Child, Youth, and Family Studies, Department of


Date of this Version



Buchheister, K, Jackson, C., & Taylor, C.E. (2019). What, how, who: Developing Mathematical Discourse. Mathematics Teaching for the Middle School. 24(4), 202 – 208.


A collaborative classroom, an open-ended problem, and a what-how-who structure can build students’ reasoning skills and allow teachers to recognize all classroom contributions.

With an increased focus on using social discourse to enhance students’ mathematical thinking and reasoning (NCTM 2014, Staples and King 2017), teachers are looking for discussion strategies that encourage middlelevel students to make sense of mathematical concepts. However, structuring these valuable discussions is complex. “Mathematical discourse should build on and honor student thinking, and provide students with opportunities to share ideas, clarify understandings, develop convincing arguments, and advance the mathematical learning of the entire class” (Smith, Steele, and Raith 2017, p. 123). In other words, teachers must carefully consider what tasks provide meaningful opportunities to explore ideas, generate hypotheses, and promote questions within a collaborative environment. Then, teachers need to consider how to structure the activity to encourage discussions and incorporate responses that contribute to understanding specific mathematical objectives. Additionally, teachers must select who will speak to “advance the mathematical storyline of the lesson” (NCTM 2014, p. 30). By intentionally focusing on these elements in mathematics instruction, middle-grades teachers can develop a classroom culture that not only emphasizes sense making but also values the intellectual capacity that students bring to the classroom (Gutiérrez 2013; Lemons-Smith 2008). In this article, we describe how teachers can promote meaningful discussions using the what-how-who structure while giving students opportunities to make sense of mathematical ideas within a social context.