new worked example: Math as Narrative
Caro Williams & I just put the finishing touches on a second worked example from the WoW research we’ve been doing here at UW-Madison. This one is entitled “Math as Narrative in WoW Forum Discussions” and builds on a previous analysis we did that focused on scientific reasoning in WoW forums in which we gathered a large representative sample of World of Warcraft discussion forum posts (1984 randomly-selected posts over 85 discussion threads) and found that 4% of the posts provided models of complex in-game phenomena that were explicitly mathematical in nature with 1% including relevant mathematical computation as a form of proof. In this study, we wanted to take a closer look at the kind of math that was going on. And what we found knocked our pants off.
This worked example details the close analysis of a single post from within this larger corpus taken from a discussion thread titled “Get Educated: The MYTH Behind Shadow Scaling” (retrieved November 3, 2006). The overall subject of the thread concerns shadow priests and the rate at which their abilities scale as they advance through the game. Throughout the discussion thread, participants exhibit a wide range of mathematical skill from “basic interpretation of the gist of the mathematical model presented” to “criticism of certain attributes or computational steps in its justification” to “wholesale criticism of the model’s terms” to “counterarguments and rebuttals that are entirely non-mathematical”. We selected this specific post, however, because of its remarkable use of narrative structure as a way to organize its mathematical argument.
Using discourse analysis methods of Gee (1996, 1999), the narrative structure framework provided by Labov (1972), and some basic mathematics (algebra, arithmetic), we show how, within 31 lines of text, the author manages to present a mathematical model for the claim that “shadow has crap scaling,” including computational evidence that his model (and therefore claim) is correct – not in the format of a standard mathematical proof but rather in the form of a story.