No one can stop me now–tonight I’m on the loose!
When I think of the phrase “on the loose,” I think of something set free, perhaps in a feral or dangerous manner. In some sense, I was on the loose yesterday. And yes, it did involve running amok a little bit!
This year, I have been in the teaching certificate program at Northwestern, and have learnt various techniques for creating more engaging classes as a teacher. Although lectures are usually seen as non-engaging and passive, there are definitely techniques to spruce them up. In math classes, this might include demonstrations, asking students to fill in steps and concepts, and other techniques are possible too.
The topic in Friday’s class was probably my favorite topic in vector calculus: the fundamental theorem of vector calculus. Why is this? There are two reasons. The first is that the concepts of potential functions, conservative vector fields, partial integration, and independence of path roll into a nice wheel of concepts that also doubles as a road map. Road maps, whether conceptual/theoretical, or literal road maps, are a constant necessity in my life.
The second reason: a conservative vector field exhibits independence of path. Because gravity is a conservative field, the work done by gravity is independent of the path taken from Point A to Point B. So, the way I demonstrate this had one form in my first few times TA’ing vector calculus, and it got more exciting in the second form.
The first form: I drew Point A and Point B on the board. Then, I asked the students to consider a conservative vector field on the board, and the work done in moving from Point A to Point B. Whether I used the straight-line path or some convoluted, “drunken-sailor” map (the latter was on some Looney Tunes short, but I cannot recall which one it was), the work done by the field in moving from Point A to Point B is the same in both cases.
The second form: I again put Point A and Point B in the room, this time not necessarily on the chalkboard. Trial number one has me calmly walking from Point A to Point B in approximately the straightest path.
But then came trial number two! No one can stop me now–this time I’m on the loose! I started at Point A, ran amok around the blackboard, into the student area, returned to the front of the classroom and DID A CARTWHEEL, and then jumped up to Point B! Yes indeed, a cartwheel in the classroom can be a useful tool if used right!
Despite the fact that I was panting a little bit, the gravitational field did the same amount of NET work on me–i.e. my gravitational potential energy had changed. However, what about the reason that I was a little short of breath? This is left as a straightforward exercise to the reader :p
Today is the one-hundred and thirtieth day of M.M.X.I.V. That makes eighteen weeks and four days.
היום עשרים וחמישה יום, שהם שלושה שבועות וארבעה ימים לעומר
Today is the tenth day of the third round of M.A.P.L.E. That makes one week and three days.