Physics is Math+

We're nearly to the end of the second trimester here at school and I've been thinking about the major differences between the two physics classes that I teach.  I have both the advanced physics class and the introductory physics course.  Now, high school physics is nothing to write home about; my course doesn't even use calculus.  However, I have nonetheless noticed a divergence in approach between these two.

While I'm still on the topic, I do wish I could teach more of the calculus to my advenced group--they're bright enough to have at least absorbed the concepts.  The school I teach at lacks Calculus as an option in the math department.  Even so, I toss into lecture sporadic conceptual notes on things like definitions of the integral or the instantaneity (I made this word up, so it is totally "a thing" now) of the derivative.  We have even learned the vector math behind the cross and dot products!

In the interests of making the class as suitable for each group as possible, the Introductory class has focused on conceptual bits such as conservation and Newton's laws.  Everything seems to come back to "An object in motion etc etc. ..." and "For every action, etc etc. ..."  The kids don't need to calculate very much.  There are a lot of questions in quizes and tests about what happens in different impossible science experiments.  We end up with a pendulum attached to a spring on a merry-go-round (which a college freshman would describe as the most nightmarish Mechanics I Homework problem in existence).  Since it is treated from a conceptual level, the kids feel engaged and they look forward to asking questions and debating.  Students who just don't "get" the math do get turned on by the concepts; many of my weaker students from the first trimester are now at the top of the class.  Needless to say that I am proud.

The Advanced group has always been computationally heavy, but these days I focus less on working through the practice problems and more on deriving the concepts behind these from base principles.  The kids still have hard calculations on tests (and medium-difficulty calculations on the quizzes), but during class, its now rare that we solve something by example.  The result is that I have one physics class where we do little calculation and focus on the concepts and one physics class where we do little calculation and focus on the concepts...hmm...

I'm not saying that they don't do any of the math in the Advanced class--just that they're all clever enough to know how to use an equation without it needing to be explained to them.  Their most recent midterm was modified from actual AP Physics C Mechanics questions (obviously I chose the questions that didn't require calculus).  As a result, a lot of our time is spent discussing the significance of terms or where an equation will come from.

I was at my best friend Ross's house the other day and we were discussing our mutual grumpiness over drinks.  He's a string-theorist and he's nearing the end of his PhD.  We attended graduate school together at RPI before he left for Northeastern. 

We obviously started talking about physics.  We came to the conclusion that Physics is just math with boundary conditions. 

I'm not going to try to say that I'm this great teacher/tutor, but I will say that I've been doing this long enough to have convinced myself that I think I know something appropriately useful.  I've had AP physics students and introductory physics students alike.  I've taught students for the SAT.  I've taught the course both with and without calculus.  Across all of these differing backgrounds and circumstances, I have had the most success stressing the same sort of sentiment.  As long as you remember a few important concepts and you have the general equations, you will always be able to solve the problem.  You just have to ask the right questions of yourself.  You just have to make the one correct assumption at the crucial moment.  Just look at the boundary conditions.