For graduate school classes, if a professor writes his own homework questions and creates his own problem sets, is he required to provide solutions to the homework problems, after the homeworks have been turned in and graded by his teaching assistant(s)?
No. The professor gets to decide if it would be more beneficial for students' learning to provide full solutions, partial solutions, or no solutions to homework problems.
This is entirely up to the policies of the university or department in question, and is likely to vary between disciplines. In the areas I'm most familiar with (STEM subjects as taught in the UK and, to a lesser extent the US), I'm not aware of any places where professors are obliged to provide solutions, though, in my experience, they usually do in at least some form. That might be by handing out printed solutions, or holding classes to go through the problems, or both, or something else. However, in arts subjects, where assignments are typically "Write an essay about subject X", there isn't really any such thing as a "solution" and one would presumably expect feedback about one's essay, rather than being given an example of a "correct" essay.
Once you're beyond undergraduate level I think that (at least in many cases) there can be a solid argument for saying to students "If you can't convincingly justify why your answer is right, why should it be considered an answer at all?". The student needs to progress beyond a secondary-school mindset at some point and actually move toward the world they're trying to prepare for -- one without a set of ideal solutions, where you have to convince people why what you did is correct.
That's not so say there's less work for the person teaching them; some kind of in depth feedback about the suitability of the justification of the answers is needed; in an academic setting the work and the value of the justifications offered should be discussed, either verbally (analogous to the feedback from a presentation or seminar) or in writing (analogous to feedback on a paper), albeit at a somewhat lower level than those activities -- such feedback can come from peers and people in the role of mentors (the professor and any assistants for example) - one or the other or both, as suits the nature of the activity.
There's not enough detail in the question to tell whether the nature of the particular activity is a case which is better fitted by requiring students to convincingly justify their answers as part of answering the question with no ideal solution to be provided, or whether it's better fitted by giving them solutions.
[Actually I think some of this kind of thing should come in much sooner, at least in the later part of undergraduate level work -- since many students who graduate and go into the workforce will be in a similar position of having to justify why their work is correct without there ever being "correct answers" available. They should have some actual practice at this in their education. On the other hand I recognize that sometimes there are policies in place which could make this more difficult with undergrads.]
On a somewhat indirectly related note -- at least for mathematically related subjects, giving students numeric solutions before they have answered the questions themselves often seems positively harmful. It very often leads students to abandon thinking about the characteristics of the problem in any deep way in favor of trying random things until they happen to match the solution, without actually coming to any kind of understanding of what they're doing; their focus is on getting the specific number in this particular instance rather than on the comprehension of ideas needed for dealing with that kind of problem.
As a quasi-answer, I'd note that for all the (university, math) classes I've taught in the last 20+ years (that is, especially after the internet...) I've provided extensive "discussion/approved-solutions" to all homework and/or exam questions, at both undergrad and grad level. Mostly, this is to show an (attempted) model for writing style, format, tone, assumed context, etc. It is only incidental to make some point about why grading was as it was, which in my view is a very minor thing. E.g., I strive to resist publicizing "grade distributions" in graduate math classes, because it creates false goals, false comparisons. I do also try to emphasize the good features of attempted discussions/solutions, rather than "failings", although, of course, the latter have to be examined... and, hopefully, students want to learn why/how they're missing a/the mark.
Also, I did wish to demonstrate irrefutably that the issues I asked student to address could be easily, fluently, in-finite-time, no fudging, no weaseling, be persuasively answered from an expert viewpoint... hoping that I do manage that on most days. :)
It seems to me that implicit in the question is a sort of quasi-litiginous attitude, that there should be an objective standard [sic] against which students can compare the grading [sic] of their attempts, to possibly argue against loss of "points". Also, there's the confounding of "assessment" with "education/feedback". I am aware that in the UK the math exams are legally required to be vetted months in advance by people at other universities. Certainly an arguable cover-your-@$$ scheme, but really very silly and resource-wasting, apart from substantially insulting to very erudite and scholarly math faculty. But that's the kind of system you'd get if/when faculty prerogatives were sufficiently weakened (e.g., in comparison to most U.S. math situations).
