Would going to Teacher's College be useful, if my ultimate goal is to become a university math professor? I am close to entering the fifth year of a five-year Concurrent Education program. What the program involves is four years spent working on a bachelor’s degree, while “on the side” taking education courses and doing placements contributing to a bachelor of education and teaching certificate. The final year of the program is regular Teacher’s College, which is a combination of education/curriculum courses and, in total, about 14 weeks of placement.

I’ve thought about dropping the education part of the program a few times since it started, but stuck with it because it left teaching open as an option, while only requiring one education course and a 3-week placement each year (which is good experience anyway). About 2 years ago, I started considering going to grad school for math, but by the end of last summer, still wasn’t 100% sure, so I didn’t write the GREs. This year I took a graduate-level algebra course, and about halfway through, realized that grad school for math is definitely something I want to pursue.

As the deadlines for applying to grad schools had passed / were soon approaching, my plan then became to finish the program and get my teaching degree, and apply for math graduate programs this December/January for entrance in Fall 2017. Spending the next year in Teacher’s College, I’ve been thinking, might actually be a good thing, as a way to set me apart on applications for grad school and for jobs in the future, as well as a way to develop good teaching and other related skills. On top of that, it would leave teaching as a back-up just in case.

I would sincerely appreciate hearing the opinions of those who are in or who have been through graduate school in math. Do you think it will it be worth it, in terms of a future as a mathematician (ideally as a math professor), to finish the teaching program? I fear that the final year of this program will be painful for me, as it will require a lot of placements, which I already mostly dread. Alternatively, if I didn’t do Teacher’s College, I could spend the next year taking more graduate courses at my university, learn more math independently, focus on the GREs and honing my applications, and try to see if any professors at my university are willing to supervise me in some research experience before entering grad school for math. 

In case it’s relevant, I come from a smallish university in Canada, which is probably not very well-known in the US, and I am graduating top of my class in math.

I’m sorry if this question is not general enough.
Spending the next year in Teacher’s College, I’ve been thinking, might actually be a good thing, as a way to set me apart on applications for grad school and for jobs in the future, as well as a way to develop good teaching and other related skills.

If you want to get into a research Ph.D. program in pure or applied math, this will do extremely little to set you apart.  Taking more graduate courses and doing well on the GRE (especially the math subject GRE) would certainly do more than education or curriculum courses.  

The most basic reason for this is that Ph.D. programs are essentially only worried about your ability to complete research in that discipline.  Any life experience or preparation that isn't relevant to that is likely to be ignored.  I suspect education courses are particularly likely to not be helpful, since (at the risk of way over-generalizing), many mathematicians have a pretty low opinion of the way classes in education are taught.  I suspect, for example, actual experience teaching in a school would be more helpful.