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What points mathematicians need in an explanation about red herring names?

When I ask this question I put myself in the position of a novice wanting to learn the culture of professional mathematician culture, and I thought it's something a math educator would be interested. Since it seems that there are people don't see why it's on-topic here, I would like to make sure about it.

What do you think?

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First, thank you for moving this to meta! The issue is that the math educators stack exchange is a forum for discussing mathematics education, pedagogy, tactics, ideas and research (that is education research, not math research). Here, you're pointing out interesting linguistic facts about mathematical naming conventions, but it's not at all clear what they have to do with education. Unless you spell out clearly how your linguistic theorizing related to teaching students, this isn't a good question for the math educators stack exchange.

On a side note: I think you are also getting some push back because you are giving the impression that mathematicians don't think about language in a logical way. As an example, you use

  • "Formal definition: A representation U(G) on V is irreducible if there is no non-trivial invariant subspace V with respect to U(G). (Wu-Ki Tung, Definition 3.5)

  • My translation: When a representation on a space is reduced to the point that only that space and {0} are its only two subspaces that can hold their vectors from being pulled out, then we have an irreducible representation."

The formal definition is a very precise logical statement. Your translation is not a completely incorrect (and incoherent) description of the mathematics, it doesn't even respect the logical (propositional) syntax of the sentence. It makes it very hard to understand then what it is you're proposing.

If you're proposal is that we should first describe mathematics propositions in a way that a laymen would understand them your in luck! There is a lot of pedagogy on that very idea. If you're interested in having a discussion about how we teach students logical prose I would suggest doing a quick google search, reading a bit about the state of the field, and posting about your questions related to education. If you're interested in discussing how linguistic structure can be translated into logic, I would suggest posting to the linguistics stack exchange.

If you're interested in why mathematics is written the way it is, I would suggest reading (and writing, having critiqued!) a lot of higher math. What you'll find is that it's actually hard to be more clear than the formal definition above.

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  • $\begingroup$ Thank for your explanation. I think naming convention is not really about educating students, but about "educating" peer researchers. If this sense is accepted as an education activity, then I think it's on-topic. The translation I make is also to illustrate the linguistic aspect of the informal proposition, not the logical one that mathematicians trying to aim at. It is intended to capture the mental state when a student first trying to understand the concept, and thus is unavoidably imprecise and unclear to someone who has gotten it. $\endgroup$ – Ooker Mar 8 '19 at 18:23
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    $\begingroup$ No problem. Yeah, this exchange is about education focused on teaching mathematics to students. I would also say if you're interested in how students perceive logical sentences our friends in analytic philosophy have thought very deeply about and written a lot on this subject. $\endgroup$ – Nate Bade Mar 8 '19 at 19:02
  • $\begingroup$ thanks. I ask about this on Math Meta: Are questions about professional mathematician culture and language on-topic? $\endgroup$ – Ooker Mar 9 '19 at 3:32
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    $\begingroup$ "Unless you spell out clearly how your linguistic theorizing related to teaching students, this isn't a good question for the math educators stack exchange." - exactly. I actually could totally imagine such a question, actually, e.g. with the concept of noncommutative rings (the OP's question about noncommutative geometry is a bit high-level). But it was not articulated thus. $\endgroup$ – kcrisman Mar 9 '19 at 12:55
  • $\begingroup$ @kcrisman how about "what is more than just cognitive linguistics and cognitive psychology in transferring math knowledge?"? $\endgroup$ – Ooker Mar 11 '19 at 4:25
  • $\begingroup$ I don't even know what that is supposed to mean. What is more than cognitive *** in transferring any knowledge, or is there even such a thing as knowledge ... Sorry, but I fear the gulf between your idea and the specifications of this site (or any math-related site, your question honestly seems far broader) may be too great to bridge. $\endgroup$ – kcrisman Mar 11 '19 at 13:17
  • $\begingroup$ @Ooker I agree with that your idea currently is too broad. When using thick terms like "cognitive linguistics and cognitive psychology" is helps to clarify what you mean. For example social, ethical, structural and behavioral consideration are all non-cognnative (ex: Turns out lead levels effect the transfer of knowledge). I think you are interested in how logical sentences are broken down, understood and represented mentally by students. If you are interested in research on that topic that could be a question for this exchange. But your true interest might hew closer to linguistics. $\endgroup$ – Nate Bade Mar 11 '19 at 15:47
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    $\begingroup$ @NateBade how about "how do instructors help students understand red herring names?"? I suppose the answer is like "patiently explain the subtleties in the word", which is not a surprised answer. But I guess this is the best version to fit this site. $\endgroup$ – Ooker Mar 14 '19 at 0:52

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