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"Course-based undergraduate research experiences" (CUREs, or CBEs) are being explored in various STEM fields, especially biology, chemistry, geology. Here is one geology link that gives a flavor: "Are you looking for a CURE?" In the US, some of this activity is funded by the National Science Foundation (NSF); e.g., see this Meeting Report. One characteristic of CUREs is that the research is "authentic": this is not just problem-based learning, but rather explorations whose outcome is unknown both to the students and to the instructor, and ideally unknown to anyone.

Has anyone attempted course-based research in undergraduate math courses?

I am particularly interested in lower-level math courses, e.g., Discrete Math, but would appreciate hearing of (or links to) any explorations along these lines.

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    $\begingroup$ Great question! I've been thinking about this since my current institution has internal funding for CURE like programs, and I have not yet been able to come up with a good research topic that is approachable to undergraduates. (It doesn't help that my institution's program is designed for freshmen and sophomores.) $\endgroup$ – Willie Wong Aug 19 '16 at 14:36
  • $\begingroup$ @WillieWong: Yes, it seems efforts are primarily focused on beginning courses. It would not be so difficult to use CURE in an advanced topics course. But I thinking of Theory of Computation, which is roughly equivalent to Discrete Mathematics. $\endgroup$ – Joseph O'Rourke Aug 19 '16 at 21:42
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    $\begingroup$ I'm not entirely sure of what counts as CURE, but I feel like Alan Schoenfeld described teaching a math course that involves something like this. He may have written about it in "Mathematical Problem Solving." $\endgroup$ – Noah Sep 11 '16 at 23:55
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Yes, however there aren't lots of great resources. For instance, I have a friend who taught a combinatorial game theory course that turned into research for many students, but I don't think he wrote anything up as a resource for "how to do it".

So I don't have any great insight into this, but there are a some papers in PRIMUS you may find useful if you can get access to them. (There is apparently even a special issue on undergrad research, perhaps some of those articles touch on class-based ones.) Note that they to some extent only indirectly touch on your question, though I think they all have some good models.

Full disclosure; I am currently an associate editor for this journal. But I'm posting these because they're the only ones I'm aware of - perhaps CMJ or another MAA journal would have some good similar articles? I'd love to see people post more answers to this important question.

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For years Bela Bajnok has been teaching such a course at Gettysburg College: go here for his description of the (series of) course(s) he teaches.

A new MAA-sponsored program called PIC Math might also be of interest to you. Here the research problems come from industry. A list of faculty who have been involved in the teaching of such a course is available.

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  • $\begingroup$ The course Bela Bajnok describes (in fact 3 courses it seems) are not integrating research into existing courses. It's not a new teaching method for existing curriculum. Rather, these are new courses created to give credit to undergraduates who do research. Furthermore, he mentions the students spend, many of them, 20 hours a week on this course. It seems to me this is not what the OP is really talking about as these courses only exist to support research, as opposed to decorating an existing course with "research". $\endgroup$ – James S. Cook Sep 14 '17 at 11:28

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