Evaluating Significant Math Discourse in a Learning Environment

Stahl, G. (2012c). Evaluating significant math discourse in a learning environment Paper presented at the 12th International Conference on Mathematical Education. Seoul, Korea.


To mathematicians since Euclid, math represents the paradigm of creative intellectual activity. Its methods set the standard throughout Western civilization for rigorous thought, problem solving and argumentation. Many schools teach math in part to instill in students a sense of deductive reasoning. Yet, too many students—and even some math teachers—end up saying that they “hate math” and that “math is boring” or that they are “not good at math” (Boaler, 2008; Lockhart, 2009). They have somehow missed the intellectual math experience—and this may limit their lifelong interest in science, engineering and technology. According to a recent “cognitive history” of the origin of deduction in Greek mathematics (Netz, 1999), the primordial math experience in 5th and 4th Century BCE was based on the confluence of labeled geometric diagrams (shared visualizations) and a language of written mathematics (asynchronous collaborative discourse), which supported the rapid evolution of math cognition in a small community of math discourse around the Mediterranean, profoundly extending mathematics and Western thinking.

The vision behind the research described in this paper is to foster communities of math discourse in networks of math teachers, in classrooms of K-12 math students and in online communities associated with the Math Forum. We want to leverage the potential of networked computers and dynamic math applications to catalyze groups of people exploring math and experiencing the intellectual excitement that Euclid’s colleagues felt—refining and testing emerging 21st Century media of collaborative math discourse and shared math visualization to support math discourse in both formal and informal settings and groupings.