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5

Thanks for the description of the kids level (below average). I actually think their time would be better spent on either doing remediation or advancement in their core topics or in just some useful use of the summer (archery, building stuff, whatever). This is NOT to discourage you, though. My advice would be to keep things light and fun. NOT rigor city....


5

This is around twice the workload (for the teacher and the students!) than during regular semesters. This means that stuff that has to "sink in" won't have time to do so. You need to take that into account. Talk to people who have taught this course (during the year, in summer), see if you can filch some notes (or at lest an outline).


4

What exactly do you want to accomplish? If it is helping a child who did poorly, I'd guess the most important ingredient is a patient tutor (probably with the same texts used during the year). If they are interested in looking deeper, perhaps a text book isn't ideal. If it is skipping ahead, better let them have their well-deserved vacation.


4

There will be an application form on the website during the application season. It gets removed during the rest of the year to make sure nobody wastes time filling it out when there's no hiring going on, but this ought to be clarified on the website. (I'll look into fixing this. Full disclosure: I've been involved with PROMYS in different ways over the ...


3

Dana Ernst has a fantastic collection of problems which he bases a course around at Northern Arizona University. Here is a link to the course: http://danaernst.com/teaching/mat220s18/ This is a collection of puzzles which do not require any background knowledge. So the focus can be purely on working on problem solving skills, communicating mathematics ...


3

Some local (or not) businesses may have fairly mathematical internships. For instance, a biotech company may have nontrivial graph theory or other discrete computational problems to solve that will require something analogous to math research, though without proofs. (I'm not making this example up.) Certain computer science internships would be heavily ...


1

The tags say "undergraduate-research", but the question seems broader than that. I'd like to point out that summer teaching is an excellent alternative to research, which can give the students a much better understanding of the material they think they know. At the advanced end, summer programs like PROMYS, Ross, Mathcamp and Hampshire hire undergraduate ...


1

As you're discovered, many such summer programs are limited to US citizens and permanent residents; my understanding is that this is due to the source of their funding. Nonetheless, some programs exist which are accessible to international students. Unfortunately, since the funding source is what limits participants to US citizens/permanent residents, ...


1

If you like mathematical physics. There is a summer school in Bogotá, Colombia. http://matematicas.uniandes.edu.co/~cursillo_gr/escuela2015/index_en.php


1

Well, many students simply won't want to learn more math during the summer, the chance that students will be more distracted is higher. You have to consider who it will be beneficial to before considering if it will be beneficial. A student who needs the extra practice for memory may want to use the books. A student who is failing or struggling may also ...


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