THERE'S FIVE LITTLE NOTCHES IN HERE: DILEMMAS IN TEACHING AND LEARNING THE CONVENTIONAL STRUCTURE OF RATE
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.