally calibrated by considering what stage of the degree the student is in, and the corresponding expectations.
For "silly errors" (spelling/grammar errors, calculation mistakes, transposition errors, copying errors, etc.) it is usually sufficient just to circle the error (I use red pen) to alert the student to the problem.  The error should be penalised appropriately, with consideration given to the totality of the question.  In most cases like this the student will be able to self-diagnose the error without any textual statement explaining it; they will see what they did wrong and why they lost marks, so there is no real need for an explanation.  For larger errors, or errors on more subtle aspects of the material, one might circle the error and then provide an accompanying textual explanation.  In some cases you might also annotate the number of marks that were lost for the error.
As to your proposal to give students the "benefit of the doubt", and avoid penalisation, that sounds silly to me.  Firstly, there is no "doubt" for which to give benefit --- they made an error and it should be penalised as such.  Secondly, marking examinations necessarily entails a judgment of work under time-constrained conditions; the mark is supposed to reflect the quality of the student's work on the exam, not your premonition of how they might do in practice if they were working without a time constraint.  And finally, because they are in their final year it is all the more important that they are becoming more accurate in their working and purging "silly errors" from their work.  Hell, some lecturers would probably go further than just circling errors at this final stage of the degree, and start writing some more blunt messages that alert them to the fact that it is unacceptable to make "silly" calculation errors in the profession --- "Wrong; your bridge just fell down and killed three people."
As one final point, if you mark work regularly, it is useful to make up some custom rubber stamps for common feedback you want to give on your exams.  When I mark assingments/exams I often penalise an initial error but then treat that error as a premise for the remainder of the question, so that even if the final answer is wrong, it doesn't get penalised a second time.  I have a little stamp made up that says "Error carries through: No further mark deducted" for this purpose.  I also sometimes point out an error that is too minor (or below the level of expectation for the course) to warrant a marking penalty.  I have another stamp that says "Error: No mark deducted" for this purpose.  This saves me getting carpel tunnel syndrome from writing the same things out over and over again on exams.

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The Ethics of Preparing for a Course Long Before Actually Taking it
I think this is an unspoken question in academia: how do you factor in the effort put forth by a student before taking your class?
I think  the answer to this question has several consequences:

it presents accurate reflection of your teaching,
it presents more accurate reflection of the quality of work of a student

It also addresses a more profound question:
Is good educational outcome measured by grades a product of privilege or a measure of intelligence?

Personal anecdote:
In my undergrad classes, I find for some courses the class will be divided into two camps - one who has done some work outside of the class (the ones who have a background), another who will try to learn the course material as the course progresses.
The results are vastly different. The ones who have done work outside of class will achieve higher grade across the board, are more motivated, ask extremely technical questions in classes, gets all the attention of the professor as the next "rising star", etc., whereas the other students who haven't had as much experience prior coming to class will try his/her hardest with uncertain outcomes and will tend to struggle a great deal more.
From my own observation, a course taught by a lecturer who uses less conventional course material seems to even out the grade much better than a lecturer who uses standard material - since in these cases, the advanced students are less able to predict what will show up on the exams.
This is most significant in computer science classes. Any computer, CS, programming classes will teach things in two folds: practical and theoretical. I find in many of my classes, a portion of the student will have a great deal of knowledge in the former, therefore significantly reducing his/her course load. How easy is it to ace an introduction to programming course if you already have years of experience in the language? These courses will always produce several students who go on doing interesting research or work at some big-name companies, and the lecturer will be praised as being effective at teaching. But it is so obvious to me, that the student - the one who has taken years of programming at middle to high school level, a summer course at another University... - is more advantaged in this area than a student who is just coming in to be acquainted with a field of study.
Hence, what is the ethics of preparing yourself for a course before it begins given such uneven playing field in today's academic setting? Will this be a mark of a motivated student who is genuinely interested to learn a subject or a student who is just trying to get ahead and earn good grades? Why should or shouldn't a student prepare himself for all the courses he will take one or two years down the road?

It sometimes is a matter of student background as well rather than his previous learning efforts.

The Ethics of Preparing for a Course Long Before Actually Taking it; I don't get, why it may be unethical.

Are you using "Ethics" in the sense of "dealing with right and wrong?" In other words, are you asking if it is right or wrong to prepare for a course long before actually taking it? If I've understood your question, then I think the answer is most certainly "no, it is not wrong." To say otherwise is tantamount to saying that it is wrong to learn outside of a class; at least, for anything that might possibly be learned in a "course" somewhere. Learning is a lifelong process that should be pursued both in and out of classrooms.

how do you factor in the effort put forth by a student before taking your class? — I don't.

Computer classes are very bad example. This field develops so fast that theory struggles to merely keep up with practice. Sadly it often leads to situations where teacher knows less than best students. Which rises hell lot of ethical questions by itself.

I get the gist of it, but the wording comes across as akin to "is stretching before exercising ethical?" ie it's not only not unethical, but it's optimal.  Main negative that comes to mind is if assigning a group project and the ahead-of-the-curve student takes control and does all the work while everybody else stands aside not knowing what's going on.

@EnthusiasticStudent: I think the ethical question relates to "Is good education outcome measured by grades ... a measure of intelligence?". If one says that it is, and if preparing for the course increases grades independent of intelligence, then it would be dishonest to both prepare and claim that it's a measure of intelligence (whatever that is). But when people assume that a person with good grades is necessarily more intelligent than one with bad grades, they commit a severe error, and it's not clear to me what worthwhile ethics can be built on a claim that they haven't ;-)

@SteveJessop So, it is better to rephrase the title of the question; because I don't think it is indicating that concept.

@EnthusiasticStudent: well, the title doesn't have to be the full question, but (assuming I'm right) I agree that the question could be clearer that the ethical issue relates to the notion that grades measure intelligence. Or aptitude at the subject; or likely ability with the subject if the student were to continue with it; or effort put into the course; or basically anything other than ability with the tasks examined, at the time examined. Grades don't measure any of those things, for all that people use grades to attempt to deduce other things based on what they think are correlations!

