
06022042
j
2012b.00244
Moschkovich, Judit N.
"I went by twos, he went by one": Multiple interpretations of inscriptions as resources for mathematical discussions.
J. Learn. Sci. 17, No. 4, 551587 (2008).
2008
Lawrence Erlbaum Ass., Mahwah, NJ
EN
C30
E40
mathematics education
discussion (teaching technique)
mathematical concepts
concept formation
teaching methods
grade 8
secondary school mathematics
bilingual students
problem solving
cooperative learning
graphs
teacher role
language usage
middle school students
research
classroom conversation
mathematics and language
verbal communication
teacher role
graph of a function
Summary: 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 a "unitized" 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. 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.