[japhyr]

I currently teach math to at-risk students. I don't read all of these submissions about math education, but I skim the comments on most of them. The comments people make change the way I teach math.

I have always done a decent job of teaching math. I focus on helping students understand concepts, even when they are focusing on mechanics. I use words like "shortcut" and "more efficient method" rather than "trick" when showing students more efficient ways to solve problems. I have students do problems and projects that relate to their post-high-school goals.

But with the routines of school life, I get away from the fun of math from time to time. The comments on these submissions often remind me to go in and just tell stories about math:

- "Hey everyone, did you know that some infinities are bigger than other infinities?"

- "Hey everyone, do you have any idea how your passwords are actually stored on facebook/ twitter/ etc.?"

- "Have any of you heard the story about the elementary teacher who got mad at their class, and told everyone to add up all the numbers from 1 to 100? One kid did it in less than a minute, do you want to see how he did it?"

Thanks everyone, for sharing your perspective on your own math education, and about how you use math in your professional lives as well. Your stories help.

[countrybama24]

No, thank you for teaching math to at-risk kids. Seriously, bravo.

[csours]

I love stories like these. I haven't gone much past calculus, what stories can I look for that will take me farther?

[wetmore]

You may recall that one can use the quadratic formula to find solutions to a quadratic equation (polynomial with highest term being x^2). Did you know that (one) guy that proved there is no such formula for quintic equations (highest term x^5) died in a duel when he was only 20? [1]

There is a town with a particular rule when it comes to facial hair: those who do not shave themselves are shaved by the barber. But then who shaves the barber? [2]

The other poster mentioned different infinities. One "size" of infinity is called "countable infinity" and is the infinity describing the size of the natural numbers (1,2,3,...). Say we have a hotel with a countable infinite number of rooms. I've been travelling all day and I show up at the hotel, and talk to the clerk at the front desk. He tells me every room is full, but when he sees the sad look on my face he tells me not to worry - he can make room for me. He simply moves the person in room 1 to room 2, the person in room 2 to room 3, room 3 to room 4, etc... And then the first room is empty for me, and everyone still has a room. [3]

[1] http://en.wikipedia.org/wiki/%C3%89variste_Galois [2] http://en.wikipedia.org/wiki/Russell's_paradox [3] http://en.wikipedia.org/wiki/Hilbert's_paradox_of_the_Grand_...