@EnthusiasticStudent It's not a perfect analogy of the question, but consider the similar case of a student whose first language is X taking the X-foreign language class at a Y-language university.  They'll probably do pretty well.  Is this an unethical way to increase their GPA?  If the whole class does this, is it unethical if the professor is recognized for teaching skill based on the fact that all the student did so well?

@JoshuaTaylor Studying beforehand, during the class and after having a class is completely ethical. There is nothing wrong/un-ethical with studying at all.

@EnthusiasticStudent That's absolutely right.  Taking a class when you're already completely familiar with the material might have unethical consequences, though.  The question mentions, for instance, "How easy is it to ace an introduction to C course if you already have years of experience in the language?"  Similarly, would be ethical for me (a native American English speaker) to enroll in "English as a Foreign Language" at a foreign university?

@JoshuaTaylor: for what it's worth, schools (by which I mean under-18 education) in the UK (and I imagine elsewhere, although I don't know) are assessed as far as is possible on their "value added" rather than their final results. If the same principle could somehow be applied to your X-language class packed with native X-speaking students, then the value added would be negligible since the students would all ace the intake exams :-) They might still learn a thing or two about the grammar of their own language, mind you.

@JoshuaTaylor When somebody attends a class, he wants to either learn something new (even he knows every thing about it) or have certificates of the course (for any personal/professional reason). Attending a class, learning something new, improving 90% of knowledge to 95% of it, etc; none of these are unethical.

@EnthusiasticStudent In principle, I agree with you.  However, in practice I think things are bit different, because classes don't exist in isolation.  For instance, one answer gives the example of taking 'advanced (or self-taught) students taking beginner-level courses for "easy credits"'.  What about the case of a professor encouraging (or requiring!) her students to take a class she's teaching, knowing that the students already know the material, but that their doing well in the class will reflect positively at a yearly performance review?

@JoshuaTaylor What about the case of a professor encouraging (or requiring!) her students to take a class she's teaching [...] This should be asked in separate question. But, back to the original question, I have seen professors who attend another professor's class just to improve their advanced knowledge. No problem and no ethical issue. Learning and attending classes have no ethical issue.

I studied S/360 Assembler Language before I even started at the college.  When it came to the assembly language course, they simply let me sit for the exam.  When I got to the end, I got up, handed in my paper, and left.  I didn't notice all the eyes on me of those who wondered who this person was who never showed up in class but finished the exam early.  (It was considered one of the hardest courses there.)  I only got two questions wrong, and those were only because they were worded ambiguously.

There is no question of ethics here.

IMO, there is no ethical problem with students preparing for a course in advance.  As Moriarty notes in their answer, what matters is that the student learns the material, not when or how they learn it.
That said, there are (at least) two actual problems that your question touches upon:

the occasional problem of advanced (or self-taught) students taking beginner-level courses for "easy credits", and
the practical problem of teaching a course for students with a highly variable baseline experience level.

The first one could be considered unethical behavior in some circumstances.  For example, let's say I'm a math major who decides to minor in biology, and the university happens to offer an "introductory math for biologists" course.  If I was unscrupulous enough, and nothing specifically forbade me from doing so, I might be able to take that course and basically just show up for the exam, getting free biology credits for stuff I learned in first-year math.
(In fact, I freely admit to having done something similar myself on occasion.  For example, one of the last courses I took as an undergrad, to make up the credits I needed to graduate, was a first-year "computer literacy" class that basically consisted of learning how to use a web browser, e-mail and a word processor.  As I had already completed a minor in computer science, as well as worked for several years as a full-time software developer, I hardly need to mention I did not find it much of a challenge.  Still, it got me the three extra credit points of "general studies" that I needed.)
It could also be argued that there is no problem: if you consider the credits to be awarded for knowing the material, then I clearly deserve them.  On the other hand, if you consider the credits to be earned for learning something, then I clearly do not (as I already got credited for learning the same material once, back when I first learned it in math class).
More generally, issues like this can occur any time an institute offers multiple introductory-level courses covering essentially the same material (but possibly from a different angle) and does not specifically forbid students from taking more than one of them.  When that happens, a student can effectively learn the material once, but get credited for it n times, where n is the number of such overlapping courses they can find.
The usual solution here is simply to try to find and close any such loopholes.  Some possible methods for doing that include:

explicitly designating certain courses as equivalent to each other, so that a student can only receive credits for one of them, and
restricting certain very basic introductory courses, like the "math for biologists" example I gave above, only to students actually majoring in the target field (here, biology).

Also, if students are going to commit such shenanigans anyway, it can be argued that they should be allowed to demonstrate their competence in a separate exam, so that they don't need to waste time and classroom space, and skew the grade distribution, by actually sitting in a class they don't need.

As for the second problem I mentioned above, i.e. teaching a class where some students already know much more of the material than others, there are several distinct approaches that people may argue, depending on their general teaching philosophies.  My personal suggestion, which I'd consider a "moderate" position, is to take a "triage" approach and mentally divide your students into distinct groups:

The advanced group consists of the students who already know much of the material, and just want to show their competence and get the official certificate for it.  Some may be hoping to learn some interesting new tidbits, but they'll still pass the course even if they learn nothing new at all.
The learning group consists of those students who actually more or less match the intended level of the course: they know the prerequisites reasonably well, and are reasonably capable learners, but don't yet know the material you'll be covering.  In many (but not all) courses, this group will make up the majority of the students, and they're the ones you should adjust your teaching pace for.
The struggling group consists of the students who lack some of the prerequisite knowledge the course assumes, or who are otherwise falling behind the rest of the class.  They'll likely need remedial teaching to have any hope of passing the course.  You should not have many students in this group; if you do, it may be sign that you're going too fast, and some of the students that should be in the "learning" group are falling behind.

It can be a temptation to focus on the "star" students in the advanced group, since they're the best in class, have the most interesting questions (if any), and generally appear to offer the most reward for the least effort.  They're also the ones most likely to end up as future grad students in your field, which makes focusing on them even more tempting.
However, the advanced students are, by definition, not the ones the course is actually intended for, and they're not the ones you're really there to teach.  Rather, your main goal with the advanced students (insofar as they come to class at all, rather than just taking the exam directly) is simply to ensure that they're not bored.  There are several ways you can achieve this, such as:

giving the advanced students additional bonus exercises or projects that go beyond the standard syllabus, or letting them pursue their own side projects;
encouraging the more advanced students to help the less advanced ones;
encouraging students to come see you outside class if they'd like to learn more about something that sparked their interest; and
if you still cannot engage some students in class, letting them skip it if they already know the material.

