design – Page 14

Category: design

Total 257 Posts

Notes From Foo

By Dan Meyer • September 1, 2009 • 14 Comments

Also: Why WCYDWT?

On the first night of Foo Camp, 250 attendees introduced themselves by name, affiliation, and three hashtags, and then descended on a gridded wall-tall conference schedule, scribbling down session titles, selecting venues, folding similar sessions into one another, scheduling roundtable discussions with people they had only met thirty minutes earlier over food.

The crowd was thick so I commandeered a Segway and steered it full-bore into the scrum, scattering people long enough to slide a session onto the closing day’s schedule: The Programming Principle That Will Save Math Education.

That’s three opportunities in three months (counting the webinar I’m conducting in October) that my patrons at O’Reilly have given me to throw a half-baked idea casserole at a bunch of really, really smart people and walk away with something quite a bit tastier.

The debate at an earlier session on the future of education was idealistic and high-minded with participants from all sectors trying to reach consensus (in sixty minutes) on merit pay, standardized testing, class size, unschooling, home schooling, charter schooling, public schooling, and probably several other intractable issues I’m now forgetting. I tried to approach my session, then, from two more assailable angles:

math curriculum, which, for whatever it does right, doesn’t a) put students in any kind of place to apply mathematical reasoning to the world around them, or b) do anything to encourage patience with problems with complicated inputs and messy outputs, which is to say, most problems worth solving. Math curriculum, speaking generally, does the opposite of those two things.
after we develop a model for good math curriculum, we don’t know how to share it.

The outcomes of merit pay and standardized testing will be decided in protracted, gruesome battles between various unions, legislators, and chancellors. The challenge of sharing good math curriculum, however, is one that the people attending my session – an intimidating array of talent, knowledge, and funding – could solve over lunch.

O’Reilly gave a blank notebook to the weekend’s participants. Not lined. Not quad-ruled. Blank. We talked about how you’d only give out lined or quad-ruled paper if you were sure the average attendee wouldn’t want to doodle.

I showed the participants how the Muji chronotebook shuns calendars and hour-blocks, opting instead for the least constrained approach to scheduling possible, a small clock in the middle of the page. This is the rule of least power, the programming principle that can save math education.

I won’t waste space here recapping my session notes. I drew heavily from these six posts:

But I realized this: I flog WCYDWT media from whatever forum I’m offered not because I think WCYDWT media is the evolutionary pinnacle of math instruction. I do think WCYDWT is leagues better than the curricular norm, particularly compared to the kind of curriculum offered by the largest textbook publishers. More crucially, though, WCYDWT is the best model I know for classroom math instruction that can also leverage Internet distribution. I can use global publishing tools to infect other math teachers with these videos and photos. I can’t do the same thing with netbooks. I can’t do the same thing with physical manipulatives. I don’t know a better model of math instruction that I can also aerosolize so easily.

[Muji notebook photo credit]

Making My Week

By Dan Meyer • August 23, 2009 • 5 Comments

Scott Elias gives an angel its wings with this one:

OSCON 2009: What Are Your Session Dealbreakers?

By Dan Meyer • July 30, 2009 • 22 Comments

The 4:30PM Wednesday slot was packed at OSCON. I’m talking about three sessions I was either “eager” or “very eager” to attend at a conference where 95% of the conference titles were outright inscrutable. (eg. “Sun GlassFish (OpenSolaris) Web Stack – The Next Generation Open Web Infrastructure” – see what I mean?) One session concerned graphic design. Another risk models. The third session listed as “Antifeatures,” a title which was tough to resist in its own right.

I told myself I’d pick one and sit through the first five minutes. If, at that point, it had met certain criteria, I’d bail on it for one of the other sessions.

If you are loathe to leave a session under any circumstances, consider yourself exempt from this writing prompt. Otherwise, if you value your time and you vote with your feet, how do you judge a session by its first five minutes? Again, it’s possible the session turned into a winner exactly six minutes in. Under these constraints, though, we don’t have the luxury of patience.

I’ll post my own criteria to the comments shortly.

OSCON 2009: My Ignite Presentation

By Dan Meyer • July 27, 2009 • 69 Comments

I was constrained by twenty slides at fifteen seconds apiece for a lean five minutes to talk about whateva to a crowd of open source software-types. I talked about a) teaching, b) why my first two years were miserable, c) the difference between teaching math and teaching citizenry, and d) what excites me lately.

[Click through to view embedded content.]

If any other pecha kucha survivors want to commiserate over the format, which required (for me) 400% more rehearsal and 90% less slidework than I’m accustomed to, the comments are all yours.

BTW: A couple of people have asked for a YouTube embed. I tried, but the audio stopped tracking with the video. Here, instead, is a link to a high-quality file.

What I Would Do With This: Glassware

By Dan Meyer • June 10, 2009 • 41 Comments

If you have never rolled a cup across a flat surface and marveled at how precisely it returns to the same place you rolled it from, it’s possible you’re the wrong audience for this post.

There is math here, certainly, but I have made it a goal this year to stall the math for as long as possible, focusing on a student’s intuition before her calculation, applying her internal framework for processing the world before applying the textbook’s framework for processing mathematics.

Bad First Question

This one sucks the air right out of the room. We’re into the math immediately, having bypassed several easy opportunities to pull in our students who hate math… and, when those students comprise your entire class, good luck with that..

Jason’s First Question

Jason Dyer suggests handing out plastic cups, letting students roll them around, then asking “why do they do that?” I have no problem with this approach. I would like to start from a position of stronger student investment, though.

My First Question

Have them roll some plastic cups around. Then toss up this slide and ask them a question that has a correct answer, yes, but which attaches little stigma to the wrong answers. It’s an educated guess and different students will make persuasive cases for all three of these. Ask them to write their guesses down, to put them on the recordIt’s extremely helpful here that the tallest glass doesn’t make the largest circle..

A Lesson Sketch

The conversation can then proceed along some interesting lines where you ask the student to:

justify her guess.
draw the kind of cup that will roll the largest circle using a fixed amount of plastic. This is fun. Many will draw a really tall cup, which isn’t the best use of limited material. A two-inch-tall cup can roll a circle that’s a mile wide.
make their ideal cup from a page of card stock. The fixed size of the card stock will normalize the results.
draw a complete picture of their cup including the auxiliary lines. Can they find the invisible center of the circle it will roll? What’s the method?

We do all of this before we start separating triangles, before we write up a proof, before we generalize a formula. We ask for all this risk-free student investment before we lower the mathematical framework down onto the problem.

Degenerate Cases

A cool feature of this formula is how well it handles degenerate cases. For example these two:

A cone’s roll-radius is the same as its slant height so letting d = 0 should (and does) eliminate D from the formula.
A cylinder will roll forever so letting D = d should (and does) return an undefined answer.

Iterate

From there you can pull out of your cupboard (digital or otherwise) any random set of cups and the students should be able to predict the roll-radius within a small margin of error.

And the framework grows stronger.

A Parting Swipe At Textbooks

I didn’t dig this out of a textbookh/t Mr. Bishop, Summer School Geometry, Ukiah High School, 1997. but this (hypothetical) scan highlights the difference between my math pedagogy and my textbook’s.

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