When choosing names for arbitrary constants either during a lesson or while working with a single student, should one use$\{n_1,n_2,n_3,\dotsc\}$ or $\{n, n', n'', \dotsc\}$ or $\{a,b,c,\dotsc\}$? Is there any evidence that one of these is easier for students to work with than others? Or is less of a barrier to understanding concepts than others?
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9$\begingroup$ Boy, I really think this just depends so much on context. It would be exceedingly interesting to see even modestly 'scientific' research into this, and just as surprising to see that it had been done! In a one-on-one I'd go with making it clear things are different if they have no natural connection (so a,b,c) but could imagine any of these. $\endgroup$– kcrismanMay 6, 2019 at 1:56
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3$\begingroup$ This depends on scope. If you need one or two doohickies that are going to get used once then discarded, prime it up. If you need something slightly more permanent, but only need one or two of them, use distinct variable names ($a,b,c$ for constants, $i,j,k,\ell,m,n$ for integers, $w,x,y,z$ for real numbers, etc). If the number of new symbols needed is large (but countable), use subscripts. Of course, it is always possible to run out of symbols---I found need to use $\omega_{\ell}^{o}$ earlier today, which sucked (that superscript is a little oh, not a zero). $\endgroup$– Xander Henderson ♦May 6, 2019 at 4:44
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$\begingroup$ @XanderHenderson I think your comment makes a fine answer, maybe with a couple of examples. I'd encourage you to post it as an answer. $\endgroup$– amWhyMay 6, 2019 at 12:51
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$\begingroup$ @Namaste In the question, Mike seems to be asking for references. I don't have any peer reviewed research to cite, and have not thought about the issue from a pedagogical perspective (only from the perspective of what is practical for me). As such, I don't think that I can really provide a good answer to the question. $\endgroup$– Xander Henderson ♦May 6, 2019 at 12:53
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2$\begingroup$ I would put primes aside for derivatives, unless it is geometry, in which case A and A' are prime examples of using prime in cases of, say, similar figures. $\endgroup$– Rusty CoreMay 6, 2019 at 16:44
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If the context is integral calculus and/or differential equations, I would definitely use $C_1$, $C_2$, etc. After all the student is used to "${}+C$". So keep it as close to what they are used to seeing and thinking about.
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$\begingroup$ You fail to answer address the various contexts which suggest different answers for different contexts. (See @Xander 's discussion in his comment above.) And importantly, you fail to answer the question: "Is there any evidence that one of these is easier for students to work with than others?" $\endgroup$– amWhyMay 7, 2019 at 0:42
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$\begingroup$ As far as not answering every usage, I don't take anything back. I gave a specific answer for an important subset. That is still helpful. And I was upfront about the restriction (if the context is). As far as "evidence", I missed that requirement. My bad. I personally think it's a bit much to ask for Google Scholar searches when not showing your own first. But then that's SE for you lately. But, yeah, missed that. $\endgroup$– guestMay 7, 2019 at 0:46
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1$\begingroup$ Another benefit of this answer: In a calculus context, using primes is likely to result in confusion between the extra constants and derivatives of the earlier constants. $\endgroup$– JasperMay 8, 2019 at 22:56