Mathematical Conversation

Teaching … is more than mere facilitation, it is a delicate and complex participation in unfolding understandings.
(Towers and Davis 2002, p. 331)

Conversation around a good problem is essential in an effective mathematics classroom. When given opportunities to explain themselves orally, students are more likely to acknowledge their preconceptions and dispel their misconceptions as they solidify their growing understanding.

Careful listening on the part of the teacher is necessary to effectively question and prompt students as they wrestle with mathematical ideas. Math discussions should encourage the sharing of students' original thoughts and also provide opportunities for interpretation and multiple correct solutions (Friesen and Stone 1996). Students should also be given opportunities to present and defend their understandings. They need to convince themselves and then convince their peers (Lappan and Ferrini-Mundy 1993). This metacognitive process of reflection and dialogue helps solidify understandings (Donovan and Bransford 2005).