Recognizing that many students struggle when transitioning from middle school to high school math, Denver Public Schools (DPS) is partnering with REL Central to better understand why some student pathways are more likely to lead to 9th grade math success and what can be done to support student success. One factor DPS is exploring is the quality of mathematical discourse that students are exposed to in math classrooms. Discourse refers to the words, conversations, and verbal tools that classrooms have in place to support students' thinking about math, communication, and problem-solving in math classrooms. The quality of the language students listen to and engage in during math instruction has been associated with higher levels of student achievement.
Math isn't just about numbers; it's also about the understanding and use of a unique language. Developing students' mathematical language plays a crucial role in building students' math proficiency. Providing opportunities for all students to engage in productive mathematical discourse may be a powerful way to improve outcomes. Mathematical language comes packed with its own set of vocabulary and meanings.1 To help their students develop a deep and rich understanding of math, educators should consider routinely connecting math language to mathematical content and representations, modeling accurate and appropriate vocabulary use in their instruction, creating frequent opportunities for student discourse, and encouraging students to focus on the language they hear and use in classrooms as they engage in productive mathematical discourse with their teacher and peers.2
Researchers have primarily focused on three aspects of productive mathematical discourse:3
- Cognitive processes: The types of conversational processes students use, like offering explanations, elaborating on peers' ideas, debating, or building consensus.
- Academic language: How the content is represented in student discourse, looking closely at how students use math vocabulary, their learning goals, or their misconceptions.
- Participation patterns: Which students participate in classroom discourse and the frequency and quality of their participation. Participation analyses often focus on observable learner characteristics, such as their gender, race, or ethnicity, as well as information like prior academic achievement.
There are few rigorous studies of discourse in the classroom. Some found that high-quality, productive classroom discourse benefits students. Specifically, productive mathematical discourse has been related to academic outcomes,4 student motivation, self-efficacy,5 and oral communication skills6 (e.g., effective and appropriate communication in social contexts), but it remains unclear which aspects of discourse may matter most.
Given that participation is often associated with characteristics of learners or teachers, what can teachers who want to bring more high-quality and inclusive discourse into their classrooms do?
Teacher pedagogy contributes to the quality of classroom discourse.7 Teachers can create opportunities for more productive discourse by changing their practice and encouraging students to co-create knowledge in the classroom through questioning and discussion, or dialogic teaching.8 Dialogic teaching involves teachers asking open-ended questions with more than one possible correct solution, requiring students to think critically and creatively. Teachers can also work to build on students' ideas to motivate them to engage in the learning process more actively.9 Districts can consider offering professional development to help their teachers improve their use of dialogic pedagogy to increase opportunities for productive student discourse.10
Districts interested in learning more about the nature of mathematical discourse taking place in their schools might start by considering the various aspects of productive student discourse and identifying which best align with their priorities and contexts. Classroom data on mathematical discourse can be captured in many ways, but most instruments focus on just one or two aspects of discourse and rely heavily on observational data. To limit the burden on teachers, districts can consider having observers go into classrooms to collect data, including discourse in current observation protocols or walk-through guides, rather than asking teachers to self-report. Districts must also consider whether the discourse will take place between a student and teacher, in small groups, or with the whole class.
So, what now?
Moving toward productive mathematical discourse is often part of a larger school culture shift. As an initial step, district and school leaders can talk about discourse as a priority and ensure discourse is reflected in current protocols and initiatives. To date, most research on classroom discourse has been qualitative and focused on characterizing the nature of discourse in K-8, ELA, or science classrooms. As more quantitative research emerges, classroom discourse is increasingly being linked to positive student outcomes. More research is needed, especially in high school math classrooms, like those in Denver Public Schools, to better understand what aspects of mathematical discourse have the most positive effect on various student outcomes. We can then work to shift school culture to better support teachers in improving their dialogic discourse practices to create more productive learning environments for all students.11
1 Pimm, 1987; Schleppegrell, 2007
2 Hughes, Powell & Stevens, 2016
3 Howe & Abedin, 2013
4 Applebee et al., 2003, Himmelsbach et al., 2023; Howe et al., 2019; Mercer & Sams, 2008; Murphy et al, 2018; Nystrand & Gamoran, 1991
5 Boheim et al., 2021; Kiemer et al., 2015
6 Van der Veen et al, 2017
7 Cohen, 2015; Howe & Abedin, 2013; McNeill & Silva, 2010; Nystrand & Gamoran, 1991
8 Alexander, 2017; Teo, 2019
9 Boheim et al, 2021
10 Boheim et al, 2021; Fishman et al., 2017; Forman et al., 2017; Kiemer et al., 2015; Kohen & Borko, 2022; McNeill & Silva, 2010; Monte-Sano et al., 2021; Murphy et al., 2018; Osborne et al., 2019; Rutherford-Quach et al., 2018
11 Boheim et al, 2021
