Physics teaching, as a profession, has come a long way since the dark days of the 1970s and 80s. Although many of the country's classes remain in a "shut up and calulate" mode, more and more physics teachers are recognizing the importance of verbal explanation and conceptual understanding. Sure, the prevalence of Webassign encourages a plug-and-chug mentality. But textbooks, teaching literature, and standardized exams (such as the SAT II, AP, and Regents) ever-increasingly prioritize questions that are not simply of the form, "calculate the acceleration."

I'm sure longtime readers recognize that I am a whole-hog supporter of this trend toward articulating physics concepts. The new AP Physics 1 and 2 exams, especially, will reward knowledgeable physics students at the expense of those who merely search the equation sheet for something with a

*Q*in it; and I am one of the loudest supporters of the new exams.People are often surprised, then, when I reveal that I firmly believe in teaching calculation in all my classes -- including AP Physics 1, including conceptual physics.

Remember, we physics teachers approach our subject with a degree of sophistication and experience that is far beyond that of our padawans. Our sophistication helps us recognize the True Meaning of Physics, which prioritizes conceptual understanding; but our students are many steps behind us. We've got to deal with students as they are, not as we idealize that they should be.

True, deep understanding begins with the basics: memorization of facts. I don't care how clever or insightful a student might be, if he can't tell me that momentum is conserved in a collision, or define acceleration as change in velocity in one second, he can't reason appropriately about physics. Recall of facts is a precursor to advanced reasoning in any subject.

For the majority of physics students, though, calculation comes next.

Physics education research pooh-poohs calculative exercises in favor of ranking tasks, semi-quantitative reasoning*, and other "Tasks Inspired By Physics Education Research." From Pearson education, promoting one of their TIPER workbooks: "

*[These books]...**reinforce the sense that the*"**ideas**of science have coherence and power that extends beyond the facts and equations.*

*i.e. "From how many times higher should a ball be dropped in order to double its time of descent**?"*I object to the pooh-pooh on a couple of levels. Firstly, such an attitude can be compared to those teachers of history who prioritize narrative over fact, or those proponents of teaching "whole language" as opposed to vocabulary and grammar. Certainly they have a point, in that an excess of memorization and drill without payoff can demotivate promising students; nevertheless, if you're actually going to learn anything about history or language, then facts and vocabulary are non-negotiable precursors.

More practically and less philosophically, actually watch students over a year as they come to grips with physics concepts. Our goal is for students to use equations as tools for understanding:

"With no initial speed, the kinematics equation reduces to

*d=*(1/2)*at*^{2}. The acceleration is the same either way because the ball is in free-fall. Since the time variable is squared and in the numerator, the distance for the ball drop must be multiplied by 2^{2}, or by a factor of four."At the beginning of a student's first year of physics, such reasoning can be beyond even very capable students. In fact, their instinctive approach is to "set up a proportion," coming to the conclusion that twice the time must mean twice the height -- logic, see? Such a student is not ready for advanced verbal reasoning yet.

What's NOT beyond anyone is a calculation: Use the equation

As the year goes on, it's my job to guide such a student away from brute force and toward more subtle reasoning. One easy idea is to award more or extra credit to those students who use a sophisticated, non-calculational approach. Or, perhaps require students to make numerous calculations to answer a ranking task; then come back and ask them to describe a way to justify the ranking without doing

The point is, a non-insignificant subset of your class needs to use calculation as a first step toward a deeper understanding of physics. Even in conceptual physics, I'm pleased with students who make up simple values to plug into equations.*

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What's NOT beyond anyone is a calculation: Use the equation

*d=v*_{0}*t+*(1/2)*at*^{2}to calculate the distance the ball falls in, say, 1 s; then do another calculation for 2 s; and see that the ball falls four times as far. This student is using calculation as a crutch, yes. But (a) he's getting the answer right, (b) he's doing correct, if brute-force, physics, and (c) he is showing progress in his physics understanding, because he reasoned from a relevant equation rather than "logic."As the year goes on, it's my job to guide such a student away from brute force and toward more subtle reasoning. One easy idea is to award more or extra credit to those students who use a sophisticated, non-calculational approach. Or, perhaps require students to make numerous calculations to answer a ranking task; then come back and ask them to describe a way to justify the ranking without doing

*any*numerical calculations.The point is, a non-insignificant subset of your class needs to use calculation as a first step toward a deeper understanding of physics. Even in conceptual physics, I'm pleased with students who make up simple values to plug into equations.*

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*My freshmen have taken to calling this approach a "false calculation" -- if the acceleration isn't known, for example, just use 1 m/s per second. This approach works for virtually any semi-quantitative question or ranking task.**When I teach AP Physics 1 in 2014-15, I intend to begin with material identical to that which I've used in AP Physics B: end-of chapter-style problems involving calculation, always mixed with some sort of descriptive prompt, and always including the requirement for presentation and communication. Once we've become comfortable approaching this newfangled course called physics,*

*then*I'll cover the same material again, this time always going beyond mere calculation.
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