Initiating and Eliciting in Teaching: A Reformulation of Telling

We address the telling/not-telling dilemma in mathematics education. Telling is instructionally important, but has been downplayed because of (a) perceived inconsistencies between telling and constructivism, (b) increased awareness of the negative   consequences of relying too heavily on telling, and (c) a focus on "non-telling" actions as pedagogical implications of constructivism. In response, we advance a theoretical reformulation of telling as the set of teaching actions that serve the function   of stimulating students' mathematical thoughts via the introduction of new ideas into a classroom conversation. We reformulate telling in three ways: (a) in terms of the function (which involves attention to the teacher's intention, the nature of the teaching   action, and the students' interpretations of the action) rather than the form of teachers'   communicative acts; (b) in terms of the conceptual rather than procedural content of the new information; and (c) in terms of its relationship to other actions rather than as an isolated action. This reformulation resolves some of the concerns with teaching as telling and helps establish the legitimacy of providing new information within a constructivist perspective on learning.