Math on the web

Here are two items that have been shared with me in the last 24 hours:

Item 1: Want To Be Better At Math? Use Hand Gestures! Jeremy Shere of Indiana Public Media. Check out this very short audio news that suggests that math instruction has been shown more effective with gestures. I flail around in front of my classroom all the time, so I guess that makes me a good teacher, right? I’d sure like to think so! 🙂  (HT: Tim Chase)

Item 2: How to Fall in Love With Math. Manil Suri, professor at a small school down the road from me (University of Maryland…maybe you’ve heard of it?), has a very nice piece on why math is a worthy object for our affection. It’s been heavily shared in the circles I travel–and for good reason. He reminds us that people fall susceptible to two very common errors when casually speaking about math: (1) We reduce it to arithmetic, as in “come on guys, do the math” or (2) we elevate it to something so ethereal that it’s impossible to grasp, as in “that mathematician talks and I don’t understand a word he says. I never was good at math.” Math, Suri says, is much more than arithmetic and much more accessible than people give it credit for. People can appreciate it without understanding every difficult nuance, just as they do art. (HT: Beth Budesheim)

 

 

 

Bring an end to the rationalization madness

In less than a month, we’ll be hosting the one and only James Tanton at our school. We’re so excited! I’m especially excited because he’s totally going to help me rally the troops in this fight:

He posted this a few years ago, but I only stumbled on it recently. I’ve been looking for Tanton videos to use in our classes so we can get all psyched up about his visit! Needless to say, I was loving this video :-).

For more on why I’m not such a big fan of ‘rationalizing the denominator’ see this post.

Composing power functions

I presented the following example in my Precalculus classes this past week and it bothered students:

Let f(x)=4x^2 and g(x)=x^{3/2}. Compute f(g(x)) and g(f(x)) and state the domain of each.

 

As usual, I’ll give you a second to think about it yourself.

..

 

 

..

 

Done yet?

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Here are the answers:

f(g(x))=4(x^{3/2})^2=4x^3, x\geq 0

g(f(x))=(4x^2)^{3/2}=8|x|^3, x\in\mathbf{R}

The reason that the first one was unsettling, I think, is because of the restricted domain (despite the fact that the simplified form of the answer seems not to imply any restrictions).

The reason the second one was unsettling is because they had forgotten that \sqrt{x^2}=|x|. It seems to be a point lost on many Algebra 2 students.