I didn’t have sound at my morning presentation at CMC-North last weekend. That was on me, and it wasn’t an enormous deal anyway. I told the people there I was sure we’d get through it together. I was right, but I had no how right I was until we were starting into my explanation of mathematical storytelling. I was showing shots from the first acts of Star Wars, Jaws, and Raiders of the Lost Ark and the absence of music in each of those scenes was pretty conspicuous. But then we heard the music. It started in the back with a few people humming out The Imperial March from Star Wars and then it rolled over the rest of the group. I added the “pew pew pew!” of the ships volleying shots back and forth.
I love this conference and I love these people. They’re smart, optimistic, and funny. The lineup is unusually strong. The venue is world class. You should stop by sometime. Here are a few things I saw and did and the digital goodies I grabbed for you while I was there.
Bix Beeman on the Math of Surveying
The official word on the Asilomar grounds is that it’s 107 acres. But how do they know? It’s a weird shape. How do you capture the area of weird shapes and, in this case, the area of weird shapes that are larger than the paper on your desk? Beeman took us up through different solution strategies, all the way from counting squares on grid paper to the matrices and determinants of the Surveyor’s Area Formula [pdf]. It would have been great if he had given us much time to play with the different methods and discuss the tradeoff between complexity and accuracy. As it was, we rushed through (eg.) Pick’s Theorem so that in the last ten minutes we could use TI calculators to calculate the area formula across all the coordinates bounding the Asilomar grounds.
All snark aside, I do not get TI technology. I’ve used an iPhone for the last four years and the C++ programming language for the last ten weeks and, suddenly, I cannot find the appeal of a device that displays a total of 128 characters at a time in black and white. I mean, try to read a single line of the spec sheet without pitying the poor copy editor who had to write it. “2.5 times the processor speed of the TI-83 Plus.” Well! “Lists store up to 999 elements.” That many! “24KB of available RAM memory.” It just feels mean, at a point.
Beeman hinted at various times that your students will become docile and engaged as they’re copying coordinates and instructions into their calculators.
I don’t actually doubt this is true. Given the choice between a demanding task and grinding, students regularly choose grinding. There’s a lot less risk. But if you give a student this page of instructions [pdf], what work is left for her to do? What are the odds she’ll be able to conceptualize and solve her own problem later?
BTW. Here’s a fundamental difference in approach. Beeman told us early on that the official survey of Asilomar was 107 acres. Then he said, “Let’s see how close we can get to that.” Me, I would have asked the class to guess how many acres comprised Asilomar. Then, after we applied our best mathematical analysis to the task, we would have checked our work against the official survey.
Dan Meyer Doing His Dan Meyer Thing
I’m finding the contours of this talk a little too familiar lately. I’ll be giving it in February at GSDMC, then in April at NCTM, at which point (fingers crossed) I’ll film it, post it to the archive, and move on.
Harold Jacobs’ Mathematical Snapshots of 2011
Someone said this was the fortieth edition of Harold Jacobs’ annual “Mathematical Snapshots” talk at Asilomar. It was my first. Basically, Jacobs has a sharp eye for mathematical moments in the news or in life. He summarizes them annually in his session and then passes them out at the end on a CD-ROM, which I have uploaded for you here. Jacobs said this was his first snapshots talk using a digital projector (rather than projecting transparencies) and, I have to say, he was a total natural with the medium.
Jacobs’ snapshots fell into one of two categories. In one case, he’d read off tidbits from the news that hinted at something mathematically interesting. Like this cornball who insists he’s proven that pi is rational and is, in fact, 3.125. These were interesting but nowhere near as impressive as the snapshots which he attempted to turn into some kind of challenge for students, giving them some part to play in the interesting mathematics. Like the Italian woman who received a $44,500 parking ticket because the police officer set the date at 208 instead of 2008. Jacobs asked students to calculate the correct fine.
Excellent curation, really. I’m not sure I needed the presentation, though. Let’s work out some kind of rotation for next year and share the CD, okay?
Michael Serra’s Math Games
I had lunch with Jodie T, whom I hadn’t seen since our days learning to teach in the same cohort at UC Davis, and we worked off the lunch coma in Michael Serra’s session on math games. There were a lot of classics (Knight’s Tour, Battleship / Treasure Hunt) but Serra applied some kind of twist to each, ratcheting up the demand (and fun) of the task just past the point where I would have quit. Definitely check out the handout.
Alan Schoenfeld on Common Core Assessments
Schoenfeld advises the SMARTER Balanced Assessment consortium. He made a case for the quality of the consortium’s work and he laid down high odds for the success of its Common Core assessments. I can’t speak to his second point. The politics of math education (particularly in California) go back to when the Hatfields accused the McCoys of de-emphasizing procedural fluency. I felt he made a strong case for the quality of the assessments, though, particularly if your alternative is the California Standards Test, as it was for everyone in the room.
