In this section of the book, three studies of mathematical talk in my fifth-grade mathematics classroom will be presented. The first of these studies, by Peggy Rittenhouse, examines, in her words, “how one teacher helped her students develop ways of talking about mathematics.” Using records of what happened during the month of September in my classroom, Rittenhouse examines the teacher's role as participant in and commentator on mathematical discourse, bringing perspectives from current work on literacy learning.

How Does the Teacher “Help” Students Learn to Talk Math?

When Rittenhouse uses the word helped to describe what the teacher did, she leaves much to the interpretation of the reader. One ambiguity in the way she formulates her research question lies in the difference between intending to do something and accomplishing it. Does she mean that she is going to describe what the teacher did and offer some grounded speculations on the intentions of these actions? Or is she claiming that the teacher was successful in helping her students and then examining evidence for what she accomplished? A second ambiguity revolves around the word helped used to describe what the teacher did. As James Gee points out in his afterthoughts to Deborah Hicks's Discourse, Learning, and Schooling, our attention to Vygotsky and the importance of the perspective of practice on language learning raises questions about the extent to which the teacher's help should be explicit (1996, p. 269).