I’ve written previously about why students shouldn’t use components until they beg. Overall, this method generates students who really understand what vectors are, and you’ll know you’re successful when students see a situation like this that asks them to find the net force,

And you hear them say something along the lines of, “I see that F1 is 4 up and 1 right, while F2 is 2 down and 3 left, and F3 is 4 to the right, so the total must be 2 up and 2 to the right.” And if you do it right, you’ll hear this a lot. Students are actively finding shortcuts, and in truth, I’m not sure they need much more to discover components completely on their own. But sometimes I can’t shake my worksheet generating habits, so I put this together, and would appreciate any feedback:

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I should note that there are complications that crop up to the graphical vector addition method. Like almost everything else, it becomes easy for students to think that adding vectors just means “making polygons” (or even worse, triangles) and so they struggle when they find that some vectors when added don’t form a closed polygon. They also really need to work to understand the meaning of “head-to-tail addition”—often it just sounds like a memorized procedure to rattle off to the question “how do we add vectors?” I have gone as far as trying to talk about seeing the vector animals in the zoo, and carefully labeling their parts—the head (arrow tip) and tail, and then asking about the two ways that we can tell them apart (by size and direction–so two vectors with the same size and direction are the same).

And then this year, I came across a problem with students learning vectors I hadn’t seen before. Thanks to a few variations on the type of question I ask (“Find the sum of these forces” vs “Find the additional force that will cause the net force to be zero”) and an untimely introduction of vector subtraction, it seems my students are having more difficulty with fully understanding vector addition. Here’s one warm-up question I created to try to tease this apart.

I’d love to know if other people have encountered similar difficulties when students are trying to make meaning our of graphical vector addition.

1. November 28, 2011 7:03 am

One thing that really helped my students with the Fnet problems was relating it back to finding the total displacement from a bunch of “walk” vectors. They could add the force vectors no problem, but then they couldn’t (at first) wrap their heads around how to draw the Fnet vector. It seemed like it was going the wrong direction (they really wanted to close the shape, not draw from where they started to where they ended up). But with adding up displacements, the direction of the total displacement is obvious to them. So if I saw them having that problem, I would get them to make up a displacement problem in the corner of their paper and then they got the Fnet direction all sorted out.

I haven’t done this with my Intro students yet, though, so we’ll see how it goes. They apparently don’t learn sine and cosine in geometry anymore, so when I tried to do this stuff earlier (like I usually do for the Intro classes), it was a huge disaster (lots of panicky, scared juniors!). So I’ve postponed until UBFPM, and we’re about to hit it.

• November 28, 2011 7:10 am

Kelly,
When did you do the vector walk activity with your students?

• November 28, 2011 7:18 am

What do you mean by vector walk? Or if you mean the”walk” vectors, that was from the summer homework.

• November 28, 2011 7:57 am

I was thinking of the vector scavenger hunt thing where you have students go around the campus to map out vectors.

2. December 10, 2011 11:30 am

John. Your warm-up question is a good example of what I have been trying to do with clicker questions this term, moving from trying to get students to confront their “misconceptions” to question types that uses compare and contrasts cases where they see that their current understanding does in fact apply for some situations. And then they can build on that understanding for other situations. So in the past I would have had a clicker question that asked just one of your three vector questions knowing that students would get confused trying to figure out if the one I gave them needed addition, subtraction or building a closed polygon. But now I would present all three and ask them to figure out which answer goes with which question.