Life has been pretty hectic lately, I moved apartments (in the same building), interviewed for a full-time position at the college I am currently teaching at, and have generally been a mess teaching 20 credits, two new classes (to me), developing interesting lectures and activities, and grading (oh the grading). I enjoy it and love the challenge all of this offers me, but makes it hard to post regular updates. Hopefully you've enjoyed (or been amused by) the worksheets, activities, and quizzes I am posting every Wednesday. Feel free to drop me a note or post a comment below if you find anything on this blog particularly engaging or interesting.
This week a seasoned math instructor asked if he could observe my class and I gladly said yes. Sure, it can be stressful having someone in your class that isn't one of your students, but I am always looking to improve my teaching, and if that means a bit of discomfort, so be it. My desire to become a better teacher is greater than my desire to avoid criticism, constructive or otherwise. Lucky for me the feedback was very constructive, and I plan on discussing it in a few posts. Here I will only talk about one part of that feedback, the balance between core skills and more abstract ideas.
They observed a day when we went over graphing functions based on their derivatives. I have had previous conversations with this instructor about this lesson, and it was by chance the they observed this class. The previous conversations were about an esoteric point about the definition of a phrase that impacts how we answer certain questions. I mentioned this in class and how the book and I differ on this one definition, and how it could change our answer.
The observer commented that this fine distinction might not be the best use of time and energy. They were worried that few students would understand what the impact of this difference is, and most students would get nothing from it. Students have a difficult enough time understanding the book's definition, mentioning my definition may confuse them.
I understand this concern, and appreciate the fact that this instructor has spent much more time with this student population. I will likely not mention this difference in definitions in future classes, but I do want to spend time explaining why I included this difference. This lesson is at the end of a section that is very computation focused where they apply different rules. With this small diversion into how the book and I differ, I was hoping to demonstrate that mathematics isn't just a matter of following rules and computing things. This aspect of having and using precise definitions is also important and one they are going to be exposed to in future classes. I still like this idea and would like to incorporate it into another lesson. If you have any ideas about how to do this, feel free to share below.
I'll be discussing the other feedback they provided in future posts. I'm doing so partially to help myself think through the feedback and to reflect on how I can use it to become a better teacher. I also want to be able to talk about these ideas without sounding defensive. I think about my teaching pretty carefully, so sometimes I get wedded to an idea without talking to others about it. When this happens and I get feedback to the contrary I can feel myself respond defensively, and I don't find that response very useful, or frankly, professional. Part of it is this math culture of being right that I've internalized, but it also comes from my own self-doubt, both things I need to shed.
On that happy note, feel free to share your comments or email me directly.