“I Went by Twos, He Went by One”: Multiple Interpretations of Inscriptions as Resources for Mathematical Discussions
Journal of the Learning Sciences, Volume 17, Issue 4 October 2008 , pages 551 - 587
Judit N. Moschkovich
This article examines a classroom discussion of multiple interpretations of the scales on two distance versus time graphs. The analysis describes how two students and a teacher used multiple meanings for phrases of the form “I went by” and coordinated these meanings with different views of the scales. Students' ambiguous and shifting meanings did not prove to be obstacles to this discussion. Instead, this teacher used student interpretations as resources, built on them, and connected them to canonical mathematical concepts—in particular by highlighting (Goodwin, 1994) a “unitized” (Lamon, 1994, 1996, 2007) view of the scales. Research in mathematics education describes teaching that promotes conceptual development as having two central features: One is that teachers and students attend explicitly to concepts, and the other is that students wrestle with important mathematics (Hiebert & Grouws, 2007). Not only does this classroom discussion provide an example that it is possible to balance these two features, but the analysis provides the details of how instruction can simultaneously provide explicit attention to concepts while allowing students to wrestle with these concepts.