Total 10 Posts

## Redesigned: Alex Eckert

Before:

An e-mail from reader Kara Monroe:

I had a moment on the bike at the gym last night thinking of all the different questions student would naturally form just from looking at the display on a stationary bike.

I’m obliged to Kara and Alex for the inspiration here. A few remarks on Alex’s video to preface my redesign:

1. I’d like my students to look at the world and formulate their own mathematical questions. Therefore I’d like to show them as good of a facsimile of the world as digital video will allow. This means no artifice like a soundtrack or text on the screen. This also means I prefer fixing a camera to a tripod so the students aren’t distracted by this third party holding the camera.
2. Part of formulating and solving a question is deciding what information is important. So I removed the part where Alex tips them to the percent and the time elapsed: “Watch closely: 31:30 … 90% complete.”
3. I don’t include this in my redesign (which I faked from elements of Alex’s video) but you’d want to film the rest of the exercise session in order to show students the answer.

After:

I take these speaking jobs for three reasons.

1. To maintain the tuna-casserole lifestyle to which I have become accustomed, even though I’m only bringing in the part-time research assistant money these days.
2. To compel me to find better structures, metaphors, visuals, and exercises for communicating good curriculum design.
3. For the helpful feedback and criticism the attendees offer.

These groups of grownups are my classroom for the foreseeable future. It’d be a waste of a blog if I didn’t share what I learned last weekend.

1. Mathematical notation isn’t a prerequisite for mathematical exploration. Mathematical notation can even deter mathematical exploration. When the textbook asks a student to “find the area of the annulus” in part (a) of the problem, there are at least two possible points of failure. One, the student doesn’t know what an “annulus” is. (Hand goes in the air.) Two, the student knows the term “annulus” but can’t connect it to its area formula. (Hand goes in the air.) ¶ That’s the outcome of teaching the formula, notation, and vocabulary first: the sense that math is something to be remembered or forgotten but not created. ¶ Meanwhile, let’s not kid ourselves. The area of an annulus isn’t difficult to derive. Let the student subtract the small circle from the big circle. Then mention, “by the way, this shape which you now feel like you own, mathematists call it an ‘annulus.’ Tuck that away.” ¶ Similarly, if I give you this pattern, I know you can draw the next three pictures in the sequence. That’ll get old so I’ll ask you to describe the pattern in words. You’ll write out, “you add two tiles to the last picture every time to get the next picture.” I’ll show you how much easier it is to write out the recursive formula An+1 = An + 2. ¶ I’ll ask you to tell me how many tiles I’ll find on the 100th picture. You’ll get tired of adding two every time, and we’ll develop the explicit formula A = 2n + 3, which makes that task so much easier. ¶ Terms like “explicit” and “recursive” and “annulus” can do one of two things to the exact same student: make the kid feel like a moron or make the kid feel like the master of the universe.
2. “Talk to someone who actually makes ticket rolls. What kind of math does he have to do to make the thing,” said Russ Campbell, a community college adjunct instructor at least twice my age. Great idea, Russ. Speaking of which, pursuant to some harebrained WCYDWT idea, I spent twenty minutes on the phone with my local and state Departments of Transportation last week and it was almost too much fun to handle, peppering questions at engineers who were all too delighted that anyone gave a damn about how they calculated recommended speeds for curved roads. More of this.

## “The best learning begins with a good worksheet.”

I wrote that. In all sincerity. On June 8, 2004. In an essay for my credentialing school entitled — of all things — “How Students Learn Math.”

This gobsmacked, gross-feeling moment is what I get for digitally cataloging every essay, handout, and lesson I have written since high school.

I am grateful, I suppose, that it only took me six years to go from “the best learning begins with a good worksheet” to the kind of instructional design that — for whatever good it does my students — has me excited to wake up in the morning, has me constantly double-checking my front pocket for a camera, has me excited to walk around and encounter math in my daily life. I’m grateful because I’m positive there exists another timeline, equally plausible to this one, where I’m still that enthusiastic about worksheets after six years, or ten years. Or an entire career. I hear that happens.

I’ll speculate twice here:

1. I don’t think any of the other ten members of my UC Davis cohort ever wrote anything as stupid as “the best learning begins with a good worksheet.”
2. I don’t think any of the other ten members of my UC Davis cohort has failed as fast, as often, or as productively as I have in the six years since we graduated.

My first post at dy/dan was four years ago today.

I am extremely grateful to a lot of different folks who have patronized my work over those four years, folks like Chris Lehmann, who threw some shine on my assessment writing in my first week of blogging; folks like Kathy Sierra, Tim O’Reilly, Nat Torkington, and my other patrons at O’Reilly Media, but especially Nat, whose promotion on the Radar got my grocery line post moving, whose invitation onto the terrifying Ignite stage at OSCON 2009 got me introduced to Brian Fitzpatrick who helped me score a job at Google where I met Maggie Johnson who helped me get into Stanford. And a lot of other folks. Especially those who stuck around during those first two years when I was basically angry all the time. All six of you.

I have blogged behind password encryption for an audience of zero and, more recently, for an audience of 6,000 subscribers. Both kinds of blogging have worked certain wonders on my teaching practice.

I’ll say this about the second kind — perhaps just as a reflection but perhaps also as a recommendation to those in the math edublogosphere who are working hard and picking up a lot of deserved press: use more readers as an excuse to fail faster, more often, and more productively.

The closer I track this blog to the theme “what I will do differently next time,” the more I draw readers who introduce me to new ideas, who offer me their time and energy to field-test my latest harebrained schemes, readers who have helped me pinball quickly from failure to success.

For the last four years.

There are worse forms of professional development than blogging.

## To My Amigos North Of The Border:

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.

## Making Multimedia Earn Its Keep

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 …

… 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?