I am a maths graduate student.
A little background: In the coming semester, I will be assisting a prof whom I admire and whom I also want to thank a lot, and I actually will have a lot of free time. Honestly though, I myself love doing those assistant tasks, and in general love managing teaching as well since I am bound to teach in college later on. Hence, I would love to use this opportunity to make his teaching run even more smoothly as much as I can. Hopefully this post can collect some ideas for me and all who might need.
I will start by some restriction: I am not going to grade papers. Also, I obviously cannot and must not replace the prof during his teaching haha. I will however conduct tutorials, but I am pretty sure I am allowed and would love to offer more help to the prof, be proactive, and initiate and suggest ideas to him to ease his teaching job.
My question: For those of you who are (perhaps college) maths teachers, or who are assistants yourselves, what do you think are many things that a maths assistant can do more to help professor in teaching?
In other words, for those who are teaching, "It will be amazing if my assistant can also ...(blank)...", or for those who are assistants, "If I have all the reasons to further improve the professor's teaching, I will ...(blank)...".
Notice the emboldened words, because I am looking for giving additional help outside of what I am obliged to do, and because I have done some of those additional help and will keep doing them, such as:
- Off-tutorial, I additionally provide timely feedback to students who are emailing me. It is actually not a must (off-tutorial), but for me, it is.
- I also report to profs instances of students having difficulty on some concepts when I see them during tutorials.
The above are tutorial-related stuff. I can google how to be a good (maths) tutor for many more. What I plan to add are (feel free to comment on these too):
- I like to attend his lectures live (if it is not pre-recorded).
- I like to help making his lecture notes more complete (if not yet), like adding what he said during lectures or correcting the notes. Especially, if his proofs leave missing details (which I can obviously expect), I can try adding them to the notes.
- I like to provide more examples + exercises, as the lack of such is not uncommon, right? xD
- I like to initiate a discussion in our uni learning platform (whether directly related to the materials or related to applications instead) to introduce perhaps some exciting stuff.
I feel like there can be more, or something that is related to the class being offline/online, but I am currently out of idea. What else do you think can be done?
Thank you very much. Apologize for the long text.
Remark: The course will be about pure math (algebra-related stuff).
EDITS: Thanks for the replies. The course is a little bit higher level course for undergraduate, and it will involve some linear algebra and abstract algebra. It is an elective course.