Internet Videos: waste of time or precalc project GOLD?

To round out every unit I teach, I ask my students to both take a test and do a project.  (Does “Do this or your grade sinks 10 points automatically” count as asking?)  I try to mix up the types of projects.  Some have students use math to create work in the artform of their choice, some analyze actual data with the stuff we’ve been learning about, and some require research about math that other people have already done.  Also some are probably just a little bit weird, like when I finished the trig unit by asking my students to write a baby book about their first ten days after adopting a trig function.

Ideally, I want my projects to be opportunities for my students to really go off into the math woods and just get into it.  I want them to get excited so that they happen to use what we’ve been learning in order to accomplish something they’re into.  Sometimes this happens, but definitely not the majority of the time.

During my first year of teaching, I came across some data about the number of views of an OK Go video on a blog about viral trends.

The data only covered the first ten days of the video’s existence.  Personally, when I saw it, my first question was: if I fit an equation to this, will it match up with how many views there are today?  And since I was in the middle of the exponent/logarithm unit with my precalc kids, my second question was: is the equation in question a logarithmic equation?

I did a little bit of messing around with a graphing calculator and had a super great nerdy time working on this by myself.  I wanted to somehow have my students go through a similar process.  Also, this was in fact a really great model of a logarithmic relationship, so I wanted them to poke around at it and get a more developed sense of logs.

Here it is:

But while I think I did a good job with the second bit, I definitely didn’t accomplish my first goal.  I gave them the best fit equation before asking them to do anything at all.  Part of my reasoning was that most of my students don’t have graphing calculators, and in my first year was wary of bringing in something as distracting as laptops so that we could use them to do the same thing.

Now that it’s two years later, I think I can definitely do this better.  Since it’s not quite yet the school year, I’m going to work on this over the next few days while my brain isn’t over-exhausted.

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