Dan Meyer

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I'm Dan and this is my blog. I'm a former high school math teacher and current head of teaching at Desmos. He / him. More here.

Snowflake Math

By Dan Meyer • December 18, 2007 • 20 Comments

[BTW: Mimi Yang’s remix is highly recommended.]

I’m about to give you what I’m convinced are good blueprints even though the house I built off of them today was pretty raggedy.

Here, three days before winter break, I wanted an activity that injected math into something mindless. I thought about snowflakes, you know, how you fold some paper, cut it here and there, and open it up only to discover you’ve recreated The Storming of the Bastille.

So here’s (what I’m convinced is) an awesome exercise in spatial intelligence for you and your students: predict what the snowflake will look like before you open it up.

I’m tempted to leave it there and let you decide how this oughtta shake out, encouraging you to please get back to me and let me know. Because what I did today didn’t have the same loose-limbed energy my best stuff usually does. This was second-rate but maybe we can spin something better out of it – you and me:

I passed out a sheet of standard letter paper and some scissors to each student.
I had them square the paper and fold it into fourths – now a smaller square.
I put up a series of slides. Each one asked them to make one cut.
They made the cuts and I said, before you open up the snowflake, sketch what you think the snowflake will look like.
They sketched it.
I walked around, observing, sometimes making comments.
They opened it up and checked themselves.

Then, without passing out more paper, we went backwardsWorking backwards from a solution to the problem, incidentally, is the most reliable way to carry your kids a few rungs up Bloom’s Taxonomy..

I gave them the result and asked them what cuts had been made to get it.
I called up five volunteers to the board to show their solutions, most of which differed only slightly from each other, a fact which offered up some good conversations starting with words like “compare” and “contrast.”

Then I passed out this worksheet, which asked for eight visualizations, the second half doubling in complexity by adding one fold to the snowflake.

Typing all that here at the end of the day, it’s kinda obvious to me that this was too much even for my Geometry sophomoresNine of whom apparently read this thing so, hey, team, no disrespect.. The spatial learners had a blast but I didn’t manage to transcend that division and pull the other intelligences over the wall like my better stuff tends to. This thing lacked a certain scaffolding. In other words, buyer beware.

Attachments:

Handout
Slidedeck [keynote]
Slidedeck [ppt]
Slidedeck [pdf for those poor ppt07 people]

Call to Action: Make it Fun

By Dan Meyer • December 17, 2007 • 16 Comments

Okay so I’m gonna cherrypick a set of your comments and decontextualize ’em to serve my point. God bless the remix culture.

fgk, on why people don’t take lessons from those who offer them:

i think a big part of why we don’t adopt [lesson plans] from others is because we don’t see it happening. when you watch a class, you can tell when something succeeds, and figure out how to incorporate that into your own teaching.

druin, on the frustrations of sharing lesson plans with others:

I think for many people the idea of sharing is lop-sided. I don’t mind sharing ideas with others, but it frustrates me when I’m the only one sharing.

sarah, assessing my lesson offerings:

The power of your narratives is the piece that keeps me hoping that something turns up in your [lessons] tab. It’s that reality check of what works. It’s hearing your voice, getting hints of your personality, helping me mentally test what I can pull off, and what, like rap music, would be obvious that I’m faking. That voice is what every lesson plan needs. [emphasis added]

So my advice is this: you have to make stories out of your lesson plans, collapsing resources into anecdotes. It’s easy to blog stories. They’re cathartic and satisfying where resource posts feel expensive. Plus people are more inclined to read stories than rubrics.

Talk about the questions you asked, the responses they gave. Share pictures or screenshots when possible. Post stories, not plans, and then attach handouts or link sources at the end. I can’t help you with the time cost but if you’re convinced you should share your resources, I promise that this is the way to make it fun for you.

Moreover, I promise that as you start receiving feedback on your stories – positive & negative – you’ll start looking for more stories to tell. Constantly. The pipe that carries interesting things from your eyes to your students’ and then to your readers’ will grow wider. It’ll move faster. If you start this in earnest, I pomise you won’t be able to turn it off.

Content, Life & Everything

By Dan Meyer • December 17, 2007 • 1 Comment

Content, Life & Everything: a Did You Know for the AdSense crowd. ¶ For instance, a sassy disembodied mouth talks to advertisers about a Google-matic future: “I may not be such an easy touch but don’t worry. I’m still human … and quite frankly i want what I always want. And it’s not just me. We. You know, your customers. We all still love being entertained, inspired, and informed. We still love great stuff.” ¶ Passed along for those who thrill to this kind of stuff.

Call to Action

By Dan Meyer • December 15, 2007 • 41 Comments

I gave myself too much credit for innovation with that DVD sub plan. Some of y’all have been pulling that rabbit out of your hat going on years now. Respect for that but here’s my question:

Why aren’t we sharing?