Although I do try to remind myself, and my students, that education, not assessment, is the goal, The System (in the U.S., and let's not talk about current events) seems evermore to declare the opposite (since it is potentially rendered numerical, etc., I guess).
I have also been told by colleagues both local and otherwise that putting good solutions-to/discussions-of the standard, iconic questions on-line "ruins things". My response is that there will certainly be bad solutions/discussions on-line, and I'd like to further education by providing good solutions on-line... rather than perpetuating some cycle of bad-online-solutions-getting-bad-grades-for-incomprehensible-reasons...
But to require faculty to spend their time creating good discussions? Impossible, in research unis in the U.S., these days, where the main measure for salary raises each year has nothing to do with teaching, course notes, discussions/solutions, etc. To require a person to do a thing which is counted as 0 or negative in their "performance review" would be bizarre. If anything, spending time on course materials is viewed as a "loser" activity, low-status, etc. So, duh, certainly not "required".
But that should not have really been the question, I think. The question should have been about whether experts should divulge models for competent function, versus keeping them a "guild secret". To that, the answer is "yes".
I'm sure the actual requirements vary. There isn't just one standard that applies worldwide. (Or even city-wide, in the city where I live.)
As the Lead Instructor of a college department, let me tell you what was required of me:
- show up
- teach students
- give students grades
- other minor amounts of requirements, like bi-monthly meetings which I viewed as nothing more annoying than relatively minor inconveniences
- Have a mid term
- Have a final exam
- have quizzes (the number of them were up to me)
I was given a list of topics I was required to discuss. I was required to discuss each of those approximately 12 topics for 5 minutes each. The rest of the class time was entirely at my discretion.
If I wanted to have more tests or fewer tests, that was okay. If I wanted to have sessions where I answered questions before an exam, or after the exam, that was okay. I could even give away answers during an exam, if I wanted to. I'm not saying that would necessarily be a good idea, but what I am saying is that I totally had the flexibility to handle things the way I wanted to. If I wanted to answer questions outside of class time, I could, but there was no requirement to.
If a student demanded answers, I could provide answers, if I wanted to. However, if I decided to do something different instead, I could. For instance, if I wished to focus on the college's goal of instilling professionalism, and discourage an unwarranted sense of entitlement, I could say that the student had no right to control me, and so I was not required to give answers.
So, based on my experience, I would assume that the professor has no such requirement unless there is a (probably written) policy that imposes such a requirement on the professor. Requirements could come other ways: there were people with authority over me, and if you got the college president to give me an order then I would be required to do that. But, otherwise, no. Instructors can potentially have a fairly large amount of freedom.
Just to give another experience, though, in a different college, I recall hearing a math instructor explain that she covered only the information that she was told to. Every math instructor in the college had the same orders from the Math Department, and every day each instructor was supposed to cover the exact same questions (from the book) as every other instructor. This instructor described a whole lot less freedom than what I experienced as an instructor (which is why I stated the first two sentences that I did).
No! But considering that feedback is a important part of self evaluation you probably should give some feedback other than grades. Giving out at least some answers can be of great help.
This is a bit of a two edged sword. On the otherhand students should know how they were graded, to check for mistakes. So they should be able to evaluate this somehow, even in the case that they are failing badly. But then you can nolonger recycle the questions as easily and some students take the short route to passing.
In any case make sure the policy is well defined.
First, it depends very much on the level of the class.
When I taught junior high and high school, I naturally went over solutions to major problems and tests in detail in class. Not that many students take it seriously, but we try. Providing model solutions and teaching students how to write properly is a vital part of their education. Those of you who try to teach undergraduates, and those of you undergrads who have survived the trial by fire of leaving high school and meeting some slightly more real expectations, know that coaching students only to check the right box on multiple choice is deadly.
As has been pointed out above, giving numerical solutions and worse yet evaluating only those same numerical solutions is anti-educational; the learning process is directly short-circuited and the students go directly to copying the answer. "Giving answers" in that case means turning the whole process into a silly meaningless ritual and is to be avoided.
