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Archive for July, 2011

I gave the opening talk at NCTM’s High School Institute yesterday in Orlando, FL. At the end, a man introduced himself as a teacher and former textbook editor and set me straight on a couple of things:

  1. Publishers decompose rich mathematical tasks into mealy, mushy little bits because teachers want them to. Teachers review those books and point to problems and say, “That’s too hard. That one too. My students can’t do that one. Break that down for me.”
  2. Same with the overly helpful pointers to previously worked examples. “You want me to assign this for homework? Only if you make a note in the margin pointing to the example problem it’s exactly like.”
  3. Same with the cornball visuals. “Too much text. Can you throw in some color?”

Publishers respond to market pressure from teachers who are responding to a similar kind of market pressure from students. I have arrived at very different responses to the same pressure. (ie. Does anyone really think students are engaged by the cartoony nonsense they find in the margins of their books?) Making myself the best advocate I can be for those responses is, of course, the challenge.

BTW: Lisa Henry posted a detailed review of my keynote. I want to highlight her remark about the #anyqs project:

I am finding more and more math around me. It pokes in my head when I least expect it.

I heard this in Grand Forks, also. The #anyqs exercise seems to be genuinely transformative for at least some teachers. Whether that transformation results in any kind of significant change in student achievement or in the disposition of their classes is an open question.

10:00AM PDT. It should be fun. If you can’t make it, Apple is archiving it and I’ll post the link later.

2011 Aug 28: You can access the webcast at this link. I’m the second speaker. I also contributed two tutorial: “Analytic Geometry” and “Mathematical Storytelling.”

Tom Woodward:

Seriously. You can’t afford to be this naive any longer. That “award” certifying you as a really super X-brand teacher, that free conference registration- these are not things they do for you out of kindness1. This is for them. Every single bit of it, bought and paid for. Their return on investment is pre-calculated. If it didn’t make them money, they would not do it.

Posted from Phoenix in a hotel ballroom with other Apple Distinguished Educators while listening to Apple Retail Market Leader Christina Sanchez (Arizona / New Mexico) sell us on selling our students on a career selling Apple products.

This is one of the most tragic math problems I’ve ever seen. (Click for larger.) Not because it’s awful, though it is, but because the awfulness conceals something amazing. I mean, how great is it that we can drop a rock in a well and the sound of the splash tells us how deep the well is. That’s wizardry!

I find it completely amazing we get to offer that power to our students. If my goal were to conceal that amazingness, though, to ensure my students would be less interested in mathematical wizardry thanks to my efforts, I’m not sure I could do any better than this problem.

Problems

  1. The student experiences act one and act two at the same time. Act one is supposed to hit you in the gut; act two in the head. The only reason your textbook tries to do both at the same time is because printing the same problem on two different pages is logistically impossible. Luckily, you aren’t bound by the same constraints.
  2. The problem starts in the second act. And what a second act. Your students have no idea why they’re wading through that long, thickety paragraph outlining the tools, information, and resources (act two) they’ll need to solve the hook (act one) which shows up long after they’ve stopped caring.
  3. And what a hook. Seriously, could someone please explain to me which interest group or political constituency is served by slurring what should have been concise, obscuring what should have been clear, and jargoning what should have been conversational. Seriously, how would a human phrase that hook? Would a human need twenty-six words?
  4. The act one visual is cheap. Again, we’re dealing with cheap clip art here only because of the constraints on an industry that’s taking on water. Don’t go down with that ship. Can you think of a better visual, one that would make students wonder, “Wow. How deep is that?” without you lifting a finger?
  5. The act three payoff is weak. Imagine all the intensity of the final assault on the Death Star in Star Wars. A planet’s survival hinges on an unimaginably long shot. Luke takes that shot as the clock winds down, a shot right at the guts of the Death Star. What if at that moment we cut to some Rebellion functionary announcing in a slow monotone, “The Rebels were successful. They destroyed the Death Star.” That’s what it’s like to read the answer to a visually compelling problem in the back of the book. Show that thing explode.

Solutions

It turns out that Hollywood occasionally makes math problems for us. Click through and have a look.

  1. Journey to the Center of the Earth (2008)
  2. The Descent

With Brendan Fraser, you get a fun check on your own answer and an explanation of why his team even cares how deep the cave is. With the Descent team, you get a much deeper cave and a stronger separation between the first and second acts. Both represent massive improvements over our status quo.

To be clear, I’m not saying you can just play act one and two and your students will trot merrily to an answer in act three, deriving that thorny equation for projectile motion all on their own while stopping periodically to smell the constructivism flowers. I’m not saying that. This problem is tricky and will likely require lots of help on your part. What I’m saying for sure is that it makes no sense to offer that mountainous paragraph of helpful text without your students knowing (to say nothing of caring) why you’re offering it.

Related:

Zac Shiner, derelict blogger, and Shira Helft, a fellow graduate from Stanford’s new math teacher cohort last year, have a great list of questions running at Building Our Classroom they’ll be taking on over the course of the summer. Zac elaborates at his blog:

Even though it’s the middle of summer, my job as a teacher seems to be unavoidable in my day to day life. I’m not just talking about the unavoidable questions of “so what do you do for a living,” but the places my mind drifts to when I have nothing else to think about. During silences in conversations, or when I close my eyes at the end of the day thoughts of my soon to be classroom are constantly filling my mind.

Zac eats, breathes, and sleeps this job.

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