Why didn’t I read about it? I’ve been issuing lousy sub plans for three years, three years which could’ve been cooler if someone I readAnd, admittedly, someone I don’t read might’ve posted it and I wouldn’t know. had made that part of his or her practice public.

One of the most shocking blog entries I read this week was Miss Profe’s Tic Tac Toe: Foreign Language Style. There was nothing obviously earthshaking about it but still I sat there with spoon frozen halfway between bowl and mouth, realizing how rarely people Around Here share lessons and activities.

Time is always a good scapegoat. These things take too much time sometimes. I wonder also, though, if we don’t post more resources because those posts are some of the least sensational. They generate the fewest commentsZero so far on Miss Profe’s.. They don’t fit into the standard post templates of a) anecdote (“my day sucked today, here’s why”) or b) manifesto (“my school district disabled the right-click today, here’s why that sucks for education”).

Lesson plan posts lack any call to action, which seems like a waste in a blogosphere where every third blog post is a call to action.

But that sucks because new teachers want your answers. That sucks because I want your answers.

I want to know how to do group work right.
I want to know how to do a good equipment check-out system so that my compasses and calculators don’t walk out the door but which doesn’t sap away instructional time.
I want to know how to incorporate some math on the sly into the day before Christmas break.

I know you’re holding. Give it up.

If you’re a blogger …

post something cool from your bag of tricks.

If you’re a reader …

put a request in the comments. Something that’s getting you down (solving equations, seating arrangements, whatever). Something you’d like to see. Or just an affirmation that you’d like to see more resources floating around the ‘sphere. You’ve gotta let ’em know it’s worth their while.

One of these days, as a blogosphere, we’ll get resource sharing rightSomehow I suspect that somewhere someone’s working on it. and this job is gonna get a lot easier and a lot more satisfying for a lot of people. Until then, as connected as this place seems, we’ll struggle alone.

How I Work: Sub Plans

By Dan Meyer • December 13, 2007 • 23 Comments

My school gives each department a monthly pull-out period for collaboration. One period.

I dig the collaboration, but calling in a sub for just one period throws off my game in a way that no one else in my department seems to mind.

Everyone else takes the loss in stride and adjusts pace to account for the lost period. Me, I tense up and pray for some freak snow flurry to close school and balance out my other periods. It’s awful. Plus I plan sub periods as strenuously as I do regular periods and wind up with with 50% more prep work the night before my department’s planning sessions.

But I think I got it right this time.

I exported the period’s Keynote slides to PNGs and recorded a voiceover track in GarageBand using my iBook’s built-in mic. Neither of those tasks required more than three clicks.

Then I pulled ’em both into Final Cut Pro …

… and lengthened each PNG to match my voice. (iMovie will do the same thing, as I recall, but I haven’t played with the newest version.) Then I burned a DVD.

Time cost: considerable. Somewhere around ninety minutes, though forty of those could be chalked under the Bumblin’ Around column, playing with formats, etc, time I’ll save next timeKeynote 4, which is to PowerPoint what an M16 is to a musket, has an “Export to iDVD” feature which is a few versions away from automating all the annoying parts of this process. At the moment the audio slips away from the video, but once Apple tightens the right belts, I won’t really have words to express my pity for PPT users. ¶ (I mean, seriously … once they get that working, I’ll strap on a wireless mic and record every lesson in real-time, exporting each day’s lesson to iPod-ready MP4 video. Why, you ask? Why not?!).

Moreover, I didn’t lose nearly as much ground as I would’ve with my usual lame sub-day regiment of handouts, book review, and a few Hail Mary’s for my sub.

Moreover, at a distance, I could …

… introduce the sub. (“Listen to Katie,” I said, just guessing at the name and gender of my sub.)
… set expectations. (“Hey, kids, it’s Mr. Meyer. You know I hate to miss fifth period but it couldn’t be helped. Assignments are worth triple today so don’t blow this.”)
… banter a bit. (“So who can tell me which conjecture cracks this thing wide open for us? [long pause] Nobody knows this one?!”)
… and freaking teach.

That last feat demanded I lighten up on my usual conviction that text rarely mixes well with PowerPoint. Ordinarily, I throw a diagram or a graph on the board and spin a conversation around it. The slides had to stand alone here, though, so I crowded ’em up more than I would’ve liked.

My sub’s only official capacity was that of Pause-Button Pusher. At various times I’d instruct “Katie” to pause the DVD so the class could work through a problem. I told the kids they could ask her to pause at any point also.

I caught the last five minutes. No one freaked out over the experiment, like, “yeah, Mr. Meyer, that was way more fun than a movie … thanks!” but the sub was keen, the kids were into the novelty of it, if nothing else, I didn’t have an educational mess to clean up the next day, and I didn’t embarrass myself by praying for snow in sunny Santa Cruz.

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