Math Carnival
The math carnivals are in full swing. I’ll be hosting one here at Random Walks in June, so get excited for that! 🙂 If you haven’t had a chance to check out Math Carnival #85 hosted by Aperiodical, go do it now. I especially like the idea of Math Busking, since I’ve done plenty of street performing as a juggler. Maybe I need to try adding math to my show!
Also found around the web
- Awesome article about correct hangman strategy which touches on cryptography and conditional probability. Very good stuff, and possibly of good use in the classroom too.
- Did you know a knight can visit every space on a chess board? I’m sure you did, but you may not have ever seen it actually happen:
- I don’t have an iPad, but if I did I would definitely get this app from IBM which presents 1000 years of math history in an interactive way. Looks great!
- These recent math videos that parody pop songs are funny.
An article from J. Michael Shaughnessy
Here’s another article from NCTM president, J. Michael Shaughnessy. He makes a point that Art Benjamin has made before, that Calculus should not be the goal of high school mathematics. I think I agree too. In general I agree with his article, but there are a few points on which I disagree.
In particular, he says, “If calculus is to be taught in high school, it should be taught at a college level.” I don’t think it hurts to teach non-AP Calculus. I say this because “Calc with Apps” is a course I teach, and I find the students really benefit from the more relaxed pace. There’s no pressure from an AP test at the end. Many come to my class lacking confidence, and leave having their confidence restored.
Shaughnessy goes on to say, “Whenever students enroll in calculus, they should have a solid mastery of algebra, geometry, and trigonometry.” I only agree with this in part. My kids have already taken Algebra 1 and 2, and Precalculus. There are definitely some algebraic rough spots that need to be smoothed out as we go through the course. But again, I find my course the perfect place to do it–since those algebraic skills are routinely needed for the Calculus. And in the end, they say they like math again.
I’ve heard from lots of kids who have gone on to take more Calculus in either high school (AP) or college and have really appreciated the informal foundation that we provided in our lower-key course.
This is Shaughnessy’s final president’s message. President-Elect Linda Gojak will be taking over. I’ll be sure to highlight some of her articles, too!
Random Walks 
Re the Shaughnessy article: One possible problem with teaching Calculus at the college level and therefore at the high school level as well is that it is too often taught as algebra; that is, as the algebra of differentials and of indefinite integrals. To avoid that, put more emphasis on the steps that give rise to the algebra in the first place, which is to say the mathematical modeling aspects of Calculus.
Some educators for this very reason suggest that we teach difference equations instead of differential equations, and finite sums instead of integrals. The results are approximate, but more intuitive. If the calculations were done in a spreadsheet, graphs could be easily generated to add to the intuition.