Spiderman and Fermi

Whoa- this semester is flying by.  I know it's only the 3rd week of class, but at this rate the semester will be done before the weekend is through.  First off, I want to acknowledge Carol Cramer's helpful comments, thanks for reading and thanks for the great suggestions.  Yesterday and today, Mrs. Colwell and I began talking about how we wish we could fit in some different activities, but how we're already pressed for time as it is.  I think we're both excited to try out some new ideas in the coming weeks, so stay tuned to see what they turn out to be and how they go.

When I came into class yesterday, I was a little surprised to find out that we were having a test, as I expected that to occur on Tuesday.  Unable to help work things out, I started thinking about possible material to present during future "warm ups."  Also, I offered to help grade exams or homework, and boy did Mrs. Colwell's eyes light up!  It was like a kid on Christmas morning.  During the warm-ups at the beginning of class, Mrs. Colwell usually grades homework while the students occupy themselves with some practice problems, or listen to me ramble on the days I show up.  Mrs. Colwell had expressed interest in hearing stories of mathematicians before, and Thursdays lesson was on variation (not the statistical one, but how a function varies wrt some part.  e.g. f(x)=3ax^2 varies linearly with a, but by the square of x).  I figured it would be a good time to pull out some cool Fermi problems.

One of the new postdocs in my lab (Aaron Santos) is about to publish a great book on Fermi calculations that I had the good fortune to proof-read.  Blatantly ripping off one of his problems for the benefit of the students, today I gave them a short history of Fermi before we dove into calculating how much Spiderman would have to eat to shoot all of that web.  For those of you interested in the answer, both classes came up with 56 lbs per day.  

Both classes seemed to enjoy this storytime/problem but the after-lunch class was way more engaged, as is their full-bellied wont.  Everyone was shouting suggestions for the length of a spiderweb-shot, the number of shots per day, estimates at shot widths, and that Batman was better than Spiderman.  It was a lot of fun, and I agree that Batman is better than Spiderman- he's just a justice-loving hard-working billionaire whereas Spiderman was randomly given superpowers by a radioactive spider.  Gotta root for the hard worker.  The thing I found interesting was that this sort of silly example was actually as engaging as it was.  I always felt that such pandering to presumed interests ran the risk of insulting the student's intelligence.

Anyway, two really cool things happened today.  In my first class, Scott came bounding up to me as class began with the answer to my brainteaser from last week.  He found that the next value in this sequence:  1, 11, 21, 1211, 111221... is 312211!  I feel like I had bet everyone $5 that they couldn't find the answer, so now I owe Scott $5.  Good thing I didn't remember in class, because I didn't even bring enough money for lunch, and had to borrow some from Mrs. Colwell (let the record show I owe her $4).  After Scott impressed me with this, he proceeded to solve a Rubik's cube to the amazement of the back row (i'm serious).  I thought "holy crap- this kid is amazing!  Guess I don't need to worry about him anymore," as he beamed confidence across the room.  After my warm-up and some lecture by Mrs. Colwell, I wandered the room looking to answer questions as the kids solved this problem:

• y(x) varies by x to the 6th power
• when x=2, y=100
• find y when x=3

When Scott raised his hand, I was expecting to see one of the homework problems, him having blown through the in-class assignment.  Instead, he was still struggling with the above problem.  We worked through it twice before the "ahhhhh... I get it now" moment.  Going back to a comment I made in a previous post, I think Scott is a great example of the students in this class: they're very very smart but don't always know how to use the tools they have.  Once we show them, they're able to rock!  This is partially why I've been emphasizing group learning as a new activity- the students will be able to help each other reach the "aha!" moment while reinforcing what they've learned.  Students of this caliber may thrive with such activities (I have no data to support this). 

The second cool thing that happened today was the after-lunch class's interest in their grades.  After getting their test scores back, Mrs. Colwell was rushed by a crowd desiring to know how they're doing.  For many of them, it wasn't very good news.  But they care!  And, just like the class before lunch, they have the raw ability.  I'm hoping that our group-learning testing in the weeks to come is well-received by the after-lunch crowd.  I think their extra energy may facilitate discussions, I think the discussions may take away some of the extra energy, and I think any deviations from the traditional lecture style will be welcome for these students.  We shall see.

Also, for the record, I did not get a perfect score on the test yesterday.