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:

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.

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."

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.

First, let's pay respect to how fast the video moves, how it sets a scene and establishes a problem in just 14 slides and 57 seconds. Webb knows his audience and its attention span. Also, none of this is stock photography. Every photo selected is of high bandwidth and relates directly to the problem. After 12 seconds, we have three different views of the lawn. After 15 seconds, a panoramic shot. I'll begin my redesign 23 seconds in, when he mentions the lawn is 75 steps across.

This is really, really close to my textbook's own installation of the problem. The text would ask a question like "how far is it around?" or something with a real-world spin like "how large would the ice rink be?" (standing in for "what is the area?") and then it would explicitly define the only variable we need: 75 steps. My students would identify the formula and then solve.

This kind of instructional design puts students in a strong position to resolve problems the textbook draws from the real world but in no position to draw up those problems for themselves. This kind of instructional design also yields predictably lopsided conversation between a teacher and his students.

The fix is simple but difficult: be less helpful.

Let's start here: is circle area just something math teachers talk about to amuse themselves or do other people care? If they care, why do they care? How do we convey that care to our students? Maybe someone needs to fertilize the lawn. Maybe someone wants to spray paint the dead lawn green in the winter. Without this component, the answer to the question "how far is it around?" is little more than mathematical trivia to many students.

So put them in a position to make a choice, a tough choice that's true to the context of the problem, a choice that math will eventually simplify.

For instance: "how many bags of fertilizer should I buy to cover the entire lawn?"

Or, a little weirder: "how many cans of spray paint should I buy to cover the entire lawn?"

In both cases, we're putting every student on, more or less, a level playing field. They are guessing at discrete numbers (ie. "fifty bags — no — sixty bags.") and drawing on their intuition, which, from my experience, is a stronger base coat of for mathematical reasoning than the usual lacquer of calculations, figures, and formula.

This approach also forces students to reconcile the fact that the problem is impossible to solve as written. This is an essential moment. They need more information, but what? What defines a circle? Would it be easier to walk across the lawn's diameter or around the lawn's circumference? Which would be more accurate? Why is the radius difficult to measure? Did Kyle really walk through the center of the lawn or does he just think he did?

When you write "75 steps" on a photo, that conversation never happens.

These two are fresh. If you subscribe now, you can say you were into them before they got big.

1.

Tony Alteparmakian is a 2009 Leader in Learning enacting Chris Lehmann's vision of classroom inversion (though I don't doubt they came to the idea separately). Their idea is that we should send our students home with what used to constitute classroom time — the lecture — and spend classroom time on labs and teacher-led enrichment of that material.

Obviously, that vision comes fully loaded with complications but Tony is resolving them one-by-one in a how-to series that has only just started.

Also, I dig his redesigns. It's hard to argue with slide transformations like these.

Before:

After:

2.

Sean Sweeney is an extra-value meal. In one corner of the edublogosphere you have the edtechnologists, the district IT staff, the ICT professionals, the policy wonks, etc., all asking huge, important questions about merit pay, technology integration, assessment, online schooling, etc., and posing reckless hypotheticals about limitless resources with nothing less than the future of education at stake, and all of it makes me grateful for guys like Sean who are driving 90MPH up the right lane, offering educators something they can use in the classroom right. now.

In considering Dan Meyer's arguments, I don't really agree with him. At all. It's all about finding the "right" photo to enhance the text.

Is that what presentation is all about? Witty aphorisms and inspiring photos?

You have a thesis. Let's assume there are very real, really real real-world implications to your thesis. Why not cut to that chase? Why make an abstract matter like edutechnology even more abstract with dramatic photography and 140-character pullquotes from your Twitter feed?

Show me something real.

Give me a space to interact with it.

Let me have your thoughts on it.

In this case, if learning really is social, please show me examples of that social learning. Or show me examples of how dangerous it is when that learning is taken out of a social context. If you find it difficult to connect your thesis to video or screenshots or sound clips ("multimedia," basically) then it's possible you are chasing down the wrong thesis or that your thesis doesn't lend itself to a presentation medium1.

I like that Darren modified the stock photography (adding the "Learning Is Social" placard) to connect it better to his thesis than the average stock photo slide but I wonder if we're approaching the question, "What is presentation?" along two different vectors.

I caught David Jakes' Black Coffee presentation on Slideshare last week and was impressed that something like 95% of its 63 slides were screenshots, archival photos, YouTube videos, newspaper clippings, etc., etc. Jakes had done his groundwork.

Something I have been completely wrong about is the best way to use slide software in a math class. A few years ago I wrote a design series explaining how I use color theory, grid systems, etc., to clarify complex procedures, but the whole thing turns out to be simultaneously a) a lot more fun and b) a lot less time-consuming than that.

My reversal in slide design reflects a shift in my math pedagogy also. Far more important to me now than "developing fluency with complex procedures" is "developing a strong framework for interpreting unfamiliar mathematics and the world."

I'm not trying to set up a false dichotomy here. We do both. Both are important. But all too often slides like that first one, with the classroom dialogue and solution method predetermined, cordon off classroom dialogue and student reflection onto very narrow paths. That kind of pedagogy does nothing to unify mathematics, tending, instead, to position complex procedures in isolation from each other, which is a very confusing way to learn math and a very laborious way to teach it.

Instead, I want my students to focus without distraction on a) how new questions are similar to old questions, b) how tougher questions demand tougher procedural skills, asking themselves c) which of their older tools can they adapt to these tougher questions?

For example, I put six equations on separate slides, equations we have seen. I asked, "how many answers are there?" One. Two. Zero. Etc.

Then I put up an inequality, tweaking the problem slightly, and quickly.

They told me there were lots of answers. I asked my students to start listing them. "7, 6, 5, 4.2, 4.1, 4," etc.This became tiresome quickly and made the introduction of a graph — a picture of all those answers — clear and necessary.

Slide software makes it easy to sequence these mathematical objects, ordering and re-ordering them to promote contrasts and complements. Slide software lets me sequence these mathematical objects quickly, from anywhere on the globe, from photos and videos I take, from movies my students watch, from textbooks too. Graphic design is useful to mathematics, but I am happy to have discovered certain constraints on that usefulness and, simultaneously, higher fruit hanging elsewhere.