After completing my first semester as a peer teacher for the Foundations of Engineering II class at Texas A&M, here are a few thoughts about what I learned.
There are many ways to complete a task and it's impossible to anticipate all of them: Even when I though I understood a topic pretty well, there were sometimes questions that I was not able to answer because the student had used a method that I'd never thought of, and ran into a roadblock that I wasn't sure how to handle. Although I may have been able to provide advice about a different method, all I could do in this situation was examine their work and see if I could find any logical errors.
The professor isn't always the best resource: Because this class is required for all incoming freshmen engineers, there is a standardized curriculum with some leeway for individual professors. There are projects and reports due for all sections, and I discovered that the professor I worked for wasn't always the most knowledgeable about cross-section assignments. I found that if I read the cross-section pages and made sure I knew details of the assignment I could answer questions better.
Grading is subjective: Even for problems that seem straightforward and have one right answer, it can be difficult to grade without knowing the intent of the question's author. For example, sometimes students skipped a step or got to the same conclusion by a different manner, but the rubric had specific markers that I was not able to check off. Although sometimes I felt that a student got the right idea of the question, I would grade strictly by the rubric with the thought that the professor could correct the grade if needed.
Working out examples is key: I found that even if I reviewed lecture slides beforehand, I was much better prepared to answer questions if I had worked out at least one problem of that type on my own to remind myself of the process.
I am looking forward to continuing as a peer teacher next fall for the Foundations of Engineering I class. With the new format of this class, I will lead recitation sections for small groups of students on my own each week. I hope to improve my speaking and teaching abilities, and I think this format will make me a better resource for students during class.