To show or not to show work

Re:To show or not to show work by chongli on Tuesday October 01, 2019 @12:16AM (#21122010)

As a 3rd year math student, I’ve seldom been required to show my work unless it was a proof. On the other hand, a lot of the questions on exams gave me a full page and awarded part marks for demonstrating any correct steps, even if the final answer was incorrect or even missing. Some of these exams were so hard you tended to pass on part marks alone and few people managed to get all the right answers. If you did know the answer you could just write it down and get full marks. That’s demonstrating a lot of self confidence (or hubris) however.

One thing I think might be interesting to try is to give the student the answer to the problem and ask them to show how to arrive at that answer. This could give them the feeling that their steps actually matter, rather than simply satisfying a teacher’s demand. For example, you could ask:

    1) Show that lim x->0 sin(2x)/x = 2

That way a student can’t get away with just writing 2.

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Re:To show or not to show work by Rainymood on Tuesday October 01, 2019 @04:32AM (#21123240)

These types of questions are nice because they allow you (1) to check your work (2) work towards the answer. On the other hand, I feel like these questions make you think less and make you less cautious about your moves because "you know where to go." Furthermore, I had this multiple times in exams where the "supposed" answer was something like n^(-1) and I was so damned sure I did everything correct and my answer was n^(-1/2). I literally wrote on my paper:

"I know that the answer is n^(-1) but I did all the steps and checked it multiple times and did not get a different answer than n^(-1/2). Sorry."

Of course, I was right and it was a small typo. A good friend of mine /crossed out/ his answer because /he thought it was wrong/ (he had my answer).

Luckily the question was scrapped and I got bonus points, but my point stands. My friend wasted a lot of time staring at a wrong answer -- giving him less time to think about the other questions!

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Re:To show or not to show work by lonelappde on Tuesday October 01, 2019 @01:16AM (#21122249)

That's tautological. Showing work is what a proof is.

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Re:To show or not to show work by ves on Tuesday October 01, 2019 @01:44AM (#21122373)

I occasionally ran into exam questions that were "discuss the motivation behind making this maneuver instead of some other maneuver in this proof we discussed in class," which is a sort of meta-showing-of-work.

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Re:To show or not to show work by im3w1l on Tuesday October 01, 2019 @04:40AM (#21123289)

Is it? Proof to me means I can say "here's the answer" without saying how I found it, maybe I just tried a few random things, and just prove that it's correct.

For instance, for a polynomial I might show that my answer solves the equation, and that I have as many solutions as the degree.

Maybe that goes for "show your work" too? As I didn't study in the US, I don't know what a teacher would expect when saying that particular phrase.

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Re:To show or not to show work by HarryHirsch on Tuesday October 01, 2019 @12:45PM (#21127548)

Yes, heuristics is important and underrated in math education, especially in the US, where they place excessive faith in rote learning.

Proofs are sometimes a little unsatisfactory, the theorem is proved satisfactorily, but all the traces how you got to the proof are covered.

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Re:To show or not to show work by 8note on Tuesday October 01, 2019 @11:34AM (#21126522)

if you're asking a proof question, it will be something of the form "prove that there are as many solutions as the degree for all polynomials" rather than a specific polynomial.

if you skip writing down each step in the proof, aka your work, you haven't completed the proof.

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