If other important factors (e.g. Research quality) are about the same, does an academic job* candidate with TA experience in many different upper division classes (e.g. Abstract algebra, real analysis and many other elective classes) have a better chance than a candidate with TA experience only in elementary lower division classes (e.g. Calculus 1 and 2)? How significant is this factor?

I'm currently one year into a math Ph.D. program and is mostly financially supported by TA work. During my first year my TA experience is limited to calculus 1 and 2 (single variable)-It's both the department's preference and my personal preference for a first year student. I'm wondering if it's a good or bad idea to keep it that way(I'll have choice either way). Does it worth investing some extra time to TA some more challenging classes?

*Here all post-doc. or faculty job, whether research or teaching orientated, are included, if your answer depends on the type of job, address it.

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    For what it's worth, one graduate program I was in had no graduate TA's teaching anything above precalculus and another graduate program I was in only let selected advanced students (have passed Ph.D. exams) teach calculus, the rest teaching college algebra or precalculus. – Dave L Renfro Jul 12 '16 at 15:01

All else being equal, then more and more diverse experience is better. The problem is that all else will not be equal.

If you teach the same course over and over again, then that course will become better (up to a point) and you will have to invest less and less time in it. So you will probably get better evaluations and have more time to do other stuff like research, at the cost of having experience teaching a narrower set of courses. If you teach more diverse courses, you will show a more diverse experience at the cost of getting somewhat worse evaluations and less time for research.

However, in my field the differences between the two aren't that big: if you are new to teaching, you'll spent a lot of time preparing regardless of whether you teach that course the first, second, or third time. The improvement in quality will be there, but that does not necessarily mean that that will translate in better evaluations. The extend to which a more diverse experience pays off depends on what is expected in your sub-sub-sub-discipline. The person that is in the best position to advise you on that is your advisor.

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