What We Know

The role of communication in learning and thinking mathematically cannot be overestimated. Discourse that promotes communication and reasoning provides students with opportunities to learn about particular topics and to reason and communicate about these topics. Discourse allows students to create their own mathematical understandings (Eisenhardt, 1999; Wood, 1993). Discourse provides opportunities for individual students to connect and integrate their mathematical learning (Lo, Wheatley, & Smith, 1994). Higher-order questions typical in discourse promote reflection and integration in a way that recall or rote response cannot (Hiebert & Wearne, 1993).

An emphasis on communication leads to higher achievement. In studies, students who constructed and provided explanations of their mathematical processes demonstrated higher achievement as a result (Fuchs et al., 1996; Nattiv, 1994; Webb, 1991). Other studies show that as students communicate mathematical understandings, defend them in the face of questions, and question others' explanations, they recognize incongruities and clarify and reformulate their mathematical understandings (Kamii, 1988; Lampert, 1992).

Discourse does not need to be teacher-student; peer interactions can also be effective. When students justify their solutions to their peers, they develop a higher level of understanding (Hatano & Inagaki, 1991). It is important, however, that students be provided guidelines for successful communication. Webb (1991) found two strong relationships between language-mediated peer interaction and achievement: a) low achievement correlates with receiving non-responsive feedback (e.g., only being told the correct answer) and b) high achievement correlates with giving elaborate and explicit explanations.

Results of the National Assessment of Educational Progress (NAEP) suggest that a greater emphasis on communication is needed to produce mathematically literate citizens (Silver, 1997). Students at all grade levels performed poorly on regular and extended constructed-response tasks of the NAEP tests (Carpenter & Lindquist, 1989; Kouba, Zawojewski, & Strutchens, 1997; Silver, 1997). When required to solve reasonably complex mathematical problems and to explain and justify key aspects of the solution, students failed to provide clear explanations of mathematical ideas.

As educators seek to involve discourse in their curriculum and instruction, they may want to note these key elements of effective mathematical discourse:

• students interpret the mathematical task;
• student interact with other students;
• teachers serve as facilitators, rather than explaining or evaluating (Lo, Wheatley, & Smith, 1994).