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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 education research (specifically for the math/physics fields) 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 think (?) it may be more productive to set the hypothesis "Posting answers is good" and look for positive evidence supporting that. In some sense the opposing practice (following the null hypothesis) doesn't need answer keys to be bad; a merely neutral effect would support their position as well. $\endgroup$ – Daniel R. Collins Mar 8 '18 at 3:48
  • $\begingroup$ Just for clarification: Do you get the solutions for homework questions somewhere (i.e., during tutorials or office hours, but not published on the lecture web page), or don't you get them at all? $\endgroup$ – Uwe Mar 8 '18 at 15:45
  • $\begingroup$ We can contact most professors personally regarding questions, via email/office hours/after class, and they'll talk us through things; it isn't a "you shouldn't have any help figuring out the answer" stance. It's more of a "you should have to go to the trouble of discussing the answer, then solve it for yourself" idea. $\endgroup$ – WillG Mar 9 '18 at 5:44
  • $\begingroup$ There is a third alternative, besides giving or not giving solutions, which is to have students work the problems in the presence of an instructor, who can aid/guide/answer as he/she finds appropriate. $\endgroup$ – Dan Fox Mar 10 '18 at 9:51
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In the paper Research on teaching and learning Mathematics at the Tertiary level, by Biza, Victor-Giraldo, Hochmuth, Khakbaz, Rasmussen, recently published by Springer (ICME 13 Topical Surveys) you find at least some evidence supporting your professors' attitude. It is said there, in fact, that analyzing the way students use mathbooks, and in particular exercises, it was found that the large majority would use solved problems to look for procedures that could be line by line transported to the problem they were working on; which is exactly the opposite of thinking about the problem.

In all new experiences of IBL the emphasis, for example, is not on the answer but on working through it.

So i would say that the "conventional wisdom" that solutions re useful does not stand on a more solid ground than your professors approach.

As a personal experience I do not provide worked out solutions to my students, but I am encouraging them to come to office hours and in such case I do not refrain from a line to line analysis of their solutions. A procedure which is much more time consuming and tiring for me then posting solutions, so that "guest" speculation is, at least in my case, completely misguided.

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  • $\begingroup$ Thanks for the research paper, it's just the type of thing I was looking for. The fact that students tend to seek out similar worked examples and repeat those methods is perhaps a sign that many students look for an "easy way out" where possible. Still, it seems distinct from the situation with solution keys. In one case, you have "I'm working on problem A, but I'll copy the methods used in example B." Whereas with answer keys, it's more like "I've worked on problem A. Now I'll see how my professor solved problem A." $\endgroup$ – WillG Mar 9 '18 at 6:23
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I would be shocked if there were any research on this, either supporting the practice or against it. It does not seem like the kind of research question people study -- simultaneously too narrow to be of much interest to the math ed research community, and too broad to answer (which students? in which classes? etc.).

Having said that, it is certainly the case that many universities have exactly the opposite practice, at least at the undergraduate level. For instance, my university offers several years' worth of past exams with answer keys for undergraduate Calculus. (See http://www.math.lsa.umich.edu/courses/115/PastExams/index.html, http://www.math.lsa.umich.edu/courses/116/Exams/index.html, http://www.math.lsa.umich.edu/courses/215/17exampractice/index.html.) This is not limited to undergraduate studies, either: the same department also hosts past qualifying review examination papers with solutions: http://dept.math.lsa.umich.edu/graduate/qualifiers/index.html#PastExams.

Again, I doubt very much that there has been any research on the effect of this, but the conventional wisdom here seems to be that this is helpful. I think what you are encountering is simply a local custom, part of the culture of your department, based on intuition and opinion. Unfortunately most of what happens in undergraduate and graduate education fits that description.

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There is some broader research to the effect that feedback is helpful in learning (anything). And comparing (after effort) to an answer key is feedback. Even if you do it all right, there is the video game reward of seeing it. I think there is a lack of practical psychology not to understand that small rewards help drive behavior--students are not computers or machines or monks.

Also, correction of errors. Also, in some cases alternate methods.

Over the last 20 years, video has become much more prominent in coaching (even the lowest youth levels--coaches use their phones).

My speculation is that some of this attitude is driven by professors who don't want to be bothered and are academicians, not teachers.

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