As for the struggling students, there is an argument to be made that you, ideally, shouldn't have any, and that even a single student falling behind is a sign that you should slow down until they can catch up.  Essentially, this approach amounts to lumping the "learning" and "struggling" groups together, adjusting your pace to the tail end of that combined group, and treating any students who progress faster as "advanced".
While there is some merit to this approach, it can also be taken too far.  Especially in higher education, it is often simply not possible to set the pace by the slowest students in class, and still have enough time to cover all the material in the allotted time.  Instead, as an alternative to simply letting these students fail, it may be more effective to set the in-class pace by the majority of the class, and to focus specific remedial efforts (such as individual tutoring, possibly by some of the more advanced students) on those that need it.
Of course, even this won't always help, and sometimes you may simply have to let a student fail.  In particular, it's important to learn to distinguish students who'd like to learn, but have a hard time doing so, from those who are simply too lazy or disinterested to learn.  The former group can be helped; the latter cannot.

+1 - well written and comprehensive! Noting that bonus / side projects that go above the learning requirements for the course probably shouldn't be worth marks. You could assign "bonus marks" to offset losses in easier questions (this would encourage the "learning" group to give the harder bits a go!), but the bonus questions shouldn't be required in order to score 100%.

Thanks, you've hit the nail on the head. Really my question should have been along the line of 'How do you balance the advanced group and everyone else'. Another issue is that the advanced group can sometimes accelerate the course in a way that puts a lot of students at a disadvantage. There has been many times when a professor has said whether he should clear something up and all you hear is the advanced group saying "No, Let's move on". Also, a group may skew the average upwards, creating an inverse bell shaped grade distribution across the class.

@IllegalImmigrant: The pacing issue has been discussed here before, and I agree with many of the suggestions (like using quick in-class exercises to gauge student progress). Even just asking students to raise their hands if they understand and want you to move on is better than having them shout it -- it's a lot easier to count hands than to listen to random shouts from the audience. (Tip: don't actually count hands when asking this; look for the students who haven't raised their hands instead. Ideally, of course, you'd hope not to find any.)

Restricting registrations is a delicate matter. For example, a Physicist knows almost all the EM a Telecom Eng needs, and almost all the Atomics a Chemist does; so even advanced courses will be "easy". But then, there are always details of the art, and focuses that are different. After seeing it in my degree, I could probably have scrapped enough points to pass without studying some related courses in other disciplines, but if I wanted to become actually good at them, I would need to take them and learn the particular details.

There's also the question of, "if a professor knows this is happening, is it ethical to accept rewards, positive reviews, etc., that are based on students doing well in the class?"

The computer literacy course at my university has an "exclusion" with any CS course.

I think you brushed being able to test out of subjects that the student is already familiar with, I liked how you mentioned that a person doing the equivalent should not be taking up space.

What happens though in this case: "the occasional problem of advanced (or self-taught) students taking beginner-level courses for "easy credits", and" but when it is a question of taking those courses because they're required, not because they're for "easy credits", and you're not allowed to skip the course, but one has enough, or nearly enough, self-learnt knowledge - also knowledge not specifically acquired for this purpose but attained naturally - to just "show up for the exam and pass", and nothing specifically forbids it, and you go do it, getting extra free time that term?

@The_Sympathizer: I'm not sure if I managed to parse your question 100% correctly; there seems to be a missing quote mark somewhere. :/ Anyway, I see no ethical issues with "getting extra free time", at least not as long as you choose to spend that time in a way that you consider ethically acceptable. (And why wouldn't you?) Degrees and course credits are (supposed to be) earned for learning, not for spending a certain amount of time doing so. If there were a magic pill anyone could take to instantly learn everything needed for a PhD, what would be wrong in taking it? I'd say nothing.

… In any case, that "extra free time" is probably mostly just credit for time you'd spent (more or less) voluntarily learning the subject on your own in the past. But even if it wasn't, it still wouldn't be an ethical issue in and of itself. The only possibly related issue, as I discussed in the answer above, is if you were in the habit of taking several such courses covering the same material to get multiple credits for learning it once. But if you're only taking the course because it's required to certify your knowledge and enable further study, that's a valid ethical justification to me.

@IlmariKaronen : In other words, it's only an ethical problem if you are somehow purposefully seeking to game the system, not because circumstances happen to collude in a certain way, right?

A student takes a course to prove he learned the stuff in the syllabus. He/she passes the course, and then has official certification that he knows that stuff.
Who cares when he learned it?
The trickiest part is keeping the course interesting for the high-flyers, without alienating the less able (or less knowledgeable) class members.

+1 And I guess it is a matter of background diversity. Some may have plenty of experience and just need a degree, while other are moving straight in from earlier study programs. One can't enforce this rule universally.

"He/she passes the course, and then has official certification that he knows that stuff. Who cares when he learned it?" Oh, the naivete. If this was the case then why did my university want to charge me 150% the course fee to challenge the exam?

@tar That sounds like a very expensive fee (unless it was a very cheap course!). If your challenge is successful, you probably will (and should!) receive a refund of that fee, and the examiner will have been proven to have made a mistake in your grading. If your challenge is unsuccessful, then it would appear that you haven't learned the course material to the examiner's satisfaction. I fail to see how this backs up your accusation of naivety.

@tar is using "challenge" in a different sense from you. He's not claiming the exam was unfair or appealing the grade. Rather, he wants to get credit for the course just by taking an exam, without doing a semester worth of homework, projects, midterm exams, attending the lectures, etc. That is called "challenging the course by exam" at US universities. Apparently his charges a fee which is greater than the ordinary tuition for the course. He doesn't get it back if he passes (though in some cases he might if he fails).

