As you might have heard on Dan Meyer's blog I've started making some of my own Graphing Stories videos. Dan Greene (other Dan) on twitter suggested I make one that shows a system of equations. I filmed one of me in a no holds barred footrace versus myself. (Don't worry, I won) Here's how it came out:

Once I'm finished I'm going to make a bigger post about all of the videos for this, and by then I will hopefully have found a way to provide them in better quality than Youtube. In the meantime, I'm looking for some input...

I'm not sure how well it translates at this angle. What do you think? Do you think what's going on in this one will be discernible to students?

Also, I'm looking to make some more of these (it's really easy now that I have a template). Anyone have any more good ideas? Let me know in the comments.

This is pretty cool, but I agree that it might be a bit tough to see when the two yous are at the same point at the same time. The title of the graph is a copy-paste error, I believe, but maybe it's serendipitous because that might be an easier video to discern what's happening... I am imagining two yous climbing a chain-link fence Spidey style, one pauses to rest, the other overtakes, etc.

ReplyDeleteThanks Dan, fixed the title. The fence climbing seems like a great idea (or maybe I could go to a rock gym or something). I was thinking "Man, where am I going to find a tall chain linked fence?" Took me a solid minute to realize that there is one in the background of the running video.

ReplyDeleteI like it. It may be tough to tell exactly when you overtake yourself, but if students have already gone through the original Graphing Stories, they should have an idea of what they are looking for.

ReplyDeleteAs for ideas: I started taking footage last year of thrown and falling objects (vertical motion). But don't know how to put them together like you and Dan M. have done. I'd also like to see something to do with projectile motion where students need to discern the difference between the horizontal and vertical components of a projectile. If you can figure out how to do that well, you'll be my hero.

Without access to a blimp for overhead coverage, I think you did a great job. As the previous reply says, they will know what to look for. The important part is that they recognize that there is a specific point at which each "you" has gone the exact same distance in the exact same time, but got there in different ways.

ReplyDeleteI will be using this in my intro to systems of equations, so thank you.

There is a very unfortunate problem with the animation of the graphs: the red and blue graphs aren't plotted at simultaneous times. For example, if you freeze the movie at 1:15, the blue graph is currently at t=5, the red graph is at approx t=5.3. At frame 1:22, the red graph is at t=10.5 and blue is at t=11.3. To the naive viewer, it looks like the blue graph is ahead!

ReplyDeleteThe fence idea has a possible disadvantage that the vertical distance up the fence matches the vertical "distance" axis of the graph. This perhaps reinforces an overly literal interpretation.

What if it were filmed from the side? Probably should be with runners going from R to L, deliberately counter to the direction in which the graph is created.

So, I found a student with a free period today and asked him to help me out and try to graph it. I gave him a little information to help (The fence is 110 ft long, the farthest distance either runner travels is 220 ft) His graph turned out very accurate, so I'm feeling much more confident about it. Even if it does turn out to be difficult, I think the ensuing conversation on what visual clues can be used would be great.

ReplyDeletecoxmathblog- I'll work on projectiles with separating vertical and horizontal, I already have some ideas. The biggest problem is that 15 second clips are much easier because of the template I have, and having something mid air, on camera for 15 seconds would be pretty ridiculous.

Brian- Awesome!

Tom- I'm aware of that problem, and I'm going to try to tweak it. Unfortunately it's a mixture of fine motor skills and technological limitations. The way I'm animating it is a bit too finicky, and if i had a steadier hand I'd probably be able to do it better. I tried a couple times to have it line up exactly, and that was as close as I could get before I decided I'd spent enough time on it. I really like the idea of having the path of movement go opposite the direction of the graph.

I wasn't able to notice that red shorts overtakes blue shorts until the slow-motion part. At both speeds, I found it impossible to see what what was going on after about the ten second mark.

ReplyDeleteCool idea, though. I wonder if it would be easier to see from a side view? With the runners running left to right instead of away from the camera?

I just had a thought that videos for related rates problems in calculus would be so powerful.

ReplyDeleteWater pouring into a vase at a particular rate, oil spilling in a lake, a ladder slipping, a bubble being filled with air at a particular rate, an airplane flying overhead, two cars driving away from each other at a right angle, etc.

I hate related rates problems because they are so contrived in textbooks. But at least filming the would give students some intuitive sense of what's going on.

http://www.samjshah.com/2008/12/08/related-rates-in-calculus/

Sam, that is an excellent idea. We'll have to collaborate on which particular problems could reasonably be filmed.

ReplyDeleteI recently had the beginning of a thought about how these could be used for Calculus. Still have the students graph the problems, but use graphs that have interesting ups and downs, and then have the students analyze acceleration/speed/position

Maybe I could somehow figure a way to get the speedometer of my car on camera. Have them graph my speed in a 15 second clip where I speed up and slow down. Ask them how far I went, what was the acceleration at time xx.

In my calculus class I sit the students in a van in batches of 6 (I'm lucky to have simple insurance rules) and drive down a road marked with flags at 100-ft intervals. Some students record the time at which we pass each flag (I wrote a program to assist with this) while three students record the value of the speedometer at 2-second intervals. So, we've collected independent speed and distance data.

ReplyDeleteThe class can then analyze the data in open office Calc (excel) or geogebra to see the relationships by differentiating or integrating. I challenge them to instruct the driver in order to create specific shapes in distance or speed graphs. The kids love it, and the graphs match surprisingly well. I only wish our vans had speedometers in km/h to simplify the necessary unit conversions!

I gotta tell you, man........ you are definitely motivating me this school year! Thanks again. Since the school recently bought interactive boards it seems the video camera will be a great resource this year for me!

ReplyDelete