The idea of math talks is simple. Listen to kids thinking about how they think about numbers, operations and other mathematical concepts. Math talks go by many names. Essentially, it is a math discussion between children, guided by an adult. The discussion holds many purposes. Math discussions provide students a chance to verbalize their internal thinking. This can be thought of as math metacognition and is one of the modes of representations necessary for mathematical proficiency. When done with a group of students, math discussions provide opportunities to consider other solution pathways. This is extremely important for children as they are trying to make connections in an among mathematical concepts. As student strategies shift from counting to composing and decomposing, listening in on other children talk about their methods can nudge others into higher level strategies.
Time and questions play a vital role in a good math discussion. In addition to providing a task that is challenging but attainable, providing ample wait time is of utmost important as students process information and attempt to construct a response. Guiding questions that help to clarify student thinking and probe understanding facilitate meaningful learning during math talks.
A third important component is representation. While children need to be able to verbalize their thinking, they need to see and create visual models of their thinking. Math talks are a time to model visual pictures of student thinking as they are describing their process and to ask them to create their own pictures of their thinking.
The last component I’ll discuss is the task. Tasks need to be challenging but attainable. If a task is too easy, there isn’t thinking involved. If the task is too challenging, students don’t have access to the task and will likely stall out. A task that requires thinking to occur is the kind of task you are looking for. When working with a group of students, it is important that the task be accessible to students with a wide variety of skills.
Stay tuned for Math Talks – a podcast and video series highlighting the ideas outlined here. Included will be analysis of student and teacher actions.