Thoughts from Winter Break

I’ve been doing a lot of thinking about the way I want my class to operate. For a long time now I’ve wanted to move away from the classical model of lecturing, practicing, and testing. It’s been a rough ride for me because I’ve been at 4 different schools in as many years. However, this year I have a school with excellent resources and a very supportive administration. I also expect to stay.

One thing I tell my students as they’re learning the math I’m teaching (and I’ve mentioned on this website time and time again) is that they’re not necessarily learning to be able to use math in everyday life (unless you’re a mathematician when was the last time you used a logarithm?), because they may not ever use i after the SAT and ACT. Rather, the reason they’re learning is to make connections and structure their thinking. While that works for some students it doesn’t for others. Continue reading


Shift Ciphers

The other week I guest taught a lesson on encryption. I only had about 30 minutes, so I couldn’t cover all of what I had written. Here is most of what I wrote. I hope my \LaTeX code compiles correctly.

 

Caesar Cipher or Fdhvdu flskhu

Encryption allows us to send messages to each other without others knowing what that message is. Here we will explore one of the most basic, yet unsecure types of ciphers, the Caesar Cipher.

To encrypt a message using the Caesar cipher we begin by placing two alphabets on top of one another. The top (lower-case) line will be our plain text, the bottom will be our cipher text.

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Trig — Why is this cool?

If you’re reading this and you’re a mathematician you may not think this is very profound. This is just a little idea I had as I was thinking about the application of the unit circle before moving on with my students to graphing sine waves and other trig functions.

ferriswheel

Say you’re on a Ferris Wheel at the county fair, and let’s superimpose the Ferris Wheel onto the unit circle. It’s easy to know when you’re all the way at the top of the Ferris Wheel (90^\circ) and when you’re all the way at the bottom (270^\circ). Halfway is also pretty easy because it’s when you’re all the way to the sides(0^\circ and 180^\circ).

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What’s the Point of this? (part 2)

My last post was about the 3 reasons I thought it was important to learn math in school, even though students may not (probably won’t) use it in everyday life. The three reasons were 1) It’s part of the liberal curriculum that we’re trying to give students of the United States, 2) appreciation for the fact that mathematics is all around us, and 3) it allows us to think in a more organized and efficient way. Continue reading