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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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    I wouldn't expect this to be subject-dependent, though I'd expect assignments and tests in college courses which are amenable to an answer key are more common in the sciences. I'm seeing a few relevant-looking results on a google search for educational impact of "solution keys", though they look pretty heavily couched in research language, so I'm unable to tell from a cursory look if they actually are relevant. – zibadawa timmy Mar 7 '18 at 7:18
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    I do not know if that helps, but there is a vast neuroscience literature on Reinforcement Learning, and how it is, for now, the dominant theoretical framework for learning in humans. Briefly, in order to learn, you need some measure of how well you are doing. On the other hand, past exams are often provided for students to understand the format and level of examination, and not for learning the material. – 101010111100 Mar 7 '18 at 8:46
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    While it's not physics, you might be interested in asking the math education stack exchange. – Javier Mar 7 '18 at 20:09
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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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