I’m drafting my pre-class reading quizzes for the summer session. Here is day one. Please comment.
Imagine you are tutoring an 8th grade student in physics. You notice that the student is a little confused about the difference between what is meant by 3:00 pm and what is meant by 3 hours. How would you explain to this student the difference between 3:00 pm and 3 hours?
You are still tutoring this same student, and notice the student is having a similar problem, except now they are confused about the difference between being at mile-marker 72 and having traveled 72 miles. How would you explain to them the difference between being at mile-marker 72 and having traveled 72 miles?
Here is a physics problem! Imagine you are driving a car along a long straight. Your friend in the passenger seat is recording where you are every hour of the trip.
Explain why your friend might reach the conclusion that the speed of the car at 3:00 PM was 24 miles/hour.
Then explain why that answer is probably not correct.
You might have noticed that the table above does not have information about where the car was at 5:00PM. This information is missing because your friend was asleep. What do you think is a good estimate for the mile-marker of the car at 5:00PM? Explain how you determined your answer and why you think this is a good estimate.
Here is one final question to consider. How much total distance did you and your friend travel between 2:00PM and 5:00PM? Why is this answer different than your answer to question 4?
What would they have read for that day?
Here is a link.
The truth is that I’m not happy about the reading. Last semester my questions were actually more oriented toward actually understanding the reading. I had questions such as, “In your own words explanation the difference between average velocity and average speed”, “What’s some ideas from the reading that was difficult to understand? What specifically are you still trying to understand about it?” I also had two multiple-choice questions. One was a strobe diagram question, asking to compare speeds. Another was a graphing question, asking to compare speeds.
I’m now trying to help orient students to important ideas and distinctions that I know are important building blocks, which I think are absent from the reading. For example, it never introduces any notions of a coordinate systems, reference point, or number line concept. Thus, it never really introduces or defines the concept of position, and how that might relate to displacement. Still, the word “origin” shows up in some of the example problems. And of course it implicitly shows up in a graph. But that seems wrong place to introduce terminology and such.
Similarly it never distinguishes “when things occur” from “how long things endure?”. Yet it still somehow manages to use the delta symbol, still with no explanation. It also somehow manages to introduce the word instantaneous in one of the example problems without any discussion.
It also never discusses the meaning of any of these ratios and how we should make sense of them as ratios. It just gives them categories such as scalar, vector, and component. I want to ask another question like, “How can your speedometer say you are going 60mph, if you haven’t actually gone 60 miles in an hour?”
The question is, “Can I really accomplish any gap-filling of this magnitude in a short series of questions?” I don’t think I can, but I think it’s better them having them try to make sense of a text that I don’t think can be made sense of. I’d rather try to introduce some distinctions that I’ll further elaborate on in class.
24 mph at 3:00 could be correct, though. We have not established constant velocity, have we?
I love the direction you’re going here-orienting your students towards ideas that their students will have, which will simultaneously allow you to work on your students’ ideas. Lovely.
For what it’s worth, I’ve gotten a lot of mileage (as it were) in College Algebra out of a simple photograph of a speedometer/odometer. One of these measures average rate of change, the other measures net change. And if there’s a trip odometer in there too, so much the better.
Someone else pointed this out on twitter, suggesting I change it to, “is probably not correct”…”or doesn’t seem to fit the data”
I like the idea of discussing speedometer/odometer picture… especially, because I’ll have them work on this video-problem later: http://vimeo.com/28533143
On the first question, “3:00” could mean any of several things, including 3 hours or 3 minutes. If you are trying to get at instant vs. duration, change to “3:00 p.m.”.