On the other hand, I took an excellent seminar in advanced combinatorics with the professor and author Kenneth Bogart, since tragically killed by a car. He was to be my advisor :-( In that seminar, we used a book on "problems in combinatorics" and nobody, professor or student, knew the "right answer". The goal of the class was to explore problems and to develop methods of solution when faced with the unknown. I well remember one day when the professor had left us with four or five problems to work on over the weekend. He asked if anyone had found a solution to #2. Three of us, out of six, raised our hands. He asked the first student to share his results. This was a stellar student, winner of many prizes. He came up to the board and wrote out a solution containing many strange symbols and a new function of his own invention. As far as we could follow at that speed, it was a good proof. Then the second student shared his results. He was a very smart and hard-working guy and had clearly spent the weekend in the library doing research. He wrote out his proof and referenced five theorems by five different authors nobody had before heard of. As far as we could follow the twists and turns of reasoning at that speed it was a good proof. Then I, and adult student, single mother returning to school after a few decades, went up to the board. I drew boxes. And boxes within boxes. I did a placement and counting argument. The professor was happy with all the answers; so happy with my style in fact that he asked to be my advisor. The point of the anecdote is that chasing after the mythical "right answer" is like chasing after unicorns. After you master rote arithmetic in elementary school -- and hopefully you get some problem-solving teaching even before that, starting early in primary school -- the topic of the math class is NOT chasing "right answers", the topic of the class is the PROCESS of using logical connections to solve problems. The answers in the back of the book are just a by-product of knowing how to solve problems.
Many people have reacted to this post more or less negatively. Clearly a lot of them feel a distaste with the question. They may not be able to articulate why they feel that distaste but it is there. Having spent my entire career in teaching at all levels, I have realized what the issue is. Elementary students and alas many secondary students being crammed for SAT's and far far too many underprepared teachers (most North American teachers last took a math class in Grade 10 and barely passed the terminal general level even then) and parents raised the same way. by poorly prepared teachers with bad curricula, all think that they must fill in "right answers" and do it snap-snap-snap at speed. This of course is antithetical to learning something in depth, to profound reasoning, to development of useful problem-solving skills for any career, or to any useful retention. Better secondary teachers and most university professors try to change this attitude but it is often too little, too late.
So the question is based on a false hypothesis. Hypothesis: Mathematics consists of a rigid set of procedures and formulas and there is a secret list of "right answers" to all and every question; Conclusion, professors, teachers and instructors must be forced to reveal the secrets to students instead of keeping them as a mystery that only they know, because we must nowadays be democratic and open up the sacred mysteries.
Answer: sorry, there is no secret book of "right answers". You are asking the wrong question.
The first question, as has been pointed out above, is "Is this person qualified to teach this subject?" This has to be judged overall; everyone has varied strengths and weaknesses and will be able to do more in some areas than others, but unfortunately yes there are some people out there who should not be in this position. If a high school math teacher cannot answer 90 percent of the questions in the textbook they are teaching, no they should not be there. Yes I have met several. And these are the people who seriously mislead students by rote copying of numerical answers.
The second question is "What am I supposed to be learning to do here?" I had one student in a college upgrading class who was brilliant in arithmetic and logic but absolutely refused to do algebra. He would never write an equation with an x, but instead wrote pages of closely argued logic and calculations. He got the "right answer" in the sense that his numbers agreed with the back of the text. He would have been a gem in a grad school class, if he could have gotten over this mental block. After the first test when he protested being marked down, I re-wrote every test question to be sure to say "Write an equation and solve it." No, he simply would not. I had to give him an F in Algebra because he would never do any algebra. A real pity and a great loss. It is the PROCESS you are meant to be learning, and in a calculus class you had better be using derivatives, in a linear algebra class matrices, in a Euclidean geometry proof theorems and deductions, and so on. So make sure you understand what processes you should know and how they are to be applied.
The third and final question to ask is "How do I know if my work is right or wrong, good or bad?" Way way back in elementary school, back in the Dark Ages when I was a child, we had an excellent arithmetic program which included plenty of problem-solving techniques and a host of methods for checking your own answers. When we reached basic algebra we were supposed to check our solutions to equations and show the check. Of course as children we hated it; it was so much writing and so tedious and what a waste of time. Luckily our teachers persisted. By the time I was in senior high school I was rarely dependent on either a teacher or an answer key to know what was going on. This dependence on an outside authority to validate you is another thing that irritates the people answering here.