@NateEldredge Ah, I didn't even know you could do that. Exams and assignments are often very different in terms of the skills they assess (especially CS!), so I'm surprised that you can do that at all. It likely costs more than the regular course because of the extra preparation involved: perhaps the assignments also have to be completed, and different versions of exams (and possibly assignments) have to be prepared for the challenger unless he sits them at the same time as the normal class. Seems perverse, but fair. I still don't see how I'm being naive!

Usually the assignments do not have to be completed, or perhaps just one or two of them.  Sometimes it is necessary to write a new exam, but more often the instructor will reuse one from a previous year, perhaps with minor modifications.  Institutions usually place rather strict limits on how many times you can do this; it's mostly used in situations where Course B has Course A as a prerequisite, but the student is already familiar with the material of Course A.  But I think it's odd for this to cost more than taking the course normally.

tar apparently thinks there are ulterior financial motives for this.  I don't know his institution so I can't guess whether he may be right.

"Who cares when he learned it?" Everyone else in the class when it's being graded on a curve.  Especially if exams are designed so that even top students should still miss some of the stuff.

@JoshuaTaylor If someone is knowledgeable, but unqualified, are you suggesting that it's not fair for him to go to University? University is competitive. If you want to be the best, you have to keep up with the best. At the undergrad level, you shouldn't usually see anything in exams that hasn't come up in lectures or assignments, so you have ample opportunity to learn everything during the course.

The only possible justification I can think of for feeling (slightly) bitter about that is if the student in question is taking a course purely for the motivation of an easy A+. However, most universities should not allow you to take an easy course if you've already done its harder equivalent.

@Moriarty I'm not suggesting any of those things.  I'm simply trying to point out that the question does have ethical aspects to it, whereas some of the commentary suggests that there are no ethical questions here at all.  Not all of them are on the student, to be sure.  I just don't think it's quite as simple as some of the commentary suggests.

@JoshuaTaylor My answer's perspective comes from the wording of the OP's question. He/she asks about the ethics of preparing yourself for a course, implying a deliberate effort targeted towards that course. That sort of preparation is OK, but it's a very different thing to just taking an "easy A+" course on a whim, which I agree is a bit dubious. I agree fully with Ilmari Karonen's discussion of the ethics.

@Moriarty Yes, OP specifically asked about "preparing for a course", but mentioned in the question that "a portion of the student will have tremendous knowledge in the former, therefore significantly reducing his/her course load. How easy is it to ace an introduction to C course if you already have years of experience in the language?" To me, that signals that OP considers those kinds of situations relevant as well.

The goal of a university course is education on a particular topic. Students who study before the class are educating themselves on that topic. Students who don't study before the class are, hopefully, being educated by the teacher on that topic. Both of these things achieve the goal.
Frankly, if you have even the slightest suspicion that it is unethical for your students to educate themselves, you are in the wrong place. There is no such thing as "too educated" in academia.

I think the question can be greatly simplified:

Should credits be awarded for effort or for knowledge?

The person who knows their stuff without having it picked up in class was obviously smart enough to pick up the stuff they needed to know on their own or before hand. Call that preparation, genius or whatever, if he or she knows their stuff, they deserve the credit, no matter how long, short, hard or easy they had to work to learn it.
Should you give credit to someone who does not know what their doing, just because they put a lot of effort and time into it? I hope not! I do not want to be operated on by a doctor that put many years of hard work into NOT KNOWING their stuff, I rather get an operation from a self taught autistic savant that spend 3 Month reading and watching videos, acing all tests, never sitting in a single class!
Sure I admire people that put a lot of effort into learning something, because they can put that much effort into something, but when a job needs to be done, the only thing that counts is, who can do the job!
It's a shame that so many Universities require students to take nonsensical courses, which they have to pay a lot of money for, rather than giving them the option to just take the test. And why do Universities that allow you to just take the test want like 50% of the tuition from students that only come in once for the test. Quite an obscene payment for the time to take the test and correct it...
Don't get me wrong, credit for effort is GREAT, ... in Kindergarten!

Well put. I have long been uninterested in my "subject", mathematics, merely as a game for grade-getting and such, or contest, either. "School" too often perverts the goals of science and scholarship. And the confusion of the "moral" virtue of "trying hard" with the actual virtue of "being effective" makes a mess. But commodification of "education" amplifies the gate-keeping ticket-taking aspect in a way that confuses many people. And, sadly, at the same time, some coursework does descend to the minimum level compatible with a derivative picture of the goals... Nevermind...

Should credits be awarded for effort or for knowledge? — Neither. They should be awarded for demonstrated skill.

Thanks, the hits it even better! Since knowing something and not being able to apply your knowledge as a skill helps nobody.

It doesn't directly apply, because it doesn't so come from prior prep work or experience, but during my doctoral program, there was a mandatory class that had two different groups in it - PhDs in that department, and PhDs outside it who, while fairly sophisticated, clearly lacked the same background in terms of coursework.
How he handled this is to divide the course into "tracks". There was a modest, "shooting for a B" track, and a much more challenging "shooting for an A" track, with a hard mode "shooting for the A+ track" that actually had little effect besides drawing a certain sort of student, since the + in a grade doesn't even exist at that institution.
The department majors were required to be on the A or A+ track, everyone else could choose. You might similarly be able to ask students to self-rate their familiarity with the subject, and strongly encourage those who rate themselves well to consider a more challenging track.

For our purposes, there are three types of students causing the concern:
1) Students who have taken similar, or comparable-level courses and are "repeating" this course for a "cheap" grade.
2) Students who have not taken comparable level courses but have "boned up" ahead of time.
3) Students who have not done 1) or 2) but whose proficiency in computers give them a "natural" advantage.
The ones we should be most concerned about are the students in the first category, the "repeaters." That is solved by establishing course levels, to say the students who have passed courses at an equal or higher level cannot take this course.
The students in category 2) don't provide much a worry. At one level, you want to applaud them for the "eager beaver" tactics, but at another level, it might not do them much good.That's because they are (probably) learning the book, or course, not the  material. As you pointed out, introducing new material dissipates their advantage most of the time.
The students in the third category are the ones you want to encourage. They are those whose general computer efficiency at work or playing computer games gives them an advantage in computer science, even if they haven't seen the material before. Why should that not be the case? Someone who has worked with hammers and nails and other tools will have an advantage in physics over someone who hasn't.
Yale math professor Serge Lang would "sort out" his students on the first day of Calculus class, by giving an algebra quiz.It was one that everyone would "pass," but some would do so faster than others, and those were the likely "A" students.