Here’s the case for quality. SBAC draws heavily from the talent pool at the Shell Centre in England, which includes Malcolm Swan, whose exemplary work I’ve covered here and here. These are exceptional educators and task designers, but you don’t have to take my word for it. The Shell Centre has released a pile of sample assessment tasks. Here’s one:
Compare that to the released questions from California’s Geometry CST [pdf]:
More? Here’s CST Algebra [pdf]:
Compared to a Shell Centre algebra assessment:
The new assessments are more challenging and they reveal more about a student’s thinking. (They’re critiquing arguments. On a math test.) Check out the rest and let me know your reservations.
CMC-North on Technology
Here’s a terrifying thought. It’s 2032. I’m fifty years old, still a CMC member, still attending Asilomar, but Merrill Hall is only half-full for the closing keynote and everyone attending has white hair. Nobody came up the ranks in the last twenty years, in large part because the CMC-N conference-going experience would still be totally at home in the 1990s, right down to the TI calculator sessions. (Sorry. No more jokes.)
There were nineteen tweets on the #cmcn11 hashtag this year, a third mine. Someone at CMC-S e-mailed me a long-ish note to ask permission to livetweet my session, which to the best of my knowledge never happened. They passed out CD-ROMs of session materials in the conference bag. There are better options for conference scheduling than PDFs but a PDF of the program would beat whatever this is:
I’d like to start an off-the-books sub-committee, a place to brainstorm some ideas to present to the conference planning committee, many of which we’ll implement ourselves at CMC-N 2012. If you’re a CMC member (either South or North) and want a piece of the action, email a good idea for upgrading the CMC conference-going experience (so I know you’re serious) to firstname.lastname@example.org.
Christopher DanielsonDecember 6, 2011 - 11:51 am -
And you know what the people running the conference fear come 2032? That Dan Meyer and his Gen-Y compatriots never stepped up to be on the board.
Christopher DanielsonDecember 6, 2011 - 11:53 am -
For the record, I’m with you on all of this, from TI to cell phones.
But you have to remember that they need to be taught. If you ran and lost, or volunteered and got rebuffed, I’d support your revolution.
But if CMC has even half the quality of our own Minnesota Council, they’re dying to have someone do the work officially. No revolution necessary.
David GarciaDecember 6, 2011 - 12:23 pm -
Regarding TI technology: Randall Munroe of xkcd summarized it best in one of his web commics: http://xkcd.com/768/
Daniel PetersDecember 6, 2011 - 1:02 pm -
Please don’t stop the jokes on TI. Did you know Nintendo’s 1989 original Game Boy boasted a resolution of 160 Ã— 144 pixels and four (!) shades of gray?
Dan MeyerDecember 6, 2011 - 1:31 pm -
Too busy running NCTM, MAA, and the National Security Council at that point, probably.
Point taken, though. There’s a sanctioned process for this kind of change that never once occurred to me for reasons I still can’t figure out.
Christopher DanielsonDecember 6, 2011 - 1:59 pm -
Yeah, on a similar note, I have complained over and over to the powers that be that when you search “final exam schedule” on my college website, you get back no useful information, and that the only place that information is kept (despite being centrally scheduled) is on one page of a pdf file of the course catalog. It is not available in any html, php, etc. code anywhere on our website. It is, for all intents and purposes, unavailable to students.
I cannot get that changed and am contemplating a revolution.
If you get the same reaction to your pleas for application of technology to the CMC conferences, I’ll be the first to sign your petition for a redress of grievances.
GregDecember 6, 2011 - 2:24 pm -
If you’re looking for ways to connect a conference to its participants through technology, I’d suggest doing some research into how South By Southwest organizes their Interactive every year. http://sxsw.com/interactive
David PetroDecember 6, 2011 - 3:31 pm -
Re TI – yes, I agree that the technology itself pails by today’s standards but here in Ontario, most schools have multiple sets of these that have been around and used since 1999. That is, one of the things that they are is robust. They are instant on, they can graph dynamically, do essentially all of the math my kids need them to do, are relatively easy to manage, and there is a tonne of resources out there for them (though perhaps not all good – given the example you showed). You would be hard pressed to find a computer that had that sort of longevity. And although there is an argument that we should always be exploiting what is available to us, the downside is that what is available will always be changing and that is hard to manage. I agree however, that it is a bit perplexing (as pointed out in the XKCD comic) that they are still priced the way they are but I guess if people are willing to pay……
On the Techiness (sp?) at math conferences I can speak from experience. Having organized the Ontario Association for Mathematics Education annual conference this year (see you at next year’s version) and trying to infuse a lot of Web 2.0 and social media, I was a bit disappointed at the lack of traction it got. We did get a lot of use out of our hash tag but primarily from only a handful of users. And even within my own committee many of the initiatives I wanted to have were met with rolling eyes. My thinking is that math teachers on the whole are still closer to Luddites than being tech savvy. For example I talked to someone today who is the same age as me but was talking about using tables when teaching about normal distribution. We still have a long way to go.
cheesemonkeysfDecember 6, 2011 - 7:02 pm -
Great summary, Dan.
