In addition to using pairs a lot, in both teacher and student mode, you're likely to encounter some version of version control along the way, though maybe not in math class at first. Instead, we're looking at chess games through the ages, realizing they all start from the same position if following strict rules (there's some weeding already, if the board is rotated 90 degrees).
In version control, you're "following all the games" but of course not really. A goal is to have all transitions be legal moves, i.e. you don't graft one "tree" to another where the move makes no sense. That's to distinguish "legal" from "motivated" or "sensible" i.e. a legal chess move may be to "just get it over with" (a formality), although for that, there's always just knocking over the King (an actual move, for those unfamiliar, and always legal during one's turn, even as a first move -- talking about your own King, not the other guy's).
Given my Python heritage, I'm drawn to Mercurial, but a cygwin session might have nothing to do with source code in the traditional sense. I might be writing a storyboard and want to see different endings.
A bevy of curriculum designers (a faculty) might pass this around, a growing blob of pithy goodness, lots of embedded forks, alternative doodles, oodles of moodles. Do these internal schisms matter to us? Quakers call it "potluck" and just keep passing it around among interested parties. Liberal arts thinking has a "live and let live" philosophy as one of its hallmarks, in need of defending from those who'd rather dumb it down more.
Each teacher "trims the tree" under pressure to localize i.e. to keep it real to the needs of students, coworkers, peers. You'll likely wanna be "a winner" in the eyes of your crew, as a part of your team. Some parts of the tree won't pertain then, e.g. if the lesson plan calls for geo-caching in the high desert, but you're more in a rain forest these days. Teachers have always had editing and synthesis responsibilities, so we're mainly talking about using new tools for grappling with some age old challenges.
Chess is a DM hallmark I'd say. You've got the notion of "rules" i.e. of "grammar", a connection you'll find in Wittgenstein a lot, his Remarks on the Foundations of Mathematics definitely a part of our teacher training syllabus.
A hallmark of the AM track is using calculators, or "baby rattles" as we sometimes call them (to go with "tree killer" textbooks).
Note: DM = digital math; AM = analog math (draws from the "discrete" versus "real analysis" distinctions of the 1900s, also from music distribution media e.g. analog was more like vinyl, spool tape, versus a saved / playable binary file (broadcasting and telephony underwent similar transformations, in the wake of the success of the Internet and QM (quantum mechanics))).
:: from planet fabulon ::
