dy/dan

I'm offering a day-long professional development session in Calgary [pdf] on 3/21/11 and Edmonton on 3/22/11. This will be my first trip to Canada. I have no idea how I'm going to get any sleep between now and March!

Perplexity: Coin of the Mathematics Classroom

Perplexity is invaluable currency in the mathematics classroom. Perplexity is the stuff of being perplexed. When students are perplexed, they aren't asking "when will we use this in real life?" because they're too busy chasing down answers to rich mathematical questions they came up with themselves. When curriculum is perplexing, the teacher doesn't have to announce the day's objective, because perplexity nudges yesterday's concept naturally into today's. In this hands-on workshop, we will discover methods for capturing perplexity, from YouTube videos, TV shows, and movies; for creating perplexity, using free and cheap technology; and for presenting perplexity, using pedagogy that draws in every learner, that knows when to give the student help and when to get out of the student's way.

Sue Van Hattum will be leading a webinar tomorrow to counterbalance the one I facilitated a week ago. Sue is the lo-fi to my hi-fi. Sue's thesis is that we can have the engagement and challenge of WCYDWT without the multimedia.

This is undoubtedly true. Consider Polya, who offered engaging, challenging problems without degrading himself by walking up a down escalator. "Into how many parts will five random planes divide space?" for instance, is challenging and engaging and offers points of entry to learners of all abilities.

So an open question: what's the point of multimedia? If it's just amusing — which is to say, engaging in the worst, most superficial way — I can do without it. My sense, though, is that the feature common to all of these problems …

1. into how many parts will five random planes divide space?
2. how long will it take Dan to walk up the down escalator?
3. how many tickets are on the roll?
4. how long will it take to fill up the water tank?
5. how fast is the runner?
6. what is the killer's shoe size?

… is that they "reveal their constraints quickly and clearly." They're Twitter-sized queries that unpack into full-bodied mathematical investigations.

Multimedia lets us reveal constraints quicker and more clearly, though that isn't a given. Multimedia can have low information resolution. (I'm talking about your stock photography, your dogs in bandanas, etc.) But the information resolution on this single image of a ticket roll blows me away. When you put the quarter next to the roll for scale, the problem literally reveals its own constraints. The learner can gather any information she wants — circumferences, radii, diameters, ticket dimensions — without the teacher having to write or say anything.

I suppose I'm trying to slip Sue a question in advance: how do I reveal the constraints of the same problem that quickly and clearly without the multimedia?

Daniel Foster's piece in the National Review Online plays pretty fast and loose with measures of central tendency:

The public/private disparity is especially stark when one focuses on public-safety compensation in places such as Oakland; police and firemen have accounted for about 75 percent of expenditures from the city’s general fund over the last five years. Average total compensation for an officer in Oakland — a city in which the median family earns $47,000 — is $162,000 per year.

Someone break it down for us in the comments.

I'll be talking with Ihor Charischak at 6:30 PM Pacific / 9:30 PM Eastern tonight in the Math 2.0 webinar. The timing catches me in the middle of a messy reconception of this WCYDWT thing. It's keeping me up at night but it's made for an exciting summer and I'd like share some of that exhilaration with y'all, benefiting at the same time from your comments, criticism, and spark.

Me:

How many pounds of extra dirt is Stanley going to dig at the end of a full year?

Mr. K:

How many cubic feet of extra dirt is Stanley going to dig at the end of a full year?

Claire Thompson, scooping both of us:

If we had a container whose base was the area of our classroom, how high would all the extra dirt pile up that Stanley shoveled?

Any job that rewards this kind of fine-toothed, detail-oriented nit-picking is fine by me.