The 2018 VDOE Mathematics SOL Institutes highlighted the importance of strengthening the teaching and learning of mathematics through facilitating meaningful mathematical discourse.
Why Discourse?
Mathematical conversations and discourse among students, at all grade and ability levels, helps build a shared understanding of mathematical ideas (NCTM, 2014). Meaningful discourse supports metacognition and teaches students how to discuss, debate, and reevaluate mathematical situations in a respectful manner (Teaching Children Mathematics, 2018). When students have the opportunity to analyze and compare each other’s approaches, the “hierarchical status among students is diminished”, and a classroom community that values input from all students created (NCTM, 2018).
Five Practices to Orchestrate Productive Discourse
Taking Action (Huinker and Bill, 2017) outlines five practices that can help teachers orchestrate productive classroom discussions:
ANTICIPATE: Anticipate likely student approaches and solution paths, as well as questions to ask students.
MONITOR: Monitor and interact to assess and advance learning as students work through mathematical tasks.
SELECT: Select particular students or groups to present and explain their mathematical work during class discussions.
SEQUENCE: Sequence selected approaches and solutions to advance student learning of mathematics.
CONNECT: Connect and compare student approaches in ways that highlight and relate important mathematical ideas.
What Does Meaningful Discourse Look Like in the Classroom?
Walter (2018) offers a comparison of traditional dialogue vs. meaningful discourse:
| Traditional Dialogue | Meaningful Discourse |
| Low-level questions (What is? Where is? Which?) | High-level questions (How? Why?) |
| Yes/no response | Open-ended questions or statements (I know…) |
| Leading questions (Is the next step to…?) | Non-leading questions (How should we proceed?) |
| Focus on procedures, steps, solutions | Focus on thoughts, strategies, discussions |
| Focus on a right answer | Focus on possible solutions |
| Depth of Knowledge (DOK) 1 or 2 | Depth of Knowledge (DOK) 3 or 4 |
| Teacher-centered | Student-centered |
If discourse in the mathematics classroom affords some students’ voices to be consistently heard over others, with few students doing most of the talking, while other students are rarely or never heard, the goal of fostering equity has yet to be achieved (Huinker and Bill, 2017). But intentionally and systematically including more voices, and valuing the contributions of each student in classroom discourse can “challenge the space of marginality” (2017).
Resources for Promoting Mathematical Discourse
VDOE 2018 Mathematics Institute Facilitating Discourse Resources
NCTM Effective Mathematics Teaching Practices
Webb’s Depth of Knowledge (DOK) Levels
Math Think Time Graphic Organizer
References
Huinker, D. Bill, V. (2017). Taking action: Implementing effective mathematics teaching practices. National Council of Teachers of Mathematics. Reston, VA.
Walter, H. A. (2018). Beyond Turn and Talk: Creating Discourse. Teaching Children Mathematics, 25(3).
National Council of Teachers of Mathematics (2018) Catalyzing change in high school mathematics: Initiating critical conversations. Reston, VA.
National Council of Teachers of Mathematics. (2014). Principles to actions: Ensuring mathematical success for all. Reston, VA.
