Conversations about numbers
Conversations about numbers
For the last two years, students in the Primary School on East Campus have been participating in Number Talks. A Number Talk is a daily routine, usually taking 5–15 minutes, that helps students to develop fluency with number. Through Number Talks, students develop an understanding of number relationships and structures, allowing them to add, subtract, multiply and divide—in their heads. While developing number sense, students are also learning key strategies that support them in other areas of the mathematics curriculum, and beyond.
During a Number Talk, students have number conversations with a focus on three main components: accuracy, flexibility and efficiency. The teacher presents a few problems for students to choose from and solve mentally. As students grapple with the relationships between the numbers in the problem, the operation involved, and the connection to the Base 10 System, they attempt to solve the problem accurately. After this ‘think time’, students share their solutions. After all solutions have been listed, students justify their reasoning behind the solutions.
This student justification of reasoning is a powerful component of Number Talks. During justification, students use metacognition and communication to walk their peers through the specific strategy they chose to solve the problem. Students listen to their peers, and respond to the justification with comments to confirm, clarify or dispute the explanation. While students listen to and explore their peers’ strategies, they are demonstrating flexibility and making meaningful connections. At the same time, students pinpoint misconceptions in their own thinking, synthesise new information from others, and adjust their own thinking to improve learning.
Finally, towards the end of a Number Talks session, the teacher guides the strategy discussion towards efficiency. This allows students to consider which of the articulated strategies is the most efficient strategy for the specific problem. If students are going to consider different alternatives, they must go one step further to consider the best alternative. When flexibility is taught in conjunction with efficiency, student reasoning grows to improve critical thinking skills.
Number Talks encourage number sense, which includes the understanding of place value and the relationship between numbers and operations. This number sense improves proficiency in all areas of mathematics. We see value in students being more than accurate; we also want them to be flexible thinkers who can discern what is both a reasonable and an efficient method for solving a problem.
The process of participating in a Number Talks session also allows students to develop aspects of the UWCSEA profile, including critical thinking, communication, collaboration and self-manager. Our goal is that students will confidently apply their mathematical understandings and skills beyond the classroom. In the words of Jaki Graham, Grade 3 teacher, “The Number Talks sessions have impacted positively on our classroom in many ways. Students aren’t afraid to make mistakes and the respect they show for each other’s ideas carries over into other collaborations in the classroom.”
Conversations about numbers can lead to powerful learning for students.