Mathematical Discourse Promotes Educational Equity
Research and Strategies for Equitable Outcomes
By Dr. Lanette Trowery, Sr. Director of Learning at McGraw Hill School and Margaret Bowman, Academic Designer at McGraw Hill School
Discourse encompasses interactions between members of the community and their attempts to develop shared meanings using a variety of tools, language, and norms (Bennett, 2014; Hicks, 1995; Lampert, Rittenhouse, and Crumbaugh, 1996; Moschkovich, 2012; Sherin, 2002; Yackel and Cobb, 1996). Discourse is a valuable learning tool, but widely underused in mathematics education.
What Does Mathematical Discourse Look Like?
Before exploring the connections between mathematical discourse and equity, it’s important to understand the interactions that define classroom discourse, and what discourse looks like in a math classroom.
💡 Research Spotlight: O’Connor, Michaels, and Chapin (2015) describe the results of a four-year study of about 500 predominantly Latinx students in grades four through six who took part in Project Challenge, a program designed to identify fourth-grade students who have the potential to excel in math and provide them with a challenging curriculum. While the study was not originally focused on classroom discussions, the researchers and teachers in the study noted that the use of talk moves appeared to play a role in the positive academic gains for the students in the study.
Talk moves — teacher revoicing, student restating, agree/disagree, adding on, wait time — are defined as ways teachers use questioning and probing when supporting student discussion and discourse. The goal of the talk moves is to “get students to make their own contributions, listen to other students, keep the focus on reasoning, and work respectfully and productively with the ideas of others” (p. 112).
Hufferd-Ackles, Fuson, and Sherin (2004) detail the development of a math-talk learning community — “a community in which individuals assist one another’s learning of mathematics by engaging in meaningful mathematical discourse” (p. 81). Extending prior research on mathematical discourse and supporting teacher change, the authors conducted a year-long study on four teachers with predominantly Latinx classrooms and the teachers’ work to develop whole-class discourse practices. The researchers found that the development of the math community was linked to four categories of teacher actions: questioning, explaining math thinking, sources of mathematical ideas, and responsibility for learning (p. 87).
Mathematical Discourse and Educational Equity
Classroom discourse has been shown to support equitable classroom environments, largely because engaging students in math discourse is important as a lever in advancing the mathematical learning of all members of the classroom community (NCTM, 2014).
💡 Research Spotlight: In two separate longitudinal studies, Boaler (2002) analyzed classrooms using a curriculum designed to support equitable teaching of mathematics. These classrooms were linguistically, ethnically, and racially diverse; the study matched each classroom with a comparable classroom that used a more procedural, teacher-focused curriculum and teaching methods. The findings showed that the schools using the open-ended approach achieved significant gains in achievement and performed better than the comparison groups. Additionally, the results showed that the gains were spread across different student groups and not contained to just higher achievers or more economically advantaged students (p. 247).
In these studies, three specific practices were noted as crucial to the positive outcomes found: introducing activities through discussion, teaching students to explain and justify, and making real-world context accessible (Boaler, 2002).
Multiple other studies conducted in classrooms with diverse learners — defined by ethnicity, achievement levels, and English language fluency — show academic improvement as well as increased participation in classroom activities (Bennett, 2014; Clark et al., 2015; Fenema et al., 1996; O’Connor, Michaels, and Chapin, 2015; Rubenstein-Avila et al., 2015). These studies demonstrate that classroom communities where discourse is supported:
- Pay attention to the ways in which students are expected to participate in learning mathematics and how they are supported
- Challenge deficit views around the discursive practice students bring with them to school, and
- Build mathematics discourse practices starting where the students are (Aquino-Sterling, Rodriguez-Valls, and Zahner, 2016; Moschkovich, 2012).
The Importance of Mathematical Discourse for English Learners
Pierce & Fontaine (2009) suggest using research-based instructional practices from reading for vocabulary development in math classrooms to support the transition from informal language to academic language. For English language learners, the focus on language practices and discourse is a crucial step in encouraging the academic self-efficacy of those students.
Teachers can support linguistic diversity in their classroom through pedagogical language knowledge, defined as “knowledge of language directly related to disciplinary teaching and learning and situated in the particular (and multiple) contexts in which teaching and learning take place” (Bunch, 2013 in (Aquino-Sterling, Rodriguez-Valls, and Zahner, 2016). Enacting pedagogical language knowledge includes developing a culture of discourse, steeped in inclusion and democracy. This culture of discourse “acknowledges and validates diverse uses of language in the classroom, while at the same time creating opportunities for students to engage in linguistic exchanges proper of formal academic and disciplinary contexts” (Aquino-Sterling, Rodriguez-Valls, and Zahner, 2016, p. 94).
Strategies for Promoting Mathematical Discourse in the Classroom
If you’re looking to leverage mathematical discourse to bring equity to your classroom, here are a few key strategies to get started:
- As the teacher, embody the role of a facilitator. Encourage rich discussion, participation, and reasoning from the students from the very beginning of the lesson.
- Establish routines, such as beginning lessons with a warm-up activity that builds students’ proficiency with number sense and sets students up to talk about their reasoning for solving unknown problems.
- Prioritize sensemaking activities that encourage students to engage in collaborative conversations to connect and apply mathematics.
- Lead whole-group discussions to connect concepts to strategies and procedures through examples and discussion — students should discuss and relate multiple representations, strategies, and procedures when solving problems.
- Promote effective self-questioning or collaboration by utilizing prompts that encourage reflection. Ask students to justify their reasoning or choice of strategy — or at a minimum, to elaborate on their thought process (Booth et al., 2017; Hattie, 2017, p. 152).
With the right emphasis on discourse and continued practice in the classroom, a more equitable environment where all students have the tools to talk about and understand math concepts is well within our reach.
For more on the importance of discourse in mathematics, and how discourse is practiced through specific instructional elements in Reveal Math K-5, see the full Reveal Math K-5 Research Foundations.
For more math tips, research, and stories, see:
About the Authors
Lanette Trowery, Ph.D. is the Senior Director of the McGraw Hill Learning Research and Strategy Team.
Lanette was in public education for more than 25 years, working as a university professor, site-based mathematics coach, elementary and middle school teacher, mathematics consultant, and a professional learning consultant, before coming to McGraw Hill in 2014. She earned her Master’s and Doctorate from the University of Pennsylvania.
Lanette’s team, Learning Research and Strategy, serves as the center of excellence for teaching and learning best practices. Her team conducts market, effectiveness, and efficacy research into products to provide insights and recommendations to product development. They collaborate across internal teams, external experts, and customers to establish guiding principles and frameworks to move from theory to practice.
Margaret Bowman is an Academic Designer in the Mathematics Department at McGraw Hill.
Margaret earned her Bachelor of Science in Education from Ashland University with a teaching license in Middle Grades Education, and her Master of Education from Tiffin University. She was a middle school Math and Language Arts teacher for six years before joining the middle school team at McGraw Hill in 2012, writing and designing print and digital curriculum.
Margaret is also a Research Associate in the Research Laboratory for Digital Learning at The Ohio State University. She is nearing completion of a PhD in Educational Studies with an emphasis in Learning Technologies. Her past research and journal publications have focused on teachers’ value for using technology in the classroom and technology’s impact on student learning. Her current research examines how students’ use of technology can improve the value they have for mathematics and their expectations that they can succeed.
References
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