This is a physics education research (PER) question. Interpreted properly, it is NOT an opinion-based question!

I am a physics grad student and several of my professors have stated that they are against the idea of posting answer keys (i.e., worked solutions) for homework and/or tests (after the assignment has been completed by the student, of course). Their argument is that having an "answer cheat sheet" discourages the student from thinking critically about the problem and presents the opportunity for students to feel like they understand how to solve a problem without actually going through the rigor themselves. In fact, the entire department apparently takes the same stance with regards to posting past qualifying exams online: they post the past exams to use for studying, but not answer keys.

My question: Does any published PER examine the pedagogical benefits and downsides of posting answer keys/worked solutions for students? I tried searching for this online, but had little success finding anything. If anyone could point me toward legitimate research on this topic, I'd appreciate it.

I should add that I was a high school physics teacher for two years, and within that arena it seemed unanimously accepted that making solutions and answer keys available was the right educational strategy. Hence my skepticism of my professors'/department's rationale. But I'm willing to see what the research says!

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    $\begingroup$ I'm voting to close this question as off-topic because it's mostly about pedagogy of physics and not physics concepts. Academia may be better suited. $\endgroup$ – Kyle Kanos Mar 7 '18 at 3:19
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    $\begingroup$ I'd add that as far as I can tell, we don't have a codified policy on physics education research questions, but as far as I can tell we've generally taken them to be de facto off topic. (See e.g. this I think this is a good question, though, and it might find a good home at a site where such questions are considered on topic. You might try Academia, as Kyle mentioned, or Mathematics Educators. $\endgroup$ – David Z Mar 7 '18 at 3:45
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    $\begingroup$ We don't have a policy on PER, and I am of two minds on the matter. On one hand, the discipline is about learning and education. On the other it is a discipline pursued by physicists: no one gets into it after taking a degree in education. $\endgroup$ – dmckee --- ex-moderator kitten Mar 7 '18 at 3:53
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    $\begingroup$ The problem with any pedagogical approach is that it presumes the generality of every student's character and attitude at all times. For a student that is capable, intrinsically interested in the specific problem, and naturally critical and integrative with knowledge, cheat sheets and reference materials are likely to be a boon. Others deviating from this prescription must be identified and dragged through the sand. (1/2) $\endgroup$ – Steve Mar 7 '18 at 4:44
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    $\begingroup$ @Qmechanic I do not know if there are studies about providing solutions (but the Finnish exam board started doing so a few years ago, I can see if that decision was based on any research). Others here might know about relevant publications in for example the American Journal of Physics, which often publishes PER research. I am surprised if such material would be regarded as off topic here. $\endgroup$ – Pieter Mar 7 '18 at 14:40

Since this question was not properly moved to Academia, I will quote the answer. Perhaps some people, like me, would me interested but are not part of Academia.

I won't have a hard answer, especially one specific to physics. I did find some papers that looked somewhat relevant though. Please take this with a grain of salt as I've mostly just skimmed them, and this isn't my academic area of expertise.

This paper found that comparing different methods of reaching an answer was more effective than looking at methods of solution sequentially. This says more about how students might best use an answer key than whether they should get one.

This 1992 paper found that practice examining worked problems or completing partially worked problems was more effective at transferring knowledge than conventional problem solving. In keeping with the first paper, this paper by the same author showed that variability in the examined worked problems was also important. This would indicate that for a subject that students generally have a hard time wrapping their head around, like physics, the ability to study completed problems at the same time may be a useful tool.

However this excellent article discusses how you can go too far the other way, with advanced learners fairing better without information they already know clogging up their study material. Overall this makes a mixed approach (some problems with worked answers for comparison, and some problems without available answers) seem best if the strength of the prior knowledge of students is unknown. (Assuming students gravitate to the type of material best for their individual needs.)

(opinion on practicality) However I'd note that in the context of a college class, giving a set of completed problems, rather than additional turned-in assignments, doesn't create a pretesting point-of-accountability to further incentivise study. Also your department policy may relate to things like professors who sometimes want to reuse questions from previous tests. So attempting to change may be resisted because you may unintentionally be asking other professors to take on more unwanted workload.

Some of the research terms I found that you might want to look at further include 'Cognitive Load Theory', 'Aptitude-Treatment Interactions', 'Expertise Reversal Effect', and 'Instructional Science'. You'd probably also be well served by skimming through a proper textbook on education techniques if you can find one that's suitably well cited.

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