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Is there evidence in the education literature to support or refute the claim that students who are given problems without solutions to work out on their own do better on different problems in the future (assuming that they took the time to do the problems)? Does it matter if they get the problems correct/incorrect?

I know there is evidence that worked examples help (Sweller and Cooper in 1985 comes to mind as the first reference point). However is there benefit after providing worked examples to provide non-worked examples? Has there been any research justifying this?

The key here is has someone actually done the research supporting this. I do believe that not seeing answers to everything helps but I don't have proof of this.

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    $\begingroup$ Good question! My intuition certainly tells me that answer only keys detract from student learning as they discourage students from thinking about the question beyond a simple solution. I too would like to know of actual scholarship on this topic, however. It's certainly the case that students are confused about this, as indicated in this question. $\endgroup$ – Mark McClure Jul 24 at 15:48
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    $\begingroup$ I have no idea about a research on this topic and don't feel inclined to research it myself because I have my own opinion — of course. When I was a kid, my homework was just exercises and word problems with no answers. Solutions had to be provided. The homework was then graded. The exercises that caused the most errors for the students were explained at the blackboard with a complete solution. OTOH, the number of exercises to do was relatively small, which allowed to discuss them later. I think this is the best approach instead of zillions of exercises that ask for nothing more but a number. $\endgroup$ – Rusty Core Jul 24 at 16:41
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    $\begingroup$ Yes I have opinions as well but I'm tired of opinion based teaching and wouldn't mind trying some evidence based teaching. I'm also implicitly thinking something more high level (the kind of mathematics where photomath/WolframAlpha etc. wouldn't have a chance of giving the correct answer...). $\endgroup$ – CAB Jul 24 at 17:22
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    $\begingroup$ Related What's the point of exercises without answers. $\endgroup$ – Namaste Jul 24 at 18:41
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    $\begingroup$ Your title, "problems without solutions", is unclear. It seems to be talking about problems that have no solutions - a topic that is covered in elementary school math (usually because of insufficient information). After careful reading it seems that you are talking about Problems without Available Answers. Perhaps you should edit the title or question to make it clearer. $\endgroup$ – Amy B Jul 28 at 4:50
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I am assuming you mean that answers are not available in the back of the textbook for the exercises assigned. If no one does find research on this, it would be pretty hard to test. Students have access to photomath, which can solve their problems for them.

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    $\begingroup$ I just downloaded Photomath, which is pretty neat! But it is certainly quite limited. I hardly think that this (or WolframAlpha or Mathways or even Chegg) could be compared to a complete, reliable, and easily accessible answer key. $\endgroup$ – Mark McClure Jul 24 at 15:49
  • $\begingroup$ I didn't realize it could be downloaded. So that means phones out during tests are even more of a problem than I had realized. (I just finished teaching a college (but really high school level) geometry course in just 6 weeks. It was mostly high school students, and there was much more cheating than is usual in my classes. For the final exam, I had to have them all put their phones in their bags, zipped, while I watched, because so many phones came out during the previous test.) $\endgroup$ – Sue VanHattum Jul 26 at 14:00

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