8

I think it is very possible to have real, meaningful research projects at all levels. As an example, I had 2 of my students in Calc 2 work on a project which started with the idea "Can we define a tangent circle instead of a tangent line?" They started by finding a formula for the center and radius of a circle given three non-colinear points: https://www....


5

Perhaps a research project could be replaced by an independent study project. The idea is to learn more math, in a more independent way. The student would still have to produce something to show what they've learned (although if the teacher found it easier, they could instead require an oral explanation of the content learned). I learned a lot on the ...


3

Opinion: I think they get enough exposure to writing reports in other subjects. Think the time is better used for drill and exams, than for writing a report. The one benefit might be learning to search the literature, but even that is probably much better done in history or science where, although rather difficult, the papers are still comprehensible. (...


3

I can only help with (3). A. This behavior is not unusual and not just with intuitionists. It's good to be able to do things in your head, but you need to "know your head" and when you will have issues. B. In general, when doing pen and paper you should try to write down all the steps prone to an error. Of course there's a balancing point. But ...


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