What is mathematical Discourse?

One of the benefits many researchers (myself included) have seen from increased mathematical discourse is an increase in student achievement. Mathematical discourse allows students to engage with a variety of strategies, therefore increasing their depth of understanding of the mathematics (Marino, 2005). The more students participated in mathematical discourse by voicing their mathematical thinking and engaging with others' ideas at high levels, the more their learning outcomes increase (Ing et al., 2015). Cobb et al. (1997) proposes that the process of learning mathematics is social and that students "actively construct their mathematical understandings as they participate in classroom social processes" (p. 264). While Gresham and Shannon (2017) report direct growth through the use of mathematical discourse and student engagement through discourse, Cobb et al. (1997) suggests that while mathematical discourse is a useful construct in the classroom, it merely suggests a possible relationship between classroom discourse and mathematical development. So while mathematical discourse may not directly affect student achievement, it opens the the door to possible growth of student understanding. 

Mathematical discourse is one practice that allows teachers to approach mathematics education in a way that is equitable for our students. Gresham and Shannon's (2017) work suggest that activities that build mathematical discourse give students voice. The discourse helps students build their sense of belonging to the classroom community, recognize contributions to the group, and have pride in their budding conceptual understanding (Gresham & Shannon, 2017). Buchheister et al. (2019) recommend using a variety of discourse formats (pairs, small groups, whole group) in order to help recognize and empower student voices in the classroom. As a variety of students are able to share in a variety of ways, students build their identities as mathematicians (Buchheister et al., 2019). In "8 Teaching Moves Supporting Equitable Participation," Wood et al. (2019) makes a similar statement - that as we assign competence to, or highlight strengths of, students, we are convincing students that they and their classmates all have important mathematical ideas to contribute to the conversation. Mathematical discourse opens up math to all students and provides opportunities for all students to be (and be seen as) successful. 

Another benefit of mathematical discourse is that it encourages participation in the lesson. This ties closely with equity, because students tend to participate to the degree that they are seen as "smart" (Wood et al., 2019). Students who are seen as smarter, by peers or by the teacher, participate more than students who aren't seen (or feel like they aren't seen) in that way. We can use mathematical discourse to increase student status, which "increases when [the student] makes a mathematical contribution that is recognized by a classmate or a teacher. As status increases, a student is likely to gain confidence and make further contributions" (Wood et al., 2019, pg 219). We see this idea supported by Ing et al. (2015) who report that student engagement is often predicted by teacher support of student participation. In their study of a 1st grade class, Gresham and Shannon (2017) noted that mathematical discourse seemed to increase student motivation to become and stay engaged in their mathematical learning and that students were eager to be involved in the learning process. Students like to talk and they like to be heard - framing math around the discussions we have allows students both of those.