# Day 130: WTF?

Today in college-prep physics we were discussing problem solving strategies. And for many kids, the default strategy is to look for a single sure-fire equation that will answer the problem in one step.

How many times have you had a student working on a problem in class or on an exam and say:

"What's the formula for mass?"

"We never learned an equation for height!"

"How can I calculate the kinetic energy if you don't give me the speed?"

Clearly these students are having a WTF moment (in more ways than one): What's The Formula?

I told the class that when they have a WTF moment, they've lost sight of the big picture and fundamental principles. Anyone have any insights on how to change student's default mode for problem solving?

WTF isn’t a totally bad strategy; it’s just too limited. (Waaay too limited!) Especially if someone is thinking only of the one variable on the left side as the only unknown and looking for all the variables on the right side as the knowns. Maybe one help would be to create a chart with all the variables related to the problem spread out in a 2-D array, and with the concepts (KE, PE, elastic E, force, momentum, ….) derived from any of the variables with lines to each of the variables. Plus maybe some lines between concepts as well to show that one concept is related to another concept plus maybe some variables (KE = momentum^2/2m…). The formulas relating the concepts to the formulas shouldn’t be on the diagram – the kids would have to memorize them and be able to recall them when they look at any of the concepts. But by looking at the diagram, they kids could easily see which concepts are related to which variables, and, hopefully, would be able to start thinking more conceptually in terms of how concepts are related to observables and how concepts are related to other concepts…. Just a suggestion! (I haven’t tried it so beware!)

When students come for extra help (and sometimes also in class), I tell them that "there isn’t a formula". For a relationship/equation to be useful, it has to be both (a) correct in the given context and (b) useful to find what you want from what you know. WTF tends to ignore criterion (a). And so the steps I teach them in individual tutorials are:(1) "What is going on?" (qualitative description)(2) "What model describes what is going on?" (selection of a model that applies in the context)(3) "What does that model say?" (memory refresher of *everything* that the model says and *all* the tools it provides, beginning with its fundamental statement — e.g. "energy is conserved" or "F-ub = ma")(4) "What of that is useful to me?"

I spent the past week trying to wrestle this sort of problem with one of my honors sections. Typing on phone, so I will be brief here, but the two most winning strategies have been… (a) give them problems with no numbers at all. Make them model the situations with no numbers, then eventually give them some numbers and make them solve it through a few times with different fundamental principles. (b) working on a problem in groups, don’t let them touch pencils or markers for the first three to five minutes. No calculators either. Just spend a few minutes only planning with your team about how you will model the problem. And, basically, just keep preaching the diagrams and get rid of equations entirely everywhere possible.