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What is the best way to use online mathematics forums, such as mathematics.stackexchange.com or Khan Academy, in mathematics instruction?

I regularly encourage my undergraduate students to participate on mathematics.stackexchange.com (and my graduate students are all on mathoverflow.net). I tell them to post any questions they might have about their homework or other topics we've discussed in class, and I am confident that they can get high-quality mathematical guidance by doing so. Many of my students have learned a lot this way. I give extra credit to any student who can accumulate sufficient reputation points, and I am significantly more impressed by students who do by answering questions rather than merely asking them. Some of my students have gotten hooked and are now active participants.

What kind of experiences do other instructors have using math.stackexchange as part of their instructional experience? Has it been successful? How have you encouraged your students to take part? Do you give credit for earning reputation points? Do you worry about the students conspiring to vote each other up? Do you discuss explicitly in class the proper way to ask a mathematics question in such a forum? What are the main stumbling issues and success stories?

For my part, it has mostly been really great, with many students getting help with issues with which they were struggling. Some of my undergraduate students, however, are initially stung by a few downvotes or critical remarks on math.SE as they ask their first few questions, when they do not yet know the proper way to ask. Some are put off by this and are too timid to participate more fully, but I always encourage them to try to preservere. Others carry on and end up asking and answering a lot of math questions there, and I believe they really learn a lot that way.

I have less experience with Khan Academy with my students, since the level is much lower, but I know from experience with my elementary school children that the Khan Academy is an excellent way to learn math. Please post an answer if you have experience using this or some other interactive online mathematics forum in your classes.

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  • $\begingroup$ Are these current/potential math majors? Or do you encourage any undergraduate students to visit math.se? $\endgroup$ – Brendan W. Sullivan Mar 23 '14 at 5:19
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    $\begingroup$ @brendansullivan07, I encourage all my undergraduates to use math.SE, whether they are math majors or not. Does it matter? $\endgroup$ – JDH Mar 23 '14 at 12:00
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I started strongly encouraging my students to participate in math.SE about a year ago. Excluding this year it was all with third year students taking group theory and/or complex analysis. This year I'm also teaching discrete maths to first year students.

What I notice is that those students who take the few hours to climb the learning curve for properly using math.SE profit enormously. It is clear that it is not primarily the strong or weak students who opt for using math.SE and they all struggle in the beginning until they figure it out. I try to help them out by giving encouraging answers and comments and improving their questions by editing them. I experimented for a short while with giving extra credit for reputation earners but I found it to be too much trouble for me so I stopped with that.

Last year I even held a workshop for undergrads on how to use math.SE but I don't have any records on the participants and how/if they used it later on.

My impression is that most students, if not promised extra credit, are too intimidated to participate. Many are ashamed to ask questions in an open forum (and then I recommend to them to use a nickname). However, those students who do figure it out perform far better than their peers.

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  • $\begingroup$ How do you become aware of when they ask a question? Do you ask them to let you know their user names? $\endgroup$ – JDH Mar 23 '14 at 13:19
  • $\begingroup$ Sometimes I just see the question being asked and I recognize it as a question I assigned as homework or tutorial questions. I also tell them they can tag me in the question if they want me to see it. And I tell them to email me questions regarding math.SE answers they got together with the link to the question. $\endgroup$ – Ittay Weiss Mar 23 '14 at 21:07
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This is an essential question. Thank you for asking it. Let me to mention some points on interactions of mathematics forums and usual academic mathematics instruction.

1. Love this point? Read more here!

  • A very successful way for introducing online math forums to people including students and teachers (which I usually use) is inciting their sense of curiosity to know what is going on in these forums. To do this one can use several methods. The simplest way is explaining an interesting and "unusual" idea which can be found in MO/MSE "uniquely". The uniqueness is important. They should be convinced that there are something special in online math forums which cannot be found in the usual texts and courses.

2. Search for ideas not for solutions!

  • Form the point of view of your students to consider online math forums as a source of interesting ideas not an easy tool for solving their problems. The first one leads them to become great adventurer researchers interested in new point of views and unknown realms of knowledge and the second one leads them to become lazy students who are searching for shortcuts continuously.

