I was offered a math PhD position with full funding by a university in Canada (which is currently on a strike), and I was also offered a position as a math teacher in a quite prestigious high school in Macau. The wage of the school is comparable to the PhD funding in Canada. I am struggling very hard to make a decision, as both positions are not easy to get. (The fully funded PhD positions are very competitive for international students)

Since I am a beginner in the area of academia of math, I am not quite sure what kinds of quality I need to look for in a graduate program to make me more well-prepared to look for a academic position in colleges. The research topics my prospective advisor do match my interest very well, but does the prestige of the school play a very big role also? Or the no. of publications is more important? Clarification of this will probably help me make my decision.

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    Welcome, Alan! The direction of your edits is actually making it more likely your question will get closed quicker. Academia SE doesn't do "shopping questions" that ask for consumer feedback on a given school or ask for a menu of options. Instead, we want to help you understand how to make your decisions better. For instance, if you were asking about what to look for to know if your prospective advisor is a good fit (not sure that math programs even start with prospective advisors), or something else tangible that would help you make your decision. Good luck! – cactus_pardner May 14 '18 at 3:20

These are two very different fields. You have to ask yourself: do you want to be a math teacher or a math researcher? Note that a PhD gears you for research positions. While professors teach, their main duty (at a R1 university) is actually research (this fact is seldom known to undergraduates). Your ability to get a professorship, get tenure, etc. is all based on research. If you are going to go down the PhD track, the choice is for a research-based career. Ask yourself if that's what you want. Choosing a career path based on what you want to do with your life is so much more important than whether a school or department is "prestigious" (which is highly variable depending on the subfield, your adviser, the fellowships/grants you get, etc.).

Caveat: there are positions at 4-year college, i.e. get a PhD and get a position to teach undergraduates.

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