I am currently a graduate student, who will (hopefully!) graduate in the next year (or two..). I have slowly come to realize that I enjoy teaching, and consequently want to do more of it! My main reasons are such:


* to gain experience
* to bolster my CV
* to learn to be a better teacher


That last point is particularly important to me, because I feel I have received insufficient training in how to teach mathematics well.


Now, I have done the usual TA thing. For the past year, I have also been an adjunct instructor at a local four-year college, so I pretty much know what it's like to be "fully responsible" for a course. What I am looking for are challenging opportunities which allow me to do some - or all - of the following:


* teach fairly sophisticated math to bright high school students / undergraduates
* engage them in innovative thinking/research
* be consistently mentored/evaluated throughout the duration of this experience


Again, the last point is rather important to me. So my question is:



> 
> Do such programs exist?
> 
> 
> 


I am sure they do, but when Googling, I invariably come up with graduate summer schools, or "local" opportunities. (By "local" here, I mean those which are only eligible to students in that particular school's graduate program.) So I am hoping someone (or several people) here know more about it than Google does.


I know that most opportunities for this summer have probably already expired, but I want to stress I am not only focused on summer sessions. In particular, I would gladly forego my usual TA appointment for a semester, to be a part of a more difficult and rewarding experience somewhere else.


Finally, I am on the fence about whether this question should be CW or not; as of now, it isn't. If people feel it should be, I will change it.


Thanks in advance.



Teaching Experience for Graduate Students.
Many small liberal arts undergraduate colleges in the US have temporary adjunct positions
often or usually filled by new Ph.D.s. These colleges generally focus more attention on teaching than do research universities, and consequently have infrastructure for mentoring and improving teaching. Many have special fellowships whose goal is specifically to mentor young postdocs interested in a teaching career. At my school, these fellowships require teaching only six courses over a three-year appointment, a generous arrangement.


The US [National Postdoctoral Association](http://www.nationalpostdoc.org/careers/career-planning-resources/186-postdoctoral-teaching-fellowships) maintains a list of such teaching fellowships,
although I am uncertain of its comprehensiveness.
One can also find specific school fellowships by web-searching "postdoctoral teaching fellowships in mathematics."


I suspect analogous *summer* teaching opportunities would be less useful in terms of development,
but perhaps(?) easier to secure. There are many summer math programs for high-schools students;
teaching at one of these would be quite enjoyable. I can only mention examples (again, in the US) rather than point
you to a comprehensive list: [Hampshire College Summer Studies in Mathematics](http://en.wikipedia.org/wiki/Hampshire_College_Summer_Studies_in_Mathematics),
[Cornell Summer Math Institute](http://www.math.cornell.edu/~smi/) [Awesome Math at Cornell/UTDallas/UCSantaCruz](http://awesomemath.org/summer-program/), [Berkeley Math Path Summer Camp](http://mathcircle.berkeley.edu/index.php?options=bmc%7Csummerprograms2010%7CSummer%2520Camps), 
[Johns Hopkins Center for Talented Youth](http://cty.jhu.edu/), etc.


