As someone who has never
crossed that threshold (from learning to teaching) there is a lot to be
learned. Before the first week of class Barry and I met to discuss the syllabus
and the components of Calculus I that we found conducive to learning and understanding
the concepts of Calculus I. Such things as applied projects, homework, quizzes,
tests, and journals we found to be essential parts to a good Calculus class.
Class journals are one thing I have never had to do for a math class, however, I completely agree with their use in Calculus. The journals ensure that students communicate with the professor, and this can be extremely valuable for both the student and professor. Student feedback is essential to gauging how well the students are grasping the class material, and journals are a source for immediate student feedback. -- Many classes (especial math and science classes) can benefit from journals.
The first week of class I spent "evaluating" Barry as he lectured. Having never taught a class before, I observed the way in which Barry spoke and wrote on the board (simple things). You can't learn from a professor who stands in the way of what he or she is writing on the board. Beyond the simple things I listened to the ways Barry would explain what he had written.
During our meetings outside of class, Barry and I discussed grading in more detail. We talked about the importance of consistent fair grading. I have graded homework for other classes before, but something I've learned already is how to grade consistently. Grading the same problem for each quiz before moving on to the next, for example, can help to be more consistent. And better yet, to go back and review each graded problem for each student to ensure that it was roughly graded with the same rigor for each student is more though. Barry mentioned how he will sort graded papers in stacks according to the letter grade, and how he will return to all the B papers, for example, and make sure each paper in that stack truly deserves a B.
We decided that as the class TA I would be responsible for constructing quizzes homework sets. Constructing three sets of homework on Webwork and one quiz, I've begun to understand the process of finding good problems for students. A good problem can show how well a class or individual understands or does not understand something. A good problem can tell a professor that either a class or student is slacking or, more likely, if every student is struggling with the same problem, that the professor is not communicating as well as he or she thought during lecture. This is another type of feedback that I learned is very crucial for a professor to pick up on. Barry has mentioned how he has learned to explain certain topic better because of such problems. Hopefully by the end of the semester I can get a little better at finding good problems!
For now we are working on finalizing the first exam. Again, we are looking for good problems that cover the material discussed during lecture, and problems that will ensure good feedback.