Newton’s Equations. Rear view, close-up on young man standing back against green chalkboard. He explains, solves physics tasks, retro style. Processing for retro bleached look, slight vignette added.

I’d like to think that this posting was inspired by one of my brothers, but he is just the third student of mine to have made one of the classic and fundamental mistakes in solving physics problems. Or any problem in the natural sciences, for that matter. And, no, I am not making fun of him in anyway. In fact, I was rather proud that he became self aware of the problem as we worked together. He articulated the same difficulties with the physics problems he was trying to solve that I have heard countless times:

“Like, I get how to solve the problem when someone shows me. But, if you just give me a problem, I have no idea where to start.”

Which, upon further prodding becomes, “I have no idea which equations to use!”

As science teachers, we do a decent job in promulgating a systematic way of solving problems. Does this sound familiar from high school?

• List the givens or known.
• Write down what is being asked for.
• Identify the equations or formulas that use the givens.
• Solve for the unknown.

It seems pretty straight forward, and logical. It’s also low on Bloom’s Taxonomy. But, it is deceptive if you want to hang your proverbial hat on it. Why? Consider this recent lesson I taught. A student of mine, a precocious AP Physics student, was preparing for her first quiz of the year. Now, she has no lack of will power, motivation, or drive to sit down and study, so that she can be successful. She articulated the same problem that my brother would a week later. We sat down at a desk, and I prompted her to pose her questions; I prefer often if students lead the dance, and I facilitate and guide, rather than direct everything myself. After about the fifth exaltation of, “Ooooooohhhh,” I asked her a simple prompt: Can you actually tell me what is going on in your physical system? (I’m sure that I said something similar to my brother, who was trying to determine the largest angle a support cable could be to support a weight without having the entire setup collapse. Useful in real life, I’d say. Imagine driving over a bridge with just a little bit too large of an angle…)

Friends, this is the missing step! And it isn’t limited to physics. I gave a blistering first exam to my AP Chemistry students the first year I started teaching the course. I needed to shake their complacency, show them how high the bar really ought to be for them (they were both quite bright and very capable), and “subtly” encourage them to step up their proverbial game. The top two students, interestingly enough for this post also brothers, earned their first failing mark, and were determined to argue their way out of it by foraging for any points that they could find. As a teacher, I actually relish when students do this, because it presents a wonderful teaching moment – to point out the lost step in problem solving! I let a wry grin come across my face, and I replied, “If you want to argue about your exam grade, then come at me like a chemist, and tell me what is going on in the beaker. If you can’t make an argument based on and articulating the actual chemistry of the problem, then I simply don’t care.”

Well, they both bristled at the notion, the righteous indignation of their teacher. And yet, one of the brothers became salutatorian of his graduating class, and remarked that it was being told over and over to, “…describe what is going on in the beaker,” that forced him to be successful. The other brother won a prize at his university for being the best organic chemistry student of his class. I’m quite proud of them both.

Allow me to restate our systematic way of solving problems, now with our missing step included:

• List the givens or known.
• Write down what is being asked for.
• Make a one to three sentence statement about the actual physics/chemistry of the problem. In other words, state what is going on in your system!
• Identify the equations or formulas that use the givens.
• Solve for the unknown.

I state this unequivocally: There is absolutely no way, no how, no if, ands, or buts about it, that anyone can solve any problem in front of them effectively, and without a generous amount of serendipity, if they do not articulate what the problem actually is, and the pertinent facts pertaining to the situation.

For a physics problem, it’s simple: a student must be able to describe the physics of the system. What forces are acting on various parts of the system, what kinds of energies are involved, if momentum is concerned, if the system is at equilibrium, if there is rotation, if a wire is stationary or moving in a magnetic field, and so on. Once a student understands the underlying physics, it because “orders of magnitude” easier to formulate a series of steps that need to be taken in order to solve the problem. And then, it becomes obvious what formula to use for each step.

Moral of this story: Never solve a physics (or chemistry) problem without making a clear and concise statement about the actual science that is going on!

It’s a hell of a life lesson, and will definitely start improving your grades in school, and, more importantly, asking the right questions during your studies!