There is actually two good questions contained here but conflating the two would be a mistake.

What to do about students who already have a lot of knowledge that would be covered in the course?
Is there a socioeconomic problem with some people having more resources and therefor being more prepared.

The reason I split these questions is that it is entirely possible for a student to use public resources, or take classes in a way that they end up not challenged by a class. And depending on the motive there should be no problem with this. If I was interested in a topic I would probably do some amount of self study before enrolling in a college course (I have finished a B.S. and am working on a M.E.), I have also taken classes at the Master's level that were far less challenging for me simply because my Bachelor's was in Math. However, if I were to take a class that I knew all the material for just to get more credits or improve my grade there is an issue because I would be taking space and resources from people who would learn more from being there. So, there is no ethical problem for a student to self study because they love the material or so that they can maximize their return on the course... in fact we should encourage them. But taking a useless class in order to meet a metric is wasteful and denies resources to others.
(For the next part my view is that of someone living in the U.S. but it is applicable widely)
As for the second question, I agree that there is a socioeconomic issue with some students having the resources to be more prepared, my question is how to we mitigate this? I would suggest a combination of more free computer and book access, better schools and more activities outside of school being available. Personally as a father I am making an investment in my son by using my wealth to enrich my child's mental abilities, and that is perfectly fine. As a people we need to do better about erasing economic gaps and realizing social gaps are not gaps at all but opportunities to grow. So ethical? On a personal level yes, on a societal level no. Who is to blame? All of us... but all of us is also the solution.

There are cases in Academia where students are held to different standards based on preparation. At my university there were some classes in mid-level physics that were cross-listed as both undergraduate and graduate classes. Typically the students were graded on two curves, one curve for undergraduates biased by actual undergraduate scores, and a second curve for graduate students biased by actual grad student scores. I thought that this approach was both merciful and a decent solution to the "different levels of preparation" issue raised by Illegal Immigrant.
When the differences between students are not easily catagorized as above, it becomes difficult to divide students into groups. This is a practical matter, not an ethical one. Unfortunately, practicalities often trump ethics in American society since Americans place a high value on simplicity and equal treatment. It is a real problem, but usually there is no admissible (constitutional) mitigation for the problem.

Whats the difference of the student (say, X) who studied long before taking the course and the student (say, Y) who failed the course the first time and have to retake it in the next year?
Seems to me that X is a better student than Y, because Y once failed the course. But in term of preparation before taking the course, both have them. And if any of them obtained an A grade in ethical way, that is, by doing their homework, and doing the tests correctly, I find there is no problem at all. We shouldn't discriminate either X,Y, or normal student in obtaining their credits/grades.
As for whether credits should be awarded to effort or to knowledge, it is at the discretion of the professor/class, the professor might give grades partially on effort (homework, essay, or project) and partially on knowledge (test results).

I cannot at all agree that it is legitimate to grade "effort", since this is not possible to measure sensibly. It's hard enough to measure "performance".

Some parts of the implicit hypotheses of the question are misguided. First, courses are about the students, not about the teachers. The teachers may give the students something, but if the students already "have too much", this is the opposite of a "problem".
Yes, it is a minor sociological problem to have highly motivated students in a room with unmotivated students. :) Hmmm. :)
Also, a "problem" to have genuinely gifted students in a room with ... uh, maybe anyone who'll "feel bad" if they can't "compete"? But, wait, why is it a competition. Oh, yes, "grades". Hm. Rewind. Don't punish kids who're talented and who've taken initiative, and don't punish kids who're just "doing the class", either. Classes should not be a test of giftedness, (or else it's a rip-off), nor should they punish it.
The notion that we can arrange to have student populations be homogeneous is ridiculous... btw.
That is, the outcomes of inhomogeneity are inevitable. If the gifted kids, or kids who've read lotta books before, already know all the usual pranks, it's fine. Don't make up extra-perverse pranks to try to bring them down, and don't assign them extra classroom chores as punishment for doing well. That is, don't add perversities to the accidents of nature and society.
When I was younger, I did often sign up for courses that I already felt I'd read about sufficiently to not feel at a disadvantage. Seemed reasonable to me. Not to mention that a sincere person might not feel constrained (as other answerers have mentioned) to wait to take a class to read the dang book. Srsly.
Should unambitious students feel intimidated by the few students who've already read all the stuff, know much more? Uh... yes. Not that they should fear that their deficit from that level will be fatal, but, yes, that that level of function is possible and reasonable and desirable. Any program that makes precocity penalizable is criminally perverse: knowing more is good; knowing less is less good.
One operational problem is that such stuff is not easily "formalizable" and "institutionalizable", but that should not be allowed to be an obstacle. It's possible to teach "typical" kids, and not torment them, without hassling exceptional kids. Obviously.

Ethics aside, as many people have noted that the concerns that arise aren't strictly ethics-dependent, there are practical issues to address.
Harvey Mudd College saw this in a big way in its CS courses, particularly the introductory sequence. Historically, they had a required intro programming course that first-term freshman took unless they placed out via AP or local exam. This left a lot of students with substantial programming background mixed with students who had none. The class dynamics were broken in many ways from this. Students with experience could answer questions and complete assignments much more readily than those without. Students without would often get disheartened, feeling like they lacked talent in comparison, rather than recognizing the difference in background from their more advanced peers.
They addressed this issue by separating incoming students into various streams until they either completed the intro course and went on to another major, or were on equal footing going into the CS-major coursework. The true intro course was split into sections between students with moderate experience, and those with little to none. Switching between them was made relatively accessible. Students with more experience to place out of the intro course, but not with all the material the school wanted them to have for the major, took an advanced intro course that covered the first in-major course's material, while those who took the plain intro would take that a second semester course covering just the more advanced material.
The consequences of this were pretty huge. Gender parity in the CS major shot up, even faster than the rapid shift of the school's overall demographics. Enrollment in subsequent CS courses and the CS major increased among all groups of students.

