Write two equations, but DON'T SOLVE

Our students come into physics expecting a frustrating math course.  Then many get even more frustrated -- not only do they have to solve math problems, but they have to create their own problems to solve, to boot!  Guh.

In an honors or AP level course, it's important early in the year to make a big show of separating the physics from the math in problem solving.  Firstly, here are some facts, concepts, and a routine that will set you on the path to a solution; then, here's how you know that the problem is set up appropriately, that doing ninth-grade algebra will in fact lead to a solution.  I go so far as to write, in big capital letters, PHYSICS IS DONE.  Students do the same, initially to poke some fun at me, but then as a way of communicating their problem solving.

The canonical technique for recognizing mathematical solvability is to write a relevant equation, then to identify known and unknown variables.  Once we have a single equation with a single unknown, the problem is solvable; similarly, two equations and two unknowns is solvable.  But don't underestimate how intimidating the actual mathematical solution process to a two-equation system is to a high school student.  They may have passed algebra 1, but I trust my students to get accurate solutions even less than I trust the evil bastards of the TSA to get me to my gate in a timely, convenient, and comfortable manner.

Very early in the school year, I assign the hanging stoplight problem.  You know, an object is suspended by two strings, each at a different angle; determine the tension in each rope.  The solution requires algebraic manipulation of a full-scale two-variable-two-equation-system.  Those of you who have assigned this problem and observed your students can probably verify my report that many of those students spend 30-60 minutes doing math, often getting lost along the way.  A significant fraction get so frustrated that they simply give up, or follow a friend's solution blindly.*

* I know this because quite often that friend's solution is itself incorrect.  

Here's a great chance to make my point about the separation of physics and math.  By this point, in class we've emphasized over and over and over the three-step approach to equilibrium problems:

1. Draw a free body diagram

2. Break angled forces into components, if necessary

3. Write (up forces = down forces) and (left forces = right forces)

The majority of the students who spent the better part of an hour on this problem didn't follow these three physics steps carefully; they got too worried about the forthcoming mathematics.  

So, why not give a quiz in which students are given explicit instructions not to solve the two-variable system?

See the quiz below.  I find that it relieves much anxiety from those who got lost in the mathematics.  It sends an important message to those who didn't follow the process, because they see just how quickly they could have gotten to the answer by, well, listening to the teacher and following his advice.

Finally, note that the AP Physics 1 exam will not ask students to solve a true two-variable system of equations, ever; but "write two equations which could, together, be used to solve" is a legitimate form of AP question.  

GCJ

Two ropes support a 33 kg stoplight, as shown above.  The goal of this problem is to find the tension in each rope, as on last night's homework problem.

I am NOT asking you to solve the problem completely in this quiz; rather, I want to see that you can quickly and accurately follow our four step procedure for solving equilibrium problems.

1. Draw a complete free body diagram of the traffic light, including descriptions of each force. 

2. Redraw the diagram, breaking force vectors into components where necessary.  Express components in terms of the given angles; i.e. do not simply write “T_x”, include the angle in your expression.

3. Write two equations.  Circle the unknowns.  DON’T SOLVE.

Report from the AP reading: Teach your class to write concise laboratory procedures. Please.

Howdy!  I've spent the last week grading, and training people to grade, the lab problem on the 2016 AP Physics 1 exam.  I'm a bit punchy, as you may expect.  Nevertheless, I encourage you to apply to be a reader -- I really, really love the people I meet here, even if I'm not always entirely enamored of grading papers for eight hours a day.

Part (a) of our question asks for a description of a laboratory procedure.  It could be answered in 20 words: "Use a meterstick to measure the height of a dropped ball before and after it bounces.  Repeat for multiple heights."

But oh, no... when America's physics students are asked to describe a procedure, they go all Better Homes and Gardens Cookery Manual on us.  Folks, it's not necessary to tell me to gather the materials, nor to remind me to first obtain a ball and a wall to throw it against.  Nor do you have to tell me that I'm going to record all data in a lab notebook, nor that I'm going to do anything carefully or exactly.  Just get to the point -- what should I measure, and how should I measure it.

Please don't underestimate the emotional impact on the exam reader of being confronted with a wall of text.  We have to grade over a hundred thousand exams.  When we turn the page and see dense writing through which we have to wade to find the important bits that earn points, we figuratively -- sometimes literally, especially near 5:00 PM -- hit ourselves in the forehead.  Now, we're professionals, and I know that we all take pride in grading each exam appropriately to the rubric.  Nevertheless, don't you think it's worth making things easy for us, when we be nearing brain fatigue?  Just as good businesspeople make it easy for customers to give them money, a good physics student makes it easy for the grader to award points.

 

Don't think I'm making fun of or whining about students here.  Writing a wall of text where a couple of sentences would suffice is a learned behaviour.   The students taking the AP exam are merely writing the same kinds of procedures that they've been writing in their own physics classes.  It is thus our collective responsibility as physics teachers to teach conciseness.  

"Okay, Greg, how do we do that?"  I hear you asking.  I have a two step plan.

(1) Give the students a word or sentence limit, and hold them to it.  For virtually any AP Physics 1 procedure, three sentences will do.  When your students list a twelvefold process, award no credit, and don't give in to the subsequent whining.

(2) Don't ever award credit for baloney.  When students have one nugget of valid description buried in a mountainside's worth of muck, just stop reading and award no credit.  The burden of proof is on the students to convince you they understand the methods they describe.  It's tempting to yield to after-the-fact whining and lawyering: "Well, if you really think about it, the meterstick could measure force if..." No and no.  

Fight the clarity and conciseness battles in October; then in May when your students take the AP exam, communicating experimental methods will be (a) easy and (b) quick.