Drawing in the sand counts as paperless
Steve Katz (@stevekatz) asked about running a paperless math classroom earlier today and, after the third tweet, I realized that this was not a topic built for 140 character chunks. What little I saw of the discussion (no hashtag!), and my initial responses, focused on tools for formalizing math symbols without paper. While important, I think that view is a bit narrow.
I went through a very typical, wealthy suburban public school system and disliked math all the way through 12th grade. I then hit a transformative teacher, got a BA in Math and taught 6th-9th grade math in CA public and independent schools for 6 years. I’m not trying to present myself as “real” mathematician or a superb math teacher, just that I’ve done a lot of different kinds of math in a variety of settings. I went in to teaching middle school math remembering nothing but my dislike of those classrooms, and tried to do better.
The Paperless Friday project makes all kind of sense as an exercise, as a broadside against complacency and un-reflective teaching practice, and as a lens through which to reevaluate our classrooms. But, to be clear, no one talks about the “paperless classroom” because they’re deeply concerned that we’ll wake up one day without paper. Paperless matters because, as my CS/CE/EE friends always taught me, “you can’t grep dead trees.” Paper is isolated, static yet ephemeral . Paperless is linkable, connected, mutable but phenomenally persistent. I’m fine with “Paperless Fridays” being a literal statement – – and there’s certainly a bunch to do with math on a Friday like that — but I think that the ideal paperless math classroom will still have a fair amount of writing.
That said, as traditionally taught 6-12 Math certainly has a paper fetish. Breaking that fascination can start really low-tech with a class set of whiteboard slates. Having students work any written exercises on a slate means that the only way to assess it is to observe directly, being present and mobile in the classroom. If such a thing as “notes” matter, they should be provided though IWB slides or video, and save class time for the actual working of math. (For several years, I tried to order 2’x4′ whiteboard stickers to cover entire tabletops in my room as a collaborative work space, but they were always backordered into oblivion come September.) The key is to honor and value written work by giving it a place in class, with peers participating and with your full attention.
As an aside, one of our math teachers uses the classroom network set from TI , where the individual graphing calculators can all dump their screen to the projector, and the teacher can push problems and quizzes out to the devices. It’s a neat system, albeit a costly, proprietary, and inflexible one. I would feel much better about if that tool set then encompassed *all* of their brute calculate/solve/simplify/graph work, and the rest of the class focused on something richer.
In math circles Lockhart’s Lament (PDF Link) is pretty ubiquitous, and it’s ABSOLUTELY worth a read if you haven’t seen it before. He savages what we recognize as the “standard” math curriculum for being the soul-killing, joy-depriving sausage mill that it is, and pushes us towards a math classroom built around actually doing math. From his central example, the notion of running a paperless math classroom should be as simple as running a paperless music classroom. Focus on composition, on solving genuine problems, on argument and exploration, rather than on rules, system or on any technique that starts with STEP 1.
Here’s where tools might be useful. A simple Google Doc with rich TeX equations might well be a better collaborative medium than the paper-version, although I will still stand up for anyone’s right to think with a pen in hand. @teachpaperless suggested Wiziq, which I haven’t looked through, but any non-tablet mode of math publication going to involve some combination of choosing symbols form a menu and/or typing mark-up. While it’s a little hurdle (especially for younger students), it’s the price of all those great “paperless” adjectives from earlier. Take real mathematical thinking, use open and free tools to create the open/shareable document of their process. Take their writing and put it where people can see, read, comment and link. Take their songs and put them up as CC-licensed mp3/oggs, or as remixable GarageBand tracks. Treat math for what it is, another beautiful product of the human imagination.
Alternately, you could just hand them all iPod Touches with twitter clients and have them do arithmetic drills via tweets and gather the responses on the board with TwitterFall. I’d suggest #missingthepoint as your tag.