Imagine mathematics classrooms where students are asking questions, sharing their work, and seeking connections across different pieces of their learning. They are not simply copying what the teacher has told them, but instead, they are actively creating mathematics in ways that make the most sense to them. At the same time, they are deepening and improving their mathematical skills by connecting new concepts to their prior knowledge. Facilitating meaningful mathematical discourse in the classroom is an art that bridges student thinking, teacher guidance, and rich mathematical content. One powerful framework for supporting discourse is outlined in The Five Practices for Orchestrating Productive Mathematics Discussions by Margaret S. Smith and Mary Kay Stein (2018) . These five practices (Anticipating, Monitoring. Selecting, Sequencing and Connecting) provide a structured yet flexible approach to turning student responses into opportunities for collective learning and deepened understan...
Mathematics is often perceived as a collection of abstract concepts, but at its core, it’s a rich network interconnected ideas and representations. The use and connection of various mathematical representations—contextual, physical, visual, verbal, and symbolic—are essential for deepening students' understanding of mathematical concepts and procedures. Why Use Multiple Representations? Utilizing multiple representations allows students to approach problems from different angles. Each representation offers unique insights that can make complex ideas more accessible. For instance, a geometric concept can be explored through physical models, visual diagrams, and symbolic equations, providing a more comprehensive understanding. When students see how these representations are interconnected, they can deepen their understanding and gain a greater appreciation for the the coherence and unity of mathematics as a discipline. Enhancing Understanding and Flexibility When students engage with...