Those of you who have never taught math or science may not understand what we go through on a day to day basis here in the blurred world of science/math (aka Physics). Let me give you some insight into my plight today while I was teaching centripetal acceleration. I have students who are actually better at math than I am. I know, I know. I shouldn't be teaching physics if I don't know more about math than my students, but here we are! I am learning so much everyday.
So, I had a student ask me a question like "where did the radians go?" We were converting between tangential velocity and angular velocity and I was doing the unit conversion, just like I always do and I thought "Yeah! Where DID the radians go?" Honestly, I don't remember. I told my students that, too. "I really don't know." I couldn't tell them. I am sure there is some technical phrase like complementary adjacent angles that would perfectly describe what happens (I know its not complementary adjacent angles, so don't even go there); but I just had to tell them: "I don't know". So, I read in the text. I can't understand it. I read again. I am STILL not satisfied with the explanation to the extent that I am comfortable explaining it to students.
You may be saying about now..."So what happened Bowie? Tell us! Tell us, please!" Well, I will: In walks another teacher who teaches Biology but knows a lot about units analysis (my term for it and I know Biology people do it too, I just don't think about them doing it.) He and I start to talk about it and are still not entirely able to figure it out to our satisfaction. Enter E.R. (his initials, not the Emergency Room), the brother of one of my best students from last year and proceeds to give us the vital piece of information required to connect the dots. Voila! I understand! It was as if the light was turned on in my head. It was something like what I imagine happens on a regular basis to my students when it all "comes together". The vital piece was that I had never been taught (surely I didn't forget) what the definition of a radian is. I just simply never bothered to find out! I never had a reason. Now I understand the "why" of the equation C=2πr for the circumference of a circle! I have known the how for a very long time. I just never knew the why!
No big surprise that I learned something new. My students never cease to amaze me by teaching me new stuff everyday. I guess its just as amazing that I am willing to learn it. Prayer: Lord please keep me willing to learn something new.
Thanks for reading.