In my honest opinion, this is more of a corollary to a fundamental systemic problem than an ethical one. The questions to be raised is why such students take those courses. There are few motivies I have personally witnessed.

To get an easy grade
The course is mandatory or a prerequisite with no way around it
Students need to fit some numerical credit criteria and they don't want to take it

All 3 of these reasons exhibit issues with how a university function. The universities seem to behave as if their priority is to give an "equally" measured certificate. Whether or not someone actually learns something seem to come second. This is not only universities' fault. Institutions of all sorts seem to use GPA as a significant measure of success. I have seen scholarships or university benefits where GPA was literally the main judging factor. This motivates people to not "risk" a lower grade in a more technical course when they can get an easy "A" by practically learning very few things.
Another issue is that the exams are in many senses unfair. It is quite possible for one to get a worse letter grade than one should given their understanding. Because of the results mentioned and many others these people are encouraged to retake the course in order to improve their passing grade rather than taking follow up courses.


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How do you enforce handwriting standards for homework assignments as a TA?
I am a TA who is helping to grade student homework assignments for an undergrad engineering course which involves a lot of mathematics. The homeworks all together count for miserly 5% and is only graded based on completeness. One of my biggest petpeeves is poor hand writing for written work. I don't exactly have good hand writing, but for things that are turned in or show other people (i.e. for communication purposes), I always ensure that the quality of work is top notch quality.
However, most students in my class have terrible handwriting to the point I cannot even decipher what they are trying to communicate. Wherever there is supposed to be a straight line, I see a curve, not even a well drawn curve. If students run out of space on their piece of paper, many resorts to cramming massive amount of calculation in the margins rather than starting a new page or even flipping the sheet over to the other side. Even worse is that most students write in pen, and when there seems to be an error, they have no qualm of scratching it out using a scribble. I am not a pen person so this is something I have difficulty in understanding. Homeworks are rarely stapled. Let's not even talk about the diagrams, I have no idea why they even bother drawing one. Most people just don't seem to care.

(a picture I found online just to give you an idea what it looks like, sometimes the entire page is crossed out because of some mistakes in the calculation)
I have been telling them to write neatly since homework 1. Yet this problem persists. The main problem is that the homework grades counts for so little, and there is nothing to enforce quality of homework. If a homework is completely done, even if the hand writing is so poor that I could not decipher exactly who handed in the assignment, I am still required to give full grade. I have talked to the professor who is running the course, and he basically gave me a "I don't want students whining over grades" sort of reply. I am powerless to change the policies of the course, and at maximum all I can do now is giving out recommendations to the students on expected, but not enforced, handwriting standards.
Is there anything I can do in my situation? I had hoped I could see a reflection of myself in this pool of students but I have yet to see that person which makes me a bit disappointed to be honest. Whether if these people go directly into the workforce, or remain in academia, clarity in communicating is very important and I fear if they do not change their habits quickly it could lead to some very negative consequences in their professional life.
Am I overreacting?
Should I tell them a white lie that I am going to give zeroes for unclear, poorly written homework but in actuality I will still give full grade for completeness?

Comments are not for extended discussion, or for writing answers; this conversation has been moved to chat and further comments are subject to deletion (since they can't be moved to chat more than once). Also see: When should I comment?

The homework is worth 5% and the professor wants to give full grades to anyone who completes it.  I'm basing my answer on the assumption that the students can get their graded assignments back after you mark them.
If that is the case, explain to them that for you to give adequate feedback, you have to be able to read the assignments.
The assignments aren't worth much, so I imagine the professor is giving them out as an opportunity for the students to make sure they understand how to do the problems assigned.  Although it may not directly change their grade, your ability to understand their answers will change the quality of feedback you can give.  Explain to the students that if they want constructive feedback, they must write neat enough for you to understand.
The professor doesn't seem to care about giving that 5% away, so you shouldn't worry about it either.  Legibility of the answers isn't as much for your benefit as it is for theirs when they receive comments back on their work.  If they don't make it legible for you; then it's just less thought that you have to put towards giving feedback (since you can't give feedback on answers you can't understand).  That way you aren't wasting your time giving feedback to students who don't really want it; and those who do want it will do a better job.

shall... not... provide... illegible feedback

My approach is simple- homework is submitted as a typed .pdf file, no exceptions.  Homework is submitted online through the course management system (Instructure's Canvas in our case), which enforces the required file extension.
Yes, this means that my students need to learn how to produce typed mathematical equations.  They're welcome to use LaTeX (probably the best choice in the long term), Google Docs (which has a pretty intuitive system for math formulas that's adequate for most purposes), MS Word (which has an awfully complicated and hard to use equation editor), Apple Pages, or whatever software they like, but they have to convert the output to pdf so that I don't have to deal with all of these different word processing software packages.

This may be fine for coursework with mostly symbols, but as soon as it requires drawing (graphs, plots, diagrams, etc), I think it becomes unreasonable to ask for typed coursework. Unless you somehow mitigate this, e.g. by providing example \LaTeX (or gnuplot, or matplotlib, or whatever) code, and/or give students extra time.

@101010111100 graphs and plots can all be done with a computer much easier than by hand:) There's matplotlib, origin, Powerpoint, Excel...

@Ajasja Agree, but only once you are experienced with the software. Ask a 1st year (or even a 2nd year) student to draw you one of those more involved state diagrams, or a non-trivial circuit diagram. Then suddenly, something which would have taken them a few minutes to draw by hand, takes them up to an hour (especially with LaTeX or gnuplot).

I suppose "typed .pdf file" does not exclude the possibility of drawing a graph by hand, scanning it, and including it as a figure in the PDF?!

I audited a math class a few years ago where this was exactly the policy. If anyone had issues with it, I was not aware, so it definitely works in the real world. It's also good preparation for whatever students do next. Whether it's business or academia, being able to produce digital documents as opposed to hand written ones will be somewhere between very helpful to required.

I actually took most of my notes in college in Word, as an electrical engineering student. The equation editor wasn't really a problem (fun fact: it accepts LaTeX-like syntax that it converts to it's graphical system on the fly—works pretty well!), though circuit diagrams were miserable (and some classes featured enough of them to force me to use pen and paper).

