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I plan to ask the following question on the main site, and not sure if it is relevant to the community. I will make the question community wiki.

I would like to ask about mathematics teaching say about the Moore Method, et cetera.

For example where I am at, they don't really dwell deeply into topics about say the dihedral group - e.g. its subgroup structure, conjugacy classes, etc and then ask us questions on them without full understanding.

I plan as well to discuss the effectiveness of structuring a course - let's call it MATH 1234 (real variables) around a textbook.

I know that this may be seen as a criticism/rant against an institution, but I hope that this question will be a chance for many mathematicians in many institutions around the world to share on how they teach and what they think should be done.

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    $\begingroup$ I am looking hard but failing to see a question. Might I respectfully suggest that as a first year undergraduate, you spend your time thinking about how to learn, and wait a little until you start thinking about how to teach. $\endgroup$ – Alex B. Oct 13 '11 at 5:57
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    $\begingroup$ @AlexB. It is related in a way the both of them. Reason being, I am classes where certain things are done in a way which I think is not proper, and would like to discuss them. I really don't think that there is a clear distinction between both. $\endgroup$ – user5783 Oct 13 '11 at 6:26
  • $\begingroup$ There certainly are positive things to be said for the Moore method, for a few subjects, one course only. $\endgroup$ – André Nicolas Oct 13 '11 at 6:42
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    $\begingroup$ @AndréNicolas What I would like to say is that I am not happy that in some courses, we touch on a few definitions and then say calculate all normal subgroups of this group. $\endgroup$ – user5783 Oct 13 '11 at 7:02
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    $\begingroup$ @Benjamin The site is not made, nor suitable for "discussing". Discussions should be carried out in a forum where posts are ordered chronologically and where random passers-by don't vote on them. I also still maintain that you could employ your time far better than discussing pedagogical issues that undergraduate lecturers face. If your lecturer's methods don't suit your way of learning, learn from a book that suits you. $\endgroup$ – Alex B. Oct 13 '11 at 9:08
  • $\begingroup$ @AlexB. I thought this site too was where one could discuss mathematics education considering the fact that it is important - otherwise why would people like Halmos or Polya spend time trying elaborate on it? $\endgroup$ – user5783 Oct 13 '11 at 22:17
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    $\begingroup$ @Benjamin: This site does not want discussions about math or math education. It just wants questions and answers. If you have a question about math education (and want an answer), then it is fine to ask about math education. It is not ok to discuss it here (there are other places for that, you might try MAA meetings, math ed colloquia, etc.). $\endgroup$ – Jack Schmidt Oct 13 '11 at 22:34
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    $\begingroup$ The quote from math.stackexchange.com/faq is: If your motivation for asking the question is “I would like to participate in a discussion about [blank]” then you should not be asking here. $\endgroup$ – Jack Schmidt Oct 13 '11 at 22:36
  • $\begingroup$ Actually, another good place to talk about a lot of this is with a study group. As long as your class is "modified" Moore method, then you are probably allowed to talk with your class mates about the problems. University is much too hard to do alone, so find a group to study with now. The people you work with now, can be the people you work with for the next four years and sometimes for much longer. $\endgroup$ – Jack Schmidt Oct 13 '11 at 22:40
  • $\begingroup$ @JackSchmidt The thing is, there are not many people I know of my peers that are interested in math. I probably know one or two people who are honours students, but apart from that no one really. $\endgroup$ – user5783 Oct 14 '11 at 2:09
  • $\begingroup$ I've added link to wikipedia, since there might be people here which do not know what Moore method is. I believe I have heard about Texas method, which seems to be something very similar (if not the same). $\endgroup$ – Martin Sleziak Oct 14 '11 at 11:04
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I am now turning my comments into an answer so that people can vote on them properly.

1) You are not proposing to ask a question, but to start a discussion. This site is not made, nor suitable for discussions. From the FAQ:

You should only ask practical, answerable questions based on actual problems that you face. Chatty, open-ended questions diminish the usefulness of our site and push other questions off the front page... If your motivation for asking the question is “I would like to participate in a discussion about __”, then you should not be asking here.

2) You are a first year undergraduate who is proposing to start a discussion about approaches to teaching undergraduate mathematics. In all likelihood, you have barely seen any undergraduate mathematics (unless you are far ahead of your peer group), and it would be extremely surprising if you had an informed view on pedagogical issues related to this material. For example, your wish to discuss certain issues is based on the fact that the lecturer's approach doesn't seem to resonate well with your mode of thinking, but you admit yourself that you have not spoken with any other fellow students about it. One person's preferred mode of learning is not nearly enough data to conclude that your lecturer's way of teaching is "not proper".

If I remember my first few years an university correctly, I was quite busy enough trying to work out the best modes of learning. You would do well to divert your energy in this direction, and not worry about the best modes of teaching the material you are being taught (no, these two are not at all the same, and you conflating the two just reinforces point 2 above).

