Important matter for debate: optimal amount of time to struggle over hard problems. Watch

jameshyland29
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I've read almost everywhere I've seen the issue addressed that it's always better to err on the side of spending too long rather than not long enough struggling over hard problems: my question is, why? Personally I suspect the advice might amount to a bit of an old wives' tale that's become a piece of gospel, propagated mostly for reasons such as the sense of achievement that results from long battles hard won. My own experience so far has been that I typically know after a minute or so whether or not I'm going to be able to do a problem, and if I'm not, then I rarely feel as though I've gained much clarity from continuing to struggle with a relatively blank mind: I recognise that the struggle is about stimulating creativity and clarification of present knowledge, but my experience has suggested that the time spent struggling might be better spent reflecting on the correct way to do a problem after learning how to do it, rather than potentially going down a lot of wrong roads, and afterwards not always being certain why they haven't worked out.

I'd be very interested to hear why advocates of the struggle believe it to be the best way.
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casperyc
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Outside lessons: as much time as you can spend(enjoy)

Exam: 1 minite per mark.
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DFranklin
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(Original post by jameshyland29)
I've read almost everywhere I've seen the issue addressed that it's always better to err on the side of spending too long rather than not long enough struggling over hard problems: my question is, why? Personally I suspect the advice might amount to a bit of an old wives' tale that's become a piece of gospel, propagated mostly for reasons such as the sense of achievement that results from long battles hard won. My own experience so far has been that I typically know after a minute or so whether or not I'm going to be able to do a problem, and if I'm not, then I rarely feel as though I've gained much clarity from continuing to struggle with a relatively blank mind: I recognise that the struggle is about stimulating creativity and clarification of present knowledge, but my experience has suggested that the time spent struggling might be better spent reflecting on the correct way to do a problem after learning how to do it, rather than potentially going down a lot of wrong roads, and afterwards not always being certain why they haven't worked out.

I'd be very interested to hear why advocates of the struggle believe it to be the best way.
So, most fundamentally; if you're only spending a minute trying to work out how to do a problem, then you're not getting a lot of practice at solving problems where it takes more than a minute to see what to do, and you're not going to get appreciably better at it.

Of course, if you don't actually have a *clue* how to solve a problem (e.g. you don't actually understand the material it's based on), then flailing around for hours on end isn't going to be terribly productive either. In which case you may well get frustrated with the "old wives' tale".

There are other factors, such as your familiarity with the material, and how difficult the problem is for your current level of development. I think when you are faced with harder problems than you're used to, it's natural to take a long time to solve each problem (and not to be able to solve many of them). I think this is all part of the learning curve - I know myself that when I'm more passive and just look up solutions, I don't learn nearly as much from them. But when you're at a point where you can usually answer the questions reasonably well, but there's a particular question you're stuck on, then it's a lot more reasonable to quickly say "I don't think I'm getting anywhere here - I just want to see how this should be done".

It must be said that "in my day", you didn't really have much choice (at STEP/S-level) but to slog through by yourself; there weren't a lot of easily available solutions. So I might be a little biased (although I have done the "use someone elses solutions" thing at degree level, and I didn't think I learned much that way). But since model solutions have become so easily available, I have *certainly* seen a marked increase of people on TSR attempting STEP/MAT who say "I've gone through all the questions, but I don't feel ready" (and then frequently do badly in the exams). It also feels there are a lot more people who don't seem to know "how to try to solve problems" - test cases, sanity checks, trying to solve a simpler version etc.

As a particular point have to say that "a minute or so" is really too little time to decide you can't do a question (obviously it's fine if you decide you *can* do it!) . I frequently spend more time than that deciding how to approach even STEP problems, let alone undergraduate / graduate problems.
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