So again, you are asking the wrong question based on a faulty hypothesis concerning what math and education are all about. It's a common enough false hypothesis. If you are a young student trapped in the system and it is your teachers feeding you this false hypothesis, very sorry, do the best you can, and read as much as you can outside of class and solve problems on places like SE to dop some real learning. It does get better. If you are already past the basics, well, sometimes we have to change our worldview. it is a real wrench at times but worth the effort. Anybody who has made it to advanced math probably remembers a wrench or two learning to look at things a new way and we are here to help.
The other answers have considered legal and pedagogical aspects, maybe sufficiently. I'd like to add another perspective: resource allocation. Professors (at least in my country, might differ in yours) have a host of duties, including
- (university) politics,
- supervision of PhD students,
- writing various reports and reviews on all kinds of things (scientific as well as non-scientific), and
- general management of the department.
It is simply impossible to pursue all these duties to perfection. Hence one of the most important decisions to be made by each professor is that of resource allocation: which fraction of his (and his employees') limited time does he or she devote to which of his duties?
Even if the professor fully believes that providing comprehensive solutions to homework problems would be desirable from a didactical point of view, it may still be a completely valid decision not to do so in order to perform better at other tasks. On a side note, I highly doubt that any dean would question such a decision.
Here are my answers to each of the questions I think you're asking.
- No, they aren't required, unless it's somewhere in your school policy--it's worthwhile to consider whom you think would do the requiring. I can't see most schools micromanaging their profs like that.
- No, I don't think they should be required, either administratively or philosophically. After all, the real point of the homework is the process.
- I do think it's wise for them to have the solutions ready, if they've made up their own problems, just to make sure they haven't flubbed something. Also, I think that, if I were teaching, I'd want to post the final answers. Again, the real point is doing the work to get to the answers, so posting the solutions gives students the chance to check their work and correct it before turning it in. That way the grade reflects what they've learned rather than where they started. (Along the same lines, I think that, ideally, homework should be attempted and graded at least twice, so the student can really engage in a feedback cycle with the material.)
- While having the solutions available can give you reassurance, you have the whole Internet (including this site!) to forge your way, and I can't tell you how lucky that is. I think you're more nervous about letting go of that safety rope, and you don't need it. Strike out on your homework confidently, and know that, pretty soon, you won't be concerned if the solutions aren't available.
- The best change I've made between graduating from undergrad in 2003 and starting grad school in 2016 is to use office hours like I'm the only student in the class. The difference between me at 21 and me at 35 is huge, and it's because now, I'm working full time and I have a family, so I'm paying for school with my own money and eking out every minute I can to spend in class and on homework. I do not waste my time, so if I don't understand, I ask a question in class. I don't care if it sounds stupid, or if everybody else knows it because my background is different than theirs, or if it's a little esoteric. If I need it to understand, I ask. Then I go to office hours and ask questions after class--last semester I went to my prof's office with questions after every single class.
If a student (almost finishing graduate one, but still one) can give his opinion, I think professors should give solutions, at every level.
If you consider them still students that have to do a homework, I think you will agree that they are still learning, still in the need for an explanation. So yes, after grading them, I think you should give the solution with the full reasoning that led to it, doing it live in a session if possible.
No, no rules are obliging you to do that, but as a professor I think your main interest is in how much the students learn, and the best way for them to learn is to let them try and after show what is the right way, to highlight their mistakes.
EDIT (to address the comments):
In Italy, where I study, every professor has a lot of liberty in the courses he gives. Every degree refers to a council where all the professors and some students (me and other two) decides about the rules and usually the content and the way a course is held (homeworks, written exams, oral exams etc) is decided mostly by the professor that gives the course. Some modifications, mostly about the content, can be started by the council, but it has really low power on the way the couse is given, on the material provided. If a professor would give homeworks without solutions, they could really do nothing about it because there is no rule that allow them to act, the professor has total control over his courses.