2012 – Page 10

Year: 2012

Total 137 Posts

Factor Dice

By Dan Meyer • September 7, 2012 • 21 Comments

Kaleb Allinson, with a great end-of-class factoring exercise:

I tell my students that my dice add to 19 and multiply to 88 and ask them to guess my dice. I try to play this at the end of class for a week or two as I have time leading up to factoring. Then when they discover how to factor, this dice guessing skill is very helpful. They always realize what I’ve done and think I’m really tricky.

There are other ways to do this, of course, but the dice randomize the factors and I think that’s important. It says to the student, “Whatever algorithm you’re rolling around in your head right now –Â it’ll work for any whole numbers. The teacher isn’t putting her thumb on the scale. She’s giving you numbers she can’t control.”

Featured Comment

timstudiesmath:

Another extension is to ‘fake the dice results’ and have students determine whether or not there IS a solution to Kaleb’s problem; can they prove they have exhausted all possibilities?

Steven Leinwand for NCTM President

By Dan Meyer • September 5, 2012 • 15 Comments

I voted for Steve Leinwand for NCTM President just now and I think you should do the same. He explains eight reasons for his candidacy on his website, which has this content license in the footer:

My mission is to promote progress in mathematics teaching and learning. Please use the material and resources on this site in any manner that facilitates the improvement of your mathematics curriculum instruction, assessment or policies.

So make that nine. Check your e-mail. Vote early. Vote often.

Featured Comments

Kelly Berg:

After the Professional Development I spent with him this summer, I would vote for him to be President of the Universe!!! Seriously… Everyone needs to vote for this guy!!!

Nathan Kraft:

I love Steve Leinwand. His video is amazing. His book is amazing. He has already influenced my teaching greatly and I can’t thank him enough. He’s got my vote!

Molly Olson:

He is so inspiring, funny, smart and thought-provoking. I appreciated his speech last year at the WMC Green Lake Math conference. I would vote for him too!

Andrew Stadel:

Can we write Steve in for the November 6 Presidential election too?

UnGoogleable Problems

By Dan Meyer • September 4, 2012 • 10 Comments

Rebeckah Peterson:

One challenge that I face, however, is that my students are used to their curiosity being satiated so quickly and easily. If they want to know the answer to something, they can just Google it. On their phone. Right there.

Chris Champion:

I’m wondering — does solving the answer to “The Ticket” permit the use of a cell phone bar code scanner? I easily got “2000”³ for the answer using the Amazon iPhone app. I had a feeling my students would find the answer that way too. Yup. It took about a minute before a student took out his phone and used Google Goggles.

I was in Kansas earlier this year when this problem reared its head and threatened to swallow up back-to-back workshops. I had shown this video and we were kicking a few questions around before eventually answering, “How much money is on the walls?”

In the first workshop, a participant asked, “Why did he do it?” and I talked about the $100,000 that Hugo Boss awards Guggenheim artists for the design of an installation. A few people snickered and I realized I had just answered our next question.

In the second workshop, we were working off Guggenheim blueprints to determine how much cash was on the walls and one group seemed disengaged. I walked over and saw New York Times coverage of the installation on several screens. The headline has the answer.

Two options here:

Throw suspicion on Google. I asked one group to please make sure there are really $100,000 on the walls. I mean, what if Feldman just quoted that sum to the New York Times but pocketed $40,000 thinking, “Who can really tell the difference between 100,000 and 60,000 bills?”
Ask a question that’s never been asked before. The point of the Guggenheim task is to have students model the total dollars using a) the surface area of the walls, b) the surface area of a dollar bill, and c) the amount one dollar bill overlaps the next. My students found an easier way to resolve their perplexity than build that model. Power to them. So I asked them, “What would the bills look like if there were a billion of them up there?” Eventually, you ask, “What’s the most cash they could pin to the walls?” In both cases, they have to construct the same model. They’re just solving for a different unknown. For the ticket roll task (original question: “Given a ticket roll, how many tickets does it contain?”) I said, “I’m inviting my 1,000,000 friends over for a party. I’ll need a ticket roll that holds that many tickets and I’m wondering how big that’ll be. Can I store it in this room? Will I need a shed? A warehouse?”

I have a lot of faith in that second option. It extends to any kind of task. Swap the known and the unknown. Pick a number with a lot of zeros and then build a story around it.

My Edstartup 101 Materials

By Dan Meyer • September 2, 2012 • 1 Comment

I’m enrolled in an online course taught by David Wiley, et al, called Ed Startup 101. Startup culture fascinates and frustrates me so I’m taking the course to learn more about it and, perhaps, to plant my own flag somewhere in the startup sand.

We’re supposed to tag and post assignments to a blog. Rather than turning this blog into my class scratchpad, I’ll be sequestering all those materials at edstartup101.mrmeyer.com, starting with an introductory post. You all tend to make me a lot smarter than I would be otherwise, so I wanted to invite you to tune in, subscribe, and comment. A little accountability would probably go a long way towards seeing me complete this course.

Hot Vacation Links

By Dan Meyer • August 30, 2012 • 4 Comments

I’m easing back off a family vacation, during which time you were all posting some fantastic stuff at a fantastic rate:

The Motion Math team posted a thoughtful behind-the-scenes expo on their latest game, Hungry Guppy.
New to me: Justin Reich’s Advice for New PhD Students. Huge: “You need to decide early on if you want to keep an academic option open. If you do, you need to devote yourself more or less entirely to academic publishing.”
PayPal-cofounder Peter Thiel ran a seminar at Stanford last quarter called “Startups,” which I couldn’t find room for in my schedule. Blake Masters summarized each class, though, and not in the usual disjointed live-tweeting style, but with well-edited narratives.
Chris Hill’s Guide for a Mentor Teacher. Thirty great points.
This does it. I’m putting a timer on Kate Nowak’s career as a classroom teacher. “I’m just temperamentally someone who enjoys a challenge and quickly tires of an insufficient level of difficulty. I am not that interested in administration, so. Either I will keep comfortably doing the same thing, or I will do otherwise.”
Chris Lehmann, no Luddite, wrote The Seductive Allure of Edu-Tech Reform. Tom Hoffman, in an uncharacteristic moment of optimism, seems convinced this bubble will burst. “Let’s take for granted that what ed-tech entrepreneurs are shooting for educationally are test score gains. If they’re getting them at any scale, for real, consistently, with at-risk kids, we’d frickin’ know about it, and truly, sales growth would be unstoppable.”
Scott McLeod has likely seen more reactionary stances against Internet access in schools than anybody, which makes his 26 Internet Safety Talking Points the authoritative piece.
Patrick Honner uses a New York Regents exam question to illustrate the ways we obscure the ladder of abstraction from our students. “Math teachers end up spending a lot of time training students to make these assumptions, probably without ever really talking explicitly about them. It’s not necessarily bad that we make such assumptions: refining and simplifying problems so they can be more easily analyzed is a crucial part of mathematical modeling and problem solving.”
I subscribed to Jeff Brenneman as part of Sam Shah’s freshman class of math ed bloggers and was rewarded with his list of advice For the Interns and the First-Years. I’ll sign off on each item, especially in hindsight of having broken each of them.

Subscribe