# Fan Cart

Via Frank’s Noschese 180 blog (with his permission).

In the comments—

- What was the student thinking? How did he or she decide to make these particular marks on the paper?
- What question or problem would you pose next to help the student make the next step toward understanding?

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It looks as if the student had N2 in mind, but has some confusion about fnet and acceleration. I can only guess that 4 x .2 = .8 was an attempt to use N2 to find ‘initial force’. The chain of adding .3 looks like an attempt to find the ‘sum of force’, or fnet. Judging from the final step of dividing by mass, I’m guessing the student was looking to use N2 to find acceleration.

What is pushing on the cart? Does that push increase as time goes on?

When I first glances at this I was sure the student was very confused. It seemed they were confusing concepts and simply multiplying and adding numbers they were given. However after some thought I realized that might not be the case. It appears the student was using momentum and then adding the impulse for each second. They found the final momentum and then divided by the mass.

I’m not sure the student knew this. I’d like to have a dialog with the student to know for sure. For me the tipping point was starting the addition chain with a negative momentum.

I agree that this student seems to be working with momentum ideas rather than force & acceleration ideas. I’d want to have a vocabulary discussion, just so that this student can successfully communicate with people using standard terminology.

Perhaps the student is thinking something like this: The fan starts off with -.8 *somethings* (which can be found by multiplying m*v) and, then each second the force changes that something by 0.3 every second. If I simply add 0.3 repeatedly until I’ve done so for 10 seconds, then I’ll have the final amount of *somethings* after the 10 seconds. Then to get back to v from *something*, I’ll have to divide by m. The process shares much in common with ideas of momentum and impulse. The extent to which this is explicit in the students’ mind cannot be determined from this work alone.

I’d be really excited about what the student had done, and ask them how they came up with this approach and what they were thinking. I’d also be tempted to point out how they multiplied by m in the first step and then divided by m in the last step, and ask about that. How did they to do that? I’d hope to compare their approach to someone who divided F by m and added that 10 times to the v. I’d want to know if the two students thought their approaches were similar or different, and in what ways. I’d hope for them to teach each others’ methods and practice using both methods to solve problems, to see if they both always work and provide the same answer, or if they ever got a different result. I’d hope to name the approaches.

The next problem I might give them is one where the force is applied for 200 seconds (see if they think of repeated addition as multiplication), and then 10.5 seconds (see if they can handle non-integer seconds).

I suppose we’d also want to ask about direction… north vs. south in relation to +/-.