A while ago k8nowak was looking for exponential data besides credit card loans and bacteria growth. Take a look at the data describing visits to my (very new) blog:
Looks a lot like exponential decay to me. In retrospect, I’m almost sad to have posted and ruined the trends. But, for those of you with very popular blogs, I think you might have an interesting option here. Have students create a webpage, right, for any old reason – to review multiplication tables or explain the distributive property or whatever. They could even just post their drawings, a math joke, short stories, whatever. When they’re done, link to it from your blog! Do it early in the morning so you don’t get the weird bump at the front edge like I did. They’re not likely to get a lot of other traffic, so I think the data might be cleaner than mine.
This is risky if you are banking on the graph being exponential, but if you’re open to a class discussion about modeling traffic, where exponential curves will probably, but not definitely, come up, I think this would be fascinating. You know, you could guess how many visits will come the next day… and then see how close you are! Would this be more interesting than loans and radioactivity?
I’d be interested in hearing from other blogs who notice peaks in traffic when someone famous gives you a reference. Is the curve always exponential decay?
Kate Nowak
December 17, 2009 at 8:56 pm
That is a cool idea! The uncertainty of the outcome makes me a little nervous in the teacherpants, though.
You could combine this with an online presentation assignment like @msgregson’s.
I am NOT famous.
Riley Lark
December 18, 2009 at 9:06 am
If you could collect many data beforehand for separate instances, you could discuss in class what usually happens before doing the live test. For example, you could show the effect happening five out of five times in trials before class (famous bloggers: take turns linking to my site? :p). Then, announce that you’re going to to send people to a class-generated page.
Day 1 after linking to class: study the prior graphs and the starting point of the class graph. “We started today with 90 hits. How many do you think we’ll get tomorrow?” Various discussion ensues, with at least a few misconceptions coming out. This takes maybe 15 minutes and you give a skills test or other activity with the rest of class.
Day 2: omg, we were right, or wrong. Can we make a better guess for day 3? What was the pattern in the other graphs? Is there a different base here (ooh, base, advanced topic time) or just a different initial point?
Day 3: omg, we were so much closer, or, wtf, the graph went UP! What’s going on here? Why is this different? (This is secretly OK because you’ve already discussed a lot of things about exponential graphs).
Or something like that. I think you could do a lot of great things even if the data doesn’t come back right. And, while that would be sad, inaccurate models are part of math, and that’s an important discussion to have with your class as well.
Would it be important to discard results from your county so that kids’ hits wouldn’t affect the graph?
Also, Kate, when you mentioned my site, seventy people came here and subscribed on google reader alone, so… I think you might be famous. I think if Johnny Depp told his fans to come and read my blog I maybe would get like, seventy ONE people. Barely a difference.
Kate Nowak
December 18, 2009 at 4:03 pm
OK well they might have come to check you out because I sent them, but they wouldn’t have subscribed if they didn’t like what they saw. Keep up the good posts! No pressure!
Anyway thanks for the idea. I’m supposed to be writing the “regressions” unit for Algebra 2, so I’ve been trying to collect data that fit various models. This might be something I try if I’m feeling audacious.