3. Need your teacher's help? Find him/her online when you want!

  • In a math department when some of its faculty members are continuously present in a particular online forum like MO it is a good idea to let students know that they can have a direct access to their teachers/advisers by participating in these forums. Surely it could be very interesting for both graduate and undergraduate students because each teacher has a limited meeting time per week.

4. Teaching MathOverflow as a part of Teaching Math.

  • It could be a good idea if those teachers who are active users of online math forums explain good asking/answering techniques in one of their lectures during their courses. One lecture per each course is completely enough and natural because one can say:
  • Dear students, in the last lecture I told you there are some useful online math forums which can help you in many aspects but like any other thing you should know how to use it! Let me to explain more...

5. Don't be so shy! No one is perfect!

  • Online math forums like real societies are full of the different persons with different personalities. One should be aware of this point that any situation is possible in these communities and so he/she should know how to react these actions. Frankly speaking unfortunately in some aspects the culture of MO (and MSE) is too unfriendly. There are users who like to call the others silly (to prove that they are so clever!). Some others are too dominative. Somebodies are narcist. Some others are good but had a bad day! There are people who don't know when they should use an implicit sentence (instead of an explicit one) to refer a specific problem on somebody's act/post/comment and so on. These aggressive behaviors could be done against anybody even against the top users. (Unfortunately recently in one of the MO set theory posts I found a bad comment by one of the good users of MO against one of your helpful comments. I don't want to mention the case explicitly but this shows that an aggressive act could be happened even for the best users of online professional forums). What one of your new students should do in such a situation? Surely you can help them about it with your advisement. What I can say to them is:
  • Don't struggle with people at all. If you are not agree with their opinion simply ignore their critic remarks and do what you want.
  • Note to friendly admonitions and use them but don't take the critics too serious. No one is perfect even the bests.
  • Some people are xenophobic against new users of the community and conservative about new ideas and methods. If you think you have something new to say don't be so shy to explain and defend it peacefully.

6. Cheating Here! Cheating There! Cheating Everywhere!

  • If you are encouraging your students to participate in MO/MSE (which is very good) please don't make it too formal for them. Math forums should be interesting for students by their usefulness as a place which young students can find precious ideas, talk with the bests of the field and feel free to share their own ideas with professionals. These are enough to encourage them for contributing continuously in the community and considering the quality of their participation as a part of their grades or a type of homeworks causes an expected phenomenon, cheating! Using an inaccurate formal numerical criterion like MO/MSE reputation makes this approach more harmful. Your face to face comments about your students contribution on MO/MSE could be much more helpful. For example:
  • Alice! I like your last post in MSE very much, if you are interested in exploring the idea you can find these references useful. Please let me know about the result of your research. What is your idea about having a short talk about the subject next week? I am sure it could be interesting for your friends too.
  • Bob! There is a very nice idea in your recent MO post but they closed it because you didn't use some asking techniques which I explained in my "How to ask a question?" lecture last month. Let me to show you how to do this.

7. A Science Fiction Future.

Network is changing the world. Let's consider 2050 A.D. when we are grandpas. It is possible to imagine online mega universities (at least in theoretical sciences like mathematics) with thousands of students and hundreds of teachers all around the world. You can wake up in your home in an island of pacific ocean, participate in set theory course of Prof. Chen at China in morning, attend the lecture of Dr. Arroway in US at afternoon and talk to Prof. X in Vega at the evening because based on Dr. Arroway's lecture, you are curious to know more about "the notion of infinity on the infinitely distant planets" (Hamming's famous paper, Mathematics on a Distant Planet is related). The current online math forums are grandpas of such world wide universities. Nowadays we can buy and sell things online so it is completely reasonable to imagin a not too far day which we can learn and teach mathematics online.

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    $\begingroup$ "A very successful way for introducing online math forums to people including students and teachers (which I usually use) is inciting their sense of curiosity to know what is going on in these forums." I like this! Once, as I was browsing MO for ideas for a measure-theory course, and came across a lovely quote by Tao about convolution (mathoverflow.net/a/5916/2383). I pointed the students to it, and asked them to explain (as one of the homework problem) what they thought it meant. $\endgroup$ – LSpice Sep 6 '14 at 7:21

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