“Why are you spending so much time on kinematics?” asks Dean Baird in his blog this morning, in the context of the Next Generation Science Standards (NGSS).

I’m not going to defend spending six weeks teaching quadratic equations, which is the position that Dean criticizes in his post. Years ago, I did that, but I’ve moved on. I do still teach kinematics, however, and now I want to clarify what aspect of kinematics I find it important to teach.

As Dean points out, the NGSS starts off with Newton’s Second Law: F = m a. Great choice. There’s a huge amount of physics in that formula: mass (not weight!) and the concept of inertia; force, including net force and vectors; and acceleration, which is not the same as velocity.

And that last point brings us to kinematics. Keep in mind that kinematics is not merely calculation and the use of formulas. Kinematics is the precise description of motion, and that includes important concepts and vocabulary.

In my class, the culmination of kinematics is not “solve this polynomial for *a* (or *x*, or *t*…).” My goal is for students to recognize the difference between acceleration and velocity. (For context, know that I teach a physics first course to ninth graders, in a state with a mandated subject-area test at the end of the year.) Yes, they do some algebra and learn to calculate an acceleration. We also use graphs, tables, motion maps, verbal descriptions, all that multiple representation stuff. And in the end, my standard for them is to determine whether an object is accelerating or not based on a given representation: Does this graph show an accelerating motion? Why or why not? How about this motion map? What about this diagram of an orbiting planet? This sentence describing a bike ride? And so on.

Recognizing acceleration is not easy. Most people don’t even perceive acceleration as they look at it. Drop a ball in class, ask the students if the speed is constant or changing, and many say the speed is the same whether the ball has fallen one centimeter or one meter. Check out Derek Muller’s video, “Can You Perceive Acceleration?” for a demonstration.

And that’s the problem with superficial coverage of kinematics. Without it, people conflate the notions of velocity and acceleration, and steadfastly maintain the Aristotelian position that all objects in motion have a net force acting upon them. Students even claim that F = ma supports them: “It’s moving, so *a* is not zero, therefore *F* is not zero”). Learning kinematics, specifically the conceptual understanding of acceleration, before Newton’s second law heads off that misconception. I push my students hard to see that distinction.

Teaching the concept of acceleration takes time and persistence, however. This difficulty makes me uneasy about the NGSS’s silence on the subject of kinematics. The standards take the concept of acceleration for granted, and I am concerned that the writers of assessments and the teachers of students will also neglect this fundamental idea. As written, the standard is about the mathematical relationship F = m a, and no understanding of the underlying meaning of the variables is necessary.

I’m not saying we have to start our year with kinematics. I’ve use several sequences: kinematics first, statics first, waves first, ray optics first… with good results. Regardless, within a topic, I hold off from the algebra until the students have understood that quantities represented by the variables. That means learning the concepts of net force, mass, and, yes, acceleration before working with the formula F = m a.

Dean describes (traditional) kinematics as “applied mathematics,” and not a proper subject for a physics class. I agree with that, so I don’t teach it that way. But I do teach (nontraditional) kinematics, and I exhort all you physics teachers not to skimp on the precise description of motion. Bear down on the concept of acceleration and make sure the students get that idea. If they can’t accurately describe what acceleration is, then F = ma is simply pure, unapplied mathematics, and you’re not doing physics at all.

So that’s my thinking. How about you? Precisely what kinematics do you teach (if any), and why (or why not)?

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