In many cases my assignments do require students to produce accurate computer generated plots of results.  Since the students have got these on the computer it's not to hard to incorporate them into their solutions.  In cases where a simple sketch of a graph might be appropriate, the students can use a drawing program to produce the sketch (or simply scan in a sketch they drew on paper.)

"but only once you are experienced with the software."  My view is from the techie side.  If you know ahead of time what software your professor suggests, or you just take a vested interest in legibility, learning it is not a big deal.....just take whatever time you would spend party.....i mean studying, and go through some tutorials......or come to SE and find out how to use LaTeX lol.

Learning to draw images that you can share is a computer skill any engineer should have.

@NZKshatriya: Or as an experienced course instructor, you could provide quick tutorials on the software they're expected to use.  Maybe even a LaTeX "course homework" package, like the thesis/dissertation packages some schools have.  E.g. MIT: http://web.mit.edu/thesis/tex/

@jamesqf Quite true.

Make a pile of homework submissions that are not legible enough for you to do a good job of grading.  Put those in a separate envelope in the professor's mailbox, along with a cover note explaining that you were not able to grade those.
Let the administrator in charge of TAs in your department know about the problem.

If you are given responsibility, and authority, to address this problem as you see fit, then I would suggest paperclipping a quarter sheet to each illegible submission, with a xeroxed note, letting the student know that the temporary grade is zero, but that if the assignment is resubmitted in legible form by (deadline), you will grade it as though it had been submitted on time.  Explain that if a student is unable to submit a legible version in writing, s/he can see you in office hours to use an alternate method of demonstrating that s/he did the work.  Keep a record of which students submitted illegible homework.  Use this list to work toward getting the homework submitted legibly and on time.

If the student is unable to submit a legible version, then it would be a good idea to get the university's disabilities office involved. Special accommodations would likely have to be made for exams as well.

@200_success Clever approach! And in some cases, potentially a correct approach.

Yes, in a situation like this, you "buck it up to the boss."

You're not overreacting. Your instincts are good, but you cannot do anything about it at this time. Do not white-lie. Krantz, How to Teach Mathematics (sec 1.5):

If there is any circumstance in which honesty is the best policy, this
  is it.

If you can decipher who wrote the assignment, give them full marks.
If you can decipher the assignment, give them feedback on the assignment.
If you can not decipher the assignment, give them feedback about that.
If you can not decipher who wrote the assignment, give them 0.  If they complain about it, then they have to identify themselves.  Then give them full marks.
If they did not do the assignment, give them 0.

The primary purpose of these homeworks is for students to get feedback from you, but if they don't want it, why force it?

Although it is plausible and practical to simply demand typeset homeworks, there might still be issues of a similar-though-different nature.
I think the more genuine point is not about handwriting per se, but about readability (which could include issues about broken fonts in electronic documents...). Non-readability is basically a no-op, and gets a "0", or perhaps a low mark and pointed warning on first occurrence.
The question of whether 5 percent is enough to motivate students is different. Odd that even kids would bother to turn in obviously illegible work for a very small percentage of grade...
Rationally, that is, game-theoretically, if you want people to do a thing, it has to be plausibly doable, and not cost more than they can pay, first, or, surely, than they are willing to pay. The idea that one explains to immature people that illegibility will do them harm, or any other such thing, is a second-order effect for kids at that age.

It can be frustrating if one does not have the power to enforce the standards that one expects. I would try to be more relaxed about it:

I would explain to the students that very poor handwriting is rude and does offend you and possible other TAs in the future.
On the other hand, I would be completely open and honest about the grading standards. If a paper full of unreadable rubbish counts 10 points, then say it. The rule is the rule.
I would try to minimize the time I spend with grading poor answers. If the student does not put effort into the answer, just barely read through it and give him the points. If I student really tries and is willing to learn, show him that you acknowledge this.

Thanks, I would say I have been approaching this issue according to your third point. I would like to give every student some feedback, but if the handwriting is so terrible and the homework is basically looks like a scratch paper, I just give them the full mark and move on. Although what frustrates me is that only 1 or 2 students have good enough quality homework that I actually give feedback to, I would like more students to be able to receive feedback as well but this can only come from more  effort on their part

Actually, they may be a variety of reasons for them not putting effort into the work: Some are just lazy, some are concentrating on other classes, some are bored by the assignments etc. You can only help those who want help.

Frankly, I am a bit confused that you are asking. The writing is of secondary importance. What is important is that the student solves the problem and that you can read and grade it. If the student fails to communicate his solution to you, it is their problem.
If half of their text is just not readable, then they did not solve the problem, and cannot get full grade for completeness. It does not matter how beautiful the handwriting is, but whether you can read it. If they write in the most beautiful calligraphy style, and then pour some coffe over it so nobody can read it anymore, then they still get 0 marks.
Speaking of which...

full grade for completeness

If this really is what your professor is suggesting, then you have wildly different problems than handwriting.
Try to get it in writing from your prof (maybe in a mail), and then basically do as he says.
If a student hands in an assignment where you cannot read the name, then do not grade it! If you cannot decipher it, then it is hardly complete, so you cannot give full marks.
If your prof is afraid of having to handle angry students, then make sure that they come to you instead of the professor.

Even worse is that most students write in pen, and when there seems to be an error, they have no qualm of scratching it out using a scribble.

Er, that is completely normal behaviour. If writing in ink and crossing out errors are unacceptable to you, then the problem is that you have bizarre and unrealistic standards.

It is completely normal behavior, given that the frequency of crossing out using scribble is low. If a page only has a handful of scribbles spread out over the entire page, I probably won't even notice it. I have not mentioned that it is unacceptable to me. But what I am seeing in the homework is that the the scribbles will span horizontally or vertically across entire page, overlapping with other answers, and the frequency will be so high that in a single line of calculation there would be multiple instances of scribble. This makes me think they are handing in scratch paper.

