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Too many students lack the luxuries of time and effort to mull exercises and problems. They must juggle MULTIPLE jobs to pay exorbitant tuition fees. Single parents or adult learners must prioritize their children or full time job. Presume these unquestionable harsh realities in the USA — please don't challenge these postulates herein.

They admit to me — after reading the textbook or watching lectures, they dive right into perusing full solutions, then asking questions about the full solution that bewilder them.

But they reaffirm this time saving method is craftier, and DOESN'T harm their learning or grades one tad! Rather than spending $t_1$ on attempting the solution (which they completely lack in reality), then $t_2$ on understanding parts of the solution that befuddle them — they find it shrewder to skip $t_1$ and start at $t_2$.

Are these students correct? Any peer reviewed evidence? Can commencing with, and tearing into, the full solutions — before and without attempting to solve exercises or problems at all — improve your learning and grades?

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    $\begingroup$ This really has nothing to do with math. You could ask the same about every other school subject: does looking at full answers to exercises without putting any effort into answering them yourself first improve learning? Why do you think looking at full solutions first should be a better idea rather than an excuse to get homework done faster? It isn’t even about school subjects. Do you expect someone can learn to swim or play a piano well (or really at all) by focusing more on watching other people swim or play a piano than on actually swimming or playing a piano themselves? $\endgroup$
    – KCd
    Jan 1, 2022 at 15:38
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    $\begingroup$ It depends on the goals. Is the point to pass the test, or to become more intelligent? $\endgroup$ Jan 1, 2022 at 17:39
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    $\begingroup$ Are you talking about situations where the result is something worth knowing (for example, the binomial theorem for positive integer exponents, and the problem is to prove this by some method) or about situations where the result is not necessarily worth knowing but the method of obtaining the result is worth knowing (for example, $\sum\limits_{n=1}^{\infty} \frac{n!}{n^n}$ is a convergent series, which can be shown by using the ratio test)? It seems to me that for the latter case, reading solutions is somewhat like watching people play tennis in order to become a better tennis player. $\endgroup$ Jan 1, 2022 at 18:42
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    $\begingroup$ (1) Some teachers assess in ways that reward this behavior and some don't, just as some teach in ways that require students to do the reading beforehand and some don't. (2) Most textbooks present "tearing into the full solutions" before presenting problems, but they call them "examples." They must think it's a good way to do things. I'm sure they'd advise students to solve problems, though. (3) Is "DOESN'T harm their learning" is self-assessment based on individual standards? Does that mean they pay their money and they're happy? For some the goal is a better job, not excellence in education. $\endgroup$
    – user1815
    Jan 1, 2022 at 19:16

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