One idea that has gained considerable attention in mathematics education is that teachers should become facilitators of mathematical discourse (Bush and Kincer 1993; Hiebert and Wearne 1993; NCTM 1991). Mathematical discourse should encourage student interpretations of a mathematical task and student-tostudent interactions (Lo and Wheatley 1994). In the majority of American classrooms, few interactions occur, because teachers dominate the discourse by asking all the questions (Cazden 1988); and if students do not know, the teachers also give the answers. As a result, “teaching by telling” is the most common pedagogy. One alternative to this practice is constructivist teaching.
Jacqueline Leonard taught for sixteen years in grades K–6.