I’m not as happy with this… not as coherently packaged as first, trying to do too much, etc. But here it is.
Question 1:
In class we discussed that 60 mph means that you travel 60 miles in each and every 1 hour of travel. What does it mean for a car to be traveling at 60 mph if it hasn’t yet gone for an hour? What does the “60” mean, for example when you’ve only traveled for 30 minutes, or 15 minutes, or 1 minute?
Question 2:
You and a friend are driving along the highway at 60 mph, exactly 9 miles away from your exit. Your friend announces, “It should take about 9 minutes to travel those 9 miles, because every mile takes one minute.”
How do you think your friend arrived at this conclusion? Is he right? Explain.
Question 3:
Your friend is back at it again, keeping track of where you are one the highway, but this time he jots down the mile-marker every ten minutes.
|
Clock Reading |
Mile-Marker |
|
6:00 AM |
15 |
|
6:10 AM |
25 |
|
6:20 AM |
36 |
|
6:30 AM |
48 |
|
6:40 AM |
61 |
|
6:50 AM |
75 |
|
7:00 AM |
— |
Are you guys driving with constant speed, increasing speed, or decreasing speed? Explain how you can tell from the data above.
Question 4:
What’s your best estimate for where your car will be at 7:00am? Explain how you came to your answer and why it makes sense to you.
Question 5:
During your drive, you and your friend start arguing about whose car is better at speeding up. Your car can go from 0-60 mph in 4 seconds. Your friend’s car that can go from 0-80 mph in 5 seconds.
Whose car would you say is better at speeding up? Explain how you reached your conclusion.
Teach. Brian. Teach. 
I’m curious whether these questions would work in class, maybe in groups. I think it’s cool to get them thinking about this stuff before they come to class, but I have to say that “reading quiz” always makes me nervous because students will feel like you’re big brother or something.
I think that if getting these questions under their belt allows you to do cool things in class, then it’s definitely worth it. Of course, in the ideal sense, students should be engaging with the material to be ready for class regardless.
Yeah, my hope is to get them thinking about some important things before class, so that we can further elaborate and build on those ideas… I’m just trying to think hard about what exactly I want students to have engaged with before class, and I’m finding that the reading doesn’t have everything, and so I’m trying to squeeze a bit more through the questions…
Have you seen this video? My students sent it to me and I think it’s fascinating – kind of gets at some of your other (earlier) questions. But mostly it’s great to see students try to figure out what Chelsea is thinking and how she’s reasoning about the problem.
I have seen this video. My brother is a HS math teacher, and he said his students were talking about it a lot in class, and so he sent in my way.
Other comment. Do you think showing this in class is viable, or too demeaning?
I showed it in class unwittingly – a student shared it. I think for a group of teachers, the math difficulties are not that surprising — and the way in which she tries to reason from something she is familiar with (a running pace) and convert that to a car’s “pace” is fascinating and not trivial reasoning. I also think it’s cool that the “rule” for 60 mph must somehow scale – so 40 mph can’t just be the same “rule” as 60 mph (I think that’s her protestation). My biggest concern as we watched was hat some in my class would have similar trouble figuring out the correct answer and feel mocked. Anyway, the initial reaction from the class was a bit inappropriate/demeaning, but after really listening to what she was saying, and how the husband’s questions were not helpful, I think it was fine.
Two things to say here. Both opinion-based. Take them for what they’re worth.
(1) Your version of question 1 from previous post was tighter and more provocative than the expanded version here. I say go with that one.
(2) The video under discussion here makes me really uncomfortable. I get that it illustrates misconceptions that it’s important for your future teachers to know about and pick apart. But they’re not uncovered in a respectful way at all. I worry about the reinforcing of toxic stereotypes-stereotypes of the scientifically literate and illiterate. I worry about consent (not from a legal standpoint, but from a karmic one). There must be better examples out there of what you would hope to illustrate.
I share both of your opinions.
I’m bothered by the 0–80 vs 0–60 comparison, as it assumes that both are constant-acceleration problems. I believe that a constant power model is more appropriate. In this particular case, that makes the difference between the cars bigger, but teaching physics is about choosing reasonable models, not about lucking out on examples where the wrong model happens to get an ok answer by luck.
Yeah, I’ve though about this a lot, and am not ignorant of the fact that it’s not constant acceleration. My teaching physics students, in fact, really struggled with difference between constant acceleration vs. constant power output.
One thing is that it still is the average acceleration over the time periods give, and. it is a way of comparing them that both has some validity, and makes some connections to how we talk about “fast” cars in everyday language. I don’t mention the word acceleration either… I suppose.
The constant power model I’m thinking is broken as well (eventually it reaches a peak speed/energy), so it’s really an issue of what I am trying to accomplish here. I want to get them beginning to thinking about having speed vs. the (average) rate at which speed is gained.
Your pointing out that the phenomena doesn’t seem to fit the bill– I’m open to better suggestions for accomplishing that goal with a better phenomena / question.
However, it’s hard to argue in this video, that an constant acceleration model is bad across range shown http://vimeo.com/28533143
I was thinking of constant power with at least the drag force proportional to
and possibly with the lower-order frictional terms as well. I agree that constant power without drag would be a worse model than constant acceleration.
If the students are too early in their physics learning to handle drag forces, then a constant acceleration model may be ok to use, but you should try to find a video of a a car accelerating to its terminal velocity, so that they can become aware of the limitations of the model as well.
They are certainly early in their learning–they haven’t even learned about acceleration yet.