This chapter explores teaching and learning mathematics. Both are complex in many dimensions, as shown by recent research that uses teaching interviews to study conceptual change (Nemirovsky, Tierney, & Ogonowski, 1993; Steffe & Cobb, 1988; Thompson, 1994) or that follows conceptual change during classroom instruction (Cobb, Wood, Yackel, & McNeal, 1992; diSessa, Hammer, Sherin, & Kolpakowski, 1991; Lampert, 1986, 1991). As we move away from theorizing about teaching and learning as the transmission of information-teachers pouring knowledge into the receptive (or not so receptive) heads of students-we need a new language to explore what teachers and learners do in interaction (Bruner, 1986; Greeno, Collins, & Resnick, 1996). This edited volume proposes thinking practices as a different kind of language for describing teaching and learning. Our contribution elaborates this language in an exploration of teaching and learning in a particular elementary school mathematics classroom.