I had two questions/observations:
1) #SignageFAIL (epic) *OR* #ActualCellPhoneBan?
Having run giant conferences myself in my checkered past, my first thought when I saw the “No Cell Phone” picture was #SignageFAIL, not #totalcellphoneban .
Do you think they were trying to enforce a total ban on cell phones in sessions (i.e., you must check your phone at the door) or did they simply communicate poorly what they were trying to request (i.e., please turn your cell phone ringer OFF before you sit down)?
2) State-of-the-Art Technologies, Meet Lagging School/District Policies
One of my biggest frustrations as a middle school math teacher is this inherently self-defeating confluence of factors:
a) EVERY kid in our school has an iPhone or an Android and enough cash flow to purchase a graphing calculator app (â‰¥$5),
b) FEW kids own a graphing calculator, and even fewer parents want to spend money on a single-purpose device that (let’s face it) their student is likely to lose, yet…
c) NOBODY is permitted to use an iPhone, Android, or iPod Touch in the classroom — not even if I confirm that they have put them into Airplane/Flight mode!!!!
This is a lose-lose-lose situation, but it’s more common than most of us would think.
And it’s one reason why — along with their dominance over the “approved standardized testing devices” market — TI is able to maintain their stranglehold in the classroom.
I don’t know what the solution is; I’m still just trying to effectively document the problem (and not sure if I’ve even gotten that far yet).
– Elizabeth (aka @cheesemonkeysf on Twitter)
TonyDecember 6, 2011 - 8:02 pm -
My sentiments regarding TI are split between David and cheesemonkeysf. I used TI 84’s for quite a while and found them to be less than intuitive and their pixelated screen to be a humongous obstacle. That said, the graphing calculator apps out there are not near as powerful as TI’s latest offering (TI Nspire). The interface makes a lot more sense and from a teacher’s standpoint, it’s more like a teaching tool than a calculator with the ability to send documents wirelessly to students, quickly assess knowledge with quick polls, and develop interactive web content with their teacher software. It’s not the only thing that I do in class, but it’s a huge part of some of the success I experience in the classroom.
Dan MeyerDecember 7, 2011 - 12:11 pm -
@Greg, great advice.
Regardless of current uptake, it will be important for new teachers to feel like their professional organizations take seriously how they interact with information and each other. Aside from that, if we believe that tool [x] can make a better conference-going experience for everybody (not just early adopters) it’s on us, then, to make that experience as easy, fun, and free as possible. For example, if we believe a Twitter hashtag can enrich the conference-going experience for everybody, then we shouldn’t stop at advertising the hashtag in the program. We should have a dedicated projector streaming those tweets somewhere for everybody to see. And so on.
David PetroDecember 7, 2011 - 12:23 pm -
Dan, I agree. And if Twitter is your “tool x”, setting up a twitter hashtag takes no effort beyond promoting it a bit. And broadcasting the results is pretty easy with a site like http://visibletweets.com/ . Also very easy to use, for example: http://visibletweets.com/#query=%23anyqs&animation=1
Jared DerksenDecember 7, 2011 - 3:02 pm -
It seems to me that we think TI calculators do what we need them to do because we have limited ourselves to doing what they can do. The tool has effected the user.
We don’t want to graph vertical lines? Other relations that are not functions?
The Casio Prizm is a step in the right direction. But a full-featured internet connected device (iOS? Android?) is clearly the best answer for a learning tool. Test security is the obstacle.
TonyDecember 7, 2011 - 5:31 pm -
The biggest obstacle that I encounter isn’t ever really the tool itself, but I understand your point about graphing vertical lines. I like their stuff but it could still use a few changes. I also agree that an iOS/Android device would be a superior tool to have, but some of my students walk in with duct tape holding their shoes together and don’t bother even thinking about ever getting their hands on an iPhone/iPod/iPad. It cracks me up to hear teachers advocate use of mobile devices because “every kid has one” or “every kid can afford an app for [x] dollars” as if the district refusing to allow students to use one is the only barrier. My school is 80% free and reduced lunch and I bet we could be 90% if some of the tweaker parents would sign the damn form. My district would have to fork out $22,000,000 to fund a one-to-one iPad program…translation…not happening. It’s much easier to stomach a class set of 40 TI-Nspire calculators at $125 a piece that includes professional development and online resources. [/RANT]
Tim EricksonDecember 16, 2011 - 6:25 pm -
Sorry I missed CMC/N this year. Loved the snarkiness about the TI. Can’t stand ’em.
AndyDecember 19, 2011 - 7:00 am -
On “survey” areas, this site shows pretty-well why the surveyor’s formula works.
Also of interest is what people did (not very long ago) before google earth and ARCGIS:
AndyDecember 19, 2011 - 7:05 am -
Oh, and be sure to see this, a ref from the bottom of the Wikipedia page.