Mathematics in the making: Mapping verbal discourse in Pólya's “Let Us Teach Guessing” lesson

This paper describes a detailed analysis of verbal discourse within an exemplary mathematics lesson—that is, George Pólya teaching in the Mathematics Association of America [MAA] video classic, “Let Us Teach Guessing” (1966). The results of the analysis reveal an inductive model of teaching that represents recursive cycles rather than linear steps. The lesson begins with a frame of reference and builds meaning cyclically/recursively through inductive processes—that is, moving from specific cases, through recursive cycles, toward more general hypotheses and rules. Additionally, connections to specific forms of talk and verbal assessment, as well as to univocal (conveying meaning) and dialogic (new meaning through dialogue) discourse, are made.