For example, even for things that are not a part of the calculation or the solution will sometimes be crossed out using a scribble, such as homework number, or description of the problem - I have no idea how they could have made a mistake when jogging down a problem. Sometimes there would be a scribble, but no correction is presented. If scribble is for erasing a mistake, then one should appropriately expect that the mistake would be subsequently addressed. Obviously that has not been the case from what I am seeing

There are other cases when there is no apparent calculation or mistakes of any sort, the student(s) would just start to write something (this is at the beginning of a problem), and after the first character, suddenly changes his or her mind about if this is a "good place" to write down the solution then cross out the entire line. So all you see in the homework are blank spaces filled with scribbles. Again, no calculation, no mistakes of any sort, just like a single character, or a symbol, then completely crossed out. The calculation would start elsewhere.

I had a professor with extremely strict homework guidelines. One example, if your name was not in the top-right corner of very first page in the format last name, first name you got a zero. You could easily spend hours on the homework and get a zero because of that. Homework that was not stapled? Zero. Homework handed in A4 instead of 8.5x11? Zero.
Being able to communicate clearly is a core concept of engineering. An engineer needs to be rigorous. Handing in sloppy work, with unintelligible writing and diagrams is hardly rigorous. Imagine them attempting to send a rover to mars with this kind of approach. It's not sustainable and thus it is your job to help inculcate these values in these aspiring minds.
Therefore, if anything, I believe you are being too lenient. Predetermined requirements, such as legibility, clarity, format, etc... should be established at the beginning of the course and then dole out grades accordingly.

Those are just arbitrary rules that have nothing to do with legibility. Sure, they're formatting, solely for the convenience of the grader. Most people, me included, would object to that level of arbitrariness. Also, that was a different professor, at the other end of the spectrum. That has very little to do with this question where the professor (for better or worse) has advised oppositely.

Those are just arbitrary rules that have nothing to do with legibility. Incorrect. "Arbitrary rules" are any rules. Legibility is one of any number of "arbitrary rules." My point is to establish a specification at the beginning of the course. Deviation from the specification results in zero grade. That is why I listed "arbitrary rules." The specification/contract must be adhered to with impartiality.
Regarding OP's particular predicament, you are 100% correct. I re-read his question and I should address the situation he faces as a failure of management (his lazy professor).

Yes, you are overreacting. You're not going to get neat homework with this policy, period. Most of these students probably don't write by hand very often, and so they have not spent the time to get good at it. That means it takes a lot of effort to make their handwriting look nice, possibly including carefully rewriting the entire problem on a new sheet off paper once they are done with it. These students have other things to do, possibly including assignments worth more points in this class, other classes, jobs, kids, etc. Time is a finite resource, and they have zero reason to spend it on this. I've had many math classes that graded practice problems in this same way, and I never bothered to do them neatly either. The grader wasn't reading through each problem to give feedback anyway, so it didn't matter. Neat handwriting may be a noble skill, but I guarantee that proper prioritization and time management are  more useful ones.
This leads me to your solution: stop trying to make sense of their work! I have never seen an instructor give feedback on homework like this. That's not the point of it. You're just going to give the same feedback 20 times anyway because half the class made the same mistake, so it's a poor use of your time, too. The purpose is to get the students to attempt the problems so that they know which ones they understand and which ones they don't. It's then their responsibility to ask for clarification the next class.  This does not require or even benefit from you being able to read their work.
Summary:
Practice homework is for practice, and a small amount of points are given to encourage people to actually practice. It's not meant for you to dissect and comment on, so don't worry if you can't do so. They should know if they got the problem wrong and can seek help if they need it.

This might be a bit hard for this year, but of future, maybe you could consider making other extra incentives available for those who submit homework.
Here's an example from a course I had:
The homework carried low amount of points (5% or 10%, can't remember now), but it was so spaced out that we'd get graded homework around 1 week before midterm exams and then the other set of homework assignments sometime before the final exam.
The assignments themselves were also quite similar to what we would normally get for the exams. So by turning in a good, readable, homework, you'd get good feedback with enough time to fix all the things you didn't understand before  the exam which carries a lot of points. On the other hand, the amount of points carried by the homework was low enough so that cheating on homework wasn't very interesting.
This way, people who cared about the course got the practice and people who only cared about the grade of the course got points and feedback for the exams.

In my university there's no standard that students have to submit electronically typed assignments. We encourage them, but it's not always easy for them to learn and many of them rather just write by hand (and scan, if the submission is online).
My general approach is to say that if I cannot read the assignment, I am not grading it; if the scan is incoherent (you answer 1A, 2C, then 3A, 2B, 3C, 2A, and so on; often due to a misplaced page in the scan), I don't grade the out-of-order answers.
One may appeal, but only by submitting a typed solution instead. It is their responsibility to make their work presentable, and to make sure that the scan is readable, in the correct order, and nothing is cut in the margins.
Others in my department often give an automatic 5-10% bonus for a typed solution as well, which can be encouraging.
In the situation where the homework only count for 5% of the grade, these might not be sufficient incentives, though. In which case your frustration might never be alleviated. Remark this to the students, and if all else fails, talk to the professor. In most cases, if something is truly unreadable, you should have some backing to give a zero grade on that particular assignment.

However, most students in my class have terrible handwriting to the point I cannot even decipher what they are trying to communicate.

Fail them. End of story.
If you can't understand the answer, you can't verify that it's correct.
Zero marks; move on.
The handwriting will quickly improve, from anybody who wishes to pass the module.
Make this policy clear in your lectures then the responsibility is known to be on the students. Frankly this should be blindingly obvious to everybody involved, but I am aware that students sadly take no responsibility for anything nowadays.

OP made clear that failing is not an option; decree from the powers-that-be.

@CaptainEmacs: I see no evidence of that in the question. Besides, if TPTB have dictated that the OP may not fail a student whose homework cannot actually be read, then, well, there's no solution. That's just silly.

OP says: 'I have talked to the professor who is running the course, and he basically gave me a "I don't want students whining over grades" sort of reply' - yes, it's silly, but some departments have targets like that, and if you are not a prof that can stand up to such pressures, that's what happens. And do not think that I abet that. Zero marks is just the response - it's just not what he seems to be allowed to do.

@CaptainEmacs: Then the institution mandates giving marks for literally nothing.

Not for nothing, but for submission, only. Yes. And that's bad. Yes.