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  • $\begingroup$ In that case, what would you advise to be the best of learning a course where there is a lot of material, not a lot of depth and we have to learn them quickly for exams? $\endgroup$ – user5783 Oct 14 '11 at 3:40
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    $\begingroup$ Dear Alex B: I don't agree with the sentiment that a first-year undergraduate should not think about teaching. First, the OP may very well want to become an educator himself, in which case thinking about such questions seems to me perfectly reasonable. Even otherwise, there are numerous opportunities in which undergraduates may unofficially play the role of a teacher to some small degree: for instance, as TAs for a class, or through high school mentoring programs. $\endgroup$ – Akhil Mathew Oct 14 '11 at 4:08
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    $\begingroup$ Dear Akhil, you are right, I should have been more specific. Of course, an undergrad has plenty of opportunities to teach and to think about teaching. But to teach something well, one normally needs to know much more than the actual material one teaches. Therefore, a first year undergraduate should not spend much time on thinking about undergraduate teaching (though I realise that there are also exceptional undergrads). Of course, he is welcome to think about teaching at other levels (indeed, I myself had taught mathematics at various levels in various settings by the time I started uni). $\endgroup$ – Alex B. Oct 14 '11 at 4:27
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    $\begingroup$ More to the point: Noone should think about how to teach subgroups if they cannot determine the subgroups of the dihedral group. $\endgroup$ – Phira Oct 14 '11 at 10:28
  • $\begingroup$ @Benjamin: How would we know what you mean by "lot of material", "not a lot of depth", and "quickly"? Maybe you just have to spend more time applying the definitions to examples? $\endgroup$ – Phira Oct 14 '11 at 10:31
  • $\begingroup$ Dear Alex, Thanks for your clarifications. $\endgroup$ – Akhil Mathew Oct 14 '11 at 23:03
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If you have "learned" the definition of, say, subgroups, but you don't know how to compute the subgroups of the dihedral group, then you have not really learned what a subgroup is.

But it is unclear what your point is. You seem to be complaining that you have to calculate properties of the dihedral group at an exam without having seen the exact same properties of the dihedral group before. This is not a bad thing, this is the point of learning a concept.

It seems to me that you complain that you don't understand the concepts that you have seen in your lecture and that you are convinced that this is the fault of the bad teaching. How do you know? Is there a parallel lecture whose students ace the same exam?

I would personally welcome a question that asks something like this (although I am not at all sure that other people feel the same):

In my first year lecture I have learned the definition of a subgroup, but I am not able to apply it to new groups that I have not seen in the lecture. How can I train the ability to apply definitions to new objects?

If the same question is asked from the point of view of the teacher, I would expect the teacher to know enough about mathematics and teaching to ask a more mathematical question more to the point, say, "What book on group theory contains lots of easy examples for calculating centers, subgroups etc that I can use as easy exercises for my students?"

This is certainly not a good place to discuss teaching strategies and not even a good place to ask for resources on certain teaching strategies.

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  • $\begingroup$ @BenjaminLim: In other words, you would have liked to see the dihedral group handled in lecture, and then given exercises to show you how to do it more easily/elegantly than whatever the instructor did in lecture? I'm sorry, but that seems like (i) asking the instructor to show you how dumb he is in doing things the hard way when there is a simpler and more elegant way of doing it that you will "find" through exercises; and (ii) a waste of lecture time. At least, that what it seems to me. $\endgroup$ – Arturo Magidin Oct 14 '11 at 16:22
  • $\begingroup$ @Benjamin Can you please write more clearly what you are talking about? What part of my post makes you clarify that your are not talking about "bashing out case by case"? And what exactly do you mean with "depth" here? Do you or don't you agree that you should be able to apply the definition of subgroups to a group you have never seen before the exam? $\endgroup$ – Phira Oct 14 '11 at 17:01
  • $\begingroup$ @ArturoMagidin Maybe I was not so clear in the beginning, but that was not what I meant. In any case, what would you suggest to a student to do if we have to learn a lot of material quickly? I always have the worry that by rushing through I will never be able to understand the concepts deep enough... $\endgroup$ – user5783 Oct 14 '11 at 21:25
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    $\begingroup$ It's a trite but true observation that you never understand the concepts deeply enough until you take the next course that requires them. Some would say that you never understand the concepts deeply enough until you have to teach the course yourself! $\endgroup$ – Gerry Myerson Oct 14 '11 at 21:51
  • $\begingroup$ @BenjaminLim: I'll echo Gerry's sentiment. It's hard to say when you "understand the concepts deep enough". Mostly, it takes using the material. I think you are getting frustrated for some reason, and have decided that it's the instruction method; and that you are trying to find someone to tell you that you are right and it's all the fault of an instructor doing things wrong somehow. $\endgroup$ – Arturo Magidin Oct 15 '11 at 2:06
  • $\begingroup$ @ArturoMagidin You are probably right in a certain way, however I am not doing badly in assignments or anything in the course. I have spoken to someone today and he has advised me accordingly. $\endgroup$ – user5783 Oct 15 '11 at 9:22
  • $\begingroup$ @BenjaminLim: I did not mean to imply (nor do I think I did) that you were doing badly; rather, I said that you are getting frustrated. I know that was frustrated in many a class in which I did well, so while one is often frustrated in classes that one is not doing well on, that is not the only possible source of frustration. $\endgroup$ – Arturo Magidin Oct 15 '11 at 19:22
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    $\begingroup$ @Gerry: And some would say that you (not you, specifically!) never understand the concepts deeply enough. $\endgroup$ – Pete L. Clark Oct 15 '11 at 19:33

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