How I Teach Calculus: A Comedy (Rates & Gas Tanks)
It seems that cars are just the best context generators ever. Lots of people use one, they cost us giant piles of money, we even start wars over getting gas for them. Working cars into math lessons is like an EpiPen for the the anaphylactic reaction that most students have to school.
By this, I do not mean the type of drudgery that gets passed off as application. You are not generating context or interest by providing all of the information about a toy system that has never and will never actually happen.
I was driving my new car and I noticed — perhaps fallaciously — that my gas gauge seemed to drop faster when the needle was below 50% than when it was more full.
I decided to take pictures of the gas gauge and odometers. I spliced them together into a kind of stop-motion video, but the timing isn’t quite right.
[This is also an experiment to see if Metallica will sue a teacher for fair educational use of their product. Anyone want to take the over-under on 5 days until a cease-and-desist order?]
Here are the images (~4MB) and extracted data (.csv), if that’s your thing.
There are a thousand questions that could arise from this, which is why I love the rich media technique (WCYDWT), and this video isn’t even that interesting really.
The point is not to teach the specific curriculum, but to trust that the important curricular points will arise through creative questions and actual thinking. All of that planning that we do (and bitch about) is actually hamstringing our students. The planning is where the thinking is, folks.
- The obvious question: What if you drive differently? Like stop-and-go vs. highway? That questions shows a lot of thinking, and requires us to go and get data that is much cleaner.
- What shape is the gas tank and how does the gas gauge work? This questions requires a lot of genuine related rates (hallelujah!) and some useful understanding of geometry (Bonjour, Canards!).
- Is it psychological, because you start worrying about running out of gas as you get less? This question is an awesome combination of psychology and math.
- There are a million more that students will come up with, both more advanced and rudimentary than these. This is called real differentiation. This is called being interested. This is called everyone freaking drives a car.
The point here is that my kids totally bought into this, and, like I said before, it’s really not that interesting. The model here is that when the teacher shows some interest in generating good prompts, the kids respond with a heightened awareness beyond what “school” normally requires.
I suppose the only thing I’ve learned in my short years is that students respond genuinely to a teacher who is invested, interesting, and totally willing to ignore the normal mode of school.
Motivationally Speaking: Star Wars I’m Aware That This Horse Is Dead, but I Whittled This Club Myself…
Great Post. I enjoyed reading your blog. I’m a math tutor. It’s very funny. Hope you post more. Kudos.
Awesome post
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I can’t access the video. In the end, did The metalllica song get you in trouble?
@Avery: It still work for me, but I did get an email from Metallica’s record company. I bet if I had just avoided using their name in the post nothing would have happened.
I think adding that note at the end at least makes it known that your use of the song was thoughtful and reasoned as opposed to just willy-nilly downloading an illegal copy and throwing it in. Thanks for the thoughtful discussion!
So I wonder what it means when it says “reproduction by a teacher or student of a small part of a work to illustrate a lesson.” In that context was the use of Metallica’s work directly illustrating a lesson or would any song (possibly one with a creative commons license) been just as effective? I guess I question this because students are already inclined to disregard copyright when it comes to music, and they probably aren’t going to consider that you as an educator felt (maybe justifiably) that using the song was within your rights under fair use for education. What message do they take away from that?
@Mary: You make a good point, but I feel the nature of copyright can’t be hinged on whether someone thinks my song choice was appropriate enough. I chose the song because it has connotations to students in Iowa because of the Iowa football team. I chose the song because it has a natural climax where I wanted it. I also chose it because the video would be nearly unbearable without something high energy. (I’m not that good at video editing yet).
As far as your fears of tacit copyright infringement lessons, I’d say that there’s more to be worried about than a teacher using a song that he already owns in one of his lessons. Students ignore copyright because the technology is available to get things for free. It is true that they have the choice not to do this, but the message I am sending is that I am applying fair use to a piece of media that I purchased in the nineties.
Do you think I should add that to the end of the video, something like: “This song was purchased and is being used under fair educational use”?
I really enjoy reading your blog. I am a pre-service math teacher and hope to offer this type of intriguing problem to my students on a regular basis. I have one aside note, considering your foray into ethics this semester I find it interesting that you would blatantly disregard copyright. By posting this to YouTube and then broadcasting it to the blog-o-sphere you lost your rights to claim fair use for education.
@Mary: Thanks for the comment. I would disagree with you that I’ve lost my right to claim fair use for the Metallica song. Although placing it on YouTube would seem to be a violation, I have restricted the ability to search for the video. The video is for purely educational purposes and has no commercial value. I would agree with you if I were using this video during a paid professional development session that I was leading.
I think Mary raises an interesting question that has been raised often on Dan Meyer’s blog too: Is sharing copyrighted material for education use a violation of fair use? I obviously don’t think so. If I were selling my videos with copyrighted content, now there’s an ethical dilemma. Here’s a link to the fair use documentation: Fair Use
My dad just bought a new car and it has a gauge that displays your current mpg as compared to your average mpg (calculated over the car’s existence). I suspect there’s an interesting psychology/math connection here too, because the “better” driver you are, the higher your average mpg and thus the harder it is for you to move the needle above that midpoint. And, given that most of our driving patterns remain relatively stable (in terms of city vs. long-haul), there’s a point at which you’d inevitably top out. Now, if you’re typically a “bad” driver, you could make yourself feel really good once in a while by cruising along and sending that needle way up.
On an unrelated-to-math note, my 5-year old son was listening in the background, and when it was over said “Mom! That was a really cool song!” I suppose this means I shall have to acquire some Metallica, to continue his musical education :)
“I suppose the only thing I’ve learned in my short years is that students respond genuinely to a teacher who is invested, interesting, and totally willing to ignore the normal mode of school.”
Amen. Best thing I’ve read all day.
Thanks!