# crumbs!

One day while doing a computation on the board in front of my students,
I accidentally wrote 1 + 1 = 1. (No idea why.)

Student: Um, don't you mean 1 + 1 = 2?

Me (embarrassed): Oh right, thanks.
[Erases mistake. Pauses.]
Wait. Is there a universe in which 1 + 1 = 1?

Class: ... [Stares blankly]

Me: That's not such a strange question. Don't you know that YOU live in a world where 11 + 1 = 0?

Class:... [Jaws drop.]

Me: Yeah! Think about it! 12 = 0 and 13 = 1 and 14 = 2 and 15 = 3... sound familiar?

Class: Military time!

Me: Exactly! [Points to clock on the wall and starts impromptu lesson on modular arithmetic.]

I hope at least one student was convinced that math is cool.

'Cause I'm convinced that making mistakes isn't always a bad thing!

# crumbs!

Not too long ago, my college-algebra students and I were chatting about graphing polynomials. At one point during our lesson, I quickly drew a smooth, wavy curve on the board and asked,

"How many roots would a polynomial with this graph have? Five? It crosses the x-axis five times."

# crumbs!

One of my students recently said to me, "I'm not good at math because I'm really slow." Right then and there, she had voiced what is one of many misconceptions that folks have about math.

But friends, speed has nothing to do with one's ability to do mathematics. In particular, being "slow" does not mean you do not have the ability to think about, understand, or enjoy the ideas of math.

Let me tell you....

# crumbs!

Physicist Freeman Dyson once observed that there are two types of mathematicians: birds -- those who fly high, enjoy the big picture, and look for unifying concepts -- and frogs -- those who dwell on the ground, find beauty in the scenery close by, and enjoy the details.

Of course, both vantage points are essential to mathematical progress, and...