This week I learned of some new possible misunderstandings that I had never considered or observed before. I received several emails this week from students asking about what is meant by the “x-component of velocity”. If you haven’t been following, my class is somewhat of “flipped” class, where students read lecture materials online and come to class to think through conceptual problems, work on solving quantitative problems, and carryout some investigations.

So far, we’ve only been talking about one-dimensional motion, but the reading material has been using “x-component” of velocity rather than just “velocity”. I can sympathize with why someone might choose to write it this way, but I think, in reality, its cumbersome, wordy, and confusing.

So I began yesterday, by asking students to talk with their neighbors about what they think “x-component of velocity” means. After some discussion, I asked to hear idea about what it could be.

Here are the two answers we heard that I had never heard before

(1) Velocity is made up of two parts (or components), the magnitude (speed) and the direction. The x-component must be either the speed or the direction.

(2) Velocity is made up of two parts (components), the Δx part and the Δt part. The x-component of velocity means you only look at the Δx.

What this shows me is that students were trying to make sense of this vocabulary as best they could. They were thinking, “component?” well that’s like a part. What parts does velocity have? It had magnitude and direction parts. It’s also calculated using distance and time parts. The x-component must be one of those parts. To me, this is completely reasonable thing to do. It’s also a good sign to me, that at least students are reading and trying to make sense of strange terminology.

I had a brief activity ready, one involving the directions given by google maps to get various places. I gave them a few examples of paths moving along North-South streets and East-West streets, some moving along both, and some moving along a diagonal street.

At the end of the day, someone asked, “Why would I ever care to describe just the x-component of velocity (as – 30 mph) when I could just describe the whole velocity as 42 mph Northwest?” I said, that’s a really good question.

I want to be clear that vectors or finding components of vectors has not been covered in this class, and that there are difficulties in students’ understanding them. I also want to be clear that the two misunderstandings are likely the result of the format of flipped class and the choice to introduce the terminology of “components” before (I believe) it made sense to do so. I don’t think these two are deep-seated confusions; rather they are the result of asking students to read something before we’ve helped them to carve out some distinctions which would have helped them to read that text.

If you are interested in how to make readings or lectures more effective, you should read this paper, called “A time for telling” by Daniel Schwartz and John Bransford. In this article, they talk about three experiments they carried out to better understand what kinds of pre-lecture or pre-reading assignments help prepare students to learn from text or lectures.

I’ve been thinking a little about the concept of components. Why, indeed, would we not just say 42 mph northwest? It seems to me that components are a math tool to aid in calculation. They’re not fundamental to physics. We need to know any forces involved for a particle’s trajectory and we say that momentum has been swapped in that direction. If you want to calculate the effect or make a nice movie or something, it’ll be much easier to do in component form, but I’m wondering if it’s necessary for learning the concept.

I am against teaching components early in physics, and possibly never in a terminal physics course. When I was HS we did vectors with ruler and protractor, and then much later using law of sines and cosines. Only in AP physics did we learn about components, and we spent a lot of time talking about dot products and projections.

@Andy,

Components are certainly not necessary to learn about vectors; I try really hard to get that across to students. Vectors are objects that exists independent of any particular representation.

@Brian,

What text is being used? It’s interesting to hear your perspective, because I teach my intro course (starting today) in a similar way (using online warmup exercises the JITT way). I’m using Knight’s text for the first time this year.

Dealing with vectors when you are considering only one-dimensional motion is tricky. I don’t think that any books do it very well.

@Chris It’s home-grown. This takes you to a somewhat outdated version. Students now have pdfs that have been tidied up a bit.