This scene unfolds daily in my fifth- and sixth-grade classroom using Exemplars, a supplemental math curriculum that assesses students' problem-solving and mathematical-communication skills while supporting higher-level thinking. But the true magic I've witnessed happens not in the individual problem-solving but in the conversations that emerge when my students wrestle with these rich, standards-based tasks together.
The Hidden Magic of Mathematical Conversations
How Exemplars Transforms My Classroom into a Community of Discovery
Aliza Gordon, Fifth- and Sixth-Grade Teacher, ME
The room is abuzz with energy as my fifth grader Chloe leans forward, her eyes bright with discovery. "Wait, wait," she says, gesturing toward the data table she drew on the whiteboard in front of her. "I think there's a pattern here that changes everything about how we calculate the best deal." Around the whiteboard, her three teammates abandon their own calculations and crowd closer. What began as a complex task about comparing phone plans has evolved into something far more profound—a genuine mathematical conversation where ideas collide, merge, and transform.
"But the true magic I've witnessed happens not in the individual problem-solving but in the conversations that emerge when my students wrestle with these rich, standards-based tasks together."
The power of these mathematical dialogues reaches beyond the classroom. When students explain their thinking to peers, something remarkable occurs: they don't just share knowledge; they construct it together. The NCTM research-informed framework emphasizes that mathematical conversations help build a shared understanding of mathematical ideas. My students offer half-formed thoughts, challenge each other's assumptions, and build on incomplete ideas. When students verbalize their mathematical thinking, they're forced to clarify and organize their thoughts in ways that deepen their own understanding.
"I've discovered that collaborative discussions create a safe space for promoting equity in the classroom."
But perhaps equally important, I've discovered that collaborative discussions create a safe space for promoting equity in the classroom. When the focus shifts from finding the right answer quickly to explaining thinking and exploring multiple solution paths, students who typically freeze up begin to participate. Students feel more confident when approached with a question like, "How did you approach this problem?" rather than "What's the answer?" Everyone has some fear of being wrong, but in collaborative discussions around Exemplars problems, there's room for uncertainty, revision, and discovery.
"Students aren't just memorizing procedures; they're making sense of mathematical relationships and building conceptual bridges."
These mathematical conversations don't just make math more engaging—they make it more learnable. Students aren't just memorizing procedures; they're making sense of mathematical relationships and building conceptual bridges. When Chloe explains her pattern discovery, she's solidifying her own understanding while helping others see new possibilities.
"Rather than learning mathematics in isolation, my students become mathematical thinkers together—questioning assumptions, testing conjectures, and building understanding through discourse."
Rather than learning mathematics in isolation, my students become mathematical thinkers together—questioning assumptions, testing conjectures, and building understanding through discourse. These collaborative conversations create students who see mathematics not as a collection of rules to memorize, but as a sense-making activity where multiple approaches lead to insight. In my classroom, mathematics becomes what it truly is: a collaborative enterprise where the journey toward understanding matters as much as the destination. I couldn’t facilitate these types of discussions with rich, interesting tasks that grab the students’ attention and keep them engaged. Exemplars provides the problems I need to address the specific standards my students are working towards, with rich, interesting problems they can have great conversations around.