The sound of the room is filled with questions, explanations, and moments of discovery: “Wait, now I see why you started that way.” “Ours looks different. Why did you divide here?” Over time, I’ve learned that this kind of talk is not noise, it’s learning. We often begin with authentic problems connected to our units of inquiry, from calculating the amount of soil needed for our school garden (mass and weight conversions), through planning a space travel mission and making sure everyone has enough oxygen (multiplication and division), to distributing water after a natural disaster (fractions). These contexts invite students to consider early on, “Why is this maths worth learning?”
Learning Together: Exploring Strategies and Ideas
We start by breaking down the first problem together, gathering what we know, and exploring possible starting points. Then students work in pairs or small groups, sometimes mixed ability, sometimes differentiated, depending on where we are in the learning process. These conversations and attempts, whether successful or not, help us see what to try next.
Shifting the Focus: From Answers to Understanding
Over time, I’ve found that focusing less on arriving at the answer and more on how students approach, represent, and communicate their thinking gives a far clearer picture of their understanding. Our co-constructed criteria reflect that:
• Knowledge
• Strategy
• Application
• Communication
These four areas form the foundation of how we approach mathematics in our classroom and directly reflect the key competencies outlined in the SIS Maths Curriculum.
The Power of Maths Talk and Reflection
Influenced by the work of mathematics educator and researcher Cathy Marks Krpan, a former professor of mine, I’ve come to see maths talk, representation, and reflection as not just beneficial but essential for deep, lasting understanding. As she reminds us, students develop stronger mathematical reasoning when they’re given opportunities to talk about, represent, and reflect on their ideas in a supportive community.
Listening as Assessment
During work time, I move around the room listening and recording how students reason, respond, and revise. These moments have become some of the most valuable formative assessment I’ve experienced. Hearing students agree,disagree, or pivot their thinking gives me far more insight than any completed task. Maths Congress: Learning From One Another When we gather for Maths Congress, students share strategies, make connections, and ask questions of one another. Peers give written feedback using “two stars and a wish”, and I add my own observations. These sessions offer deep insight, especially before a written test, allowing me to identify misconceptions and organise breakout groups for extra support. Maths Congress is a space where ideas are explored rather than evaluated, where students learn that multiple approaches not only exist but are valuable. Dafni captured it simply: “I get to see what others are doing and learn ways to solve problems.”
A Shared Journey in Mathematics
This process has shown me that when students are invited to think aloud, reflect, and learn from one another, mathematics becomes a shared journey. It builds confidence, encourages flexible thinking, and offers meaningful evidence of learning, leading to deeper understanding and stronger outcomes.
Author: Emily Gray, Primary Teacher and Head of Kindergarten & Primary, SIS Rotkreuz-Zug