Traditionally, math class was a quiet place. Kids alone in rows busy calculating with limited back and forth. A competition to see who could find the correct answer the fastest. The idea that discussion was a necessary tool for deepening and consolidating understanding was a foreign concept, given that much of mathematics was conveyed as symbols and numbers. There was a right and a wrong answer – so what was there really to talk about? Yet the kind of communication we want students to engage in is so much more than simply answering questions or reciting procedures. Of course these are a part of any math class, but they shouldn’t comprise most instructional time, as they often do.
Talking about math is not something that comes naturally to kids.
There needs to be a shift from focussing on finding the answer to discussing the problem. When this happens there is a collective easing and the pressure is off of students who are reluctant to share their ideas for fear of getting it wrong. The potential embarrassment is not worth the risk. More than any other subject, math creates this anxiety among the less confident. As a result, executive functions such as working memory and regulating behaviour suffer and math proficiency is not fully developed (see research here). To alleviate this stress, teachers can redirect attention back to the problem. We’re in this together to find a solution.
With enough practice, these four simple questions will lead to profound math talk:
- How do you know?
- Can you prove that?
- Can someone else disprove what’s been said?
Effective approaches to encourage math talk are Gallery Walks, Math Congress and Bansho (see here). In order to make students more comfortable sharing their mathematical thinking, the following strategies and sentence starters are a great way to scaffold dialogues. It is in these moments that some of the best consolidation of learning happens. Sometimes we don’t know what we truly know until we give it a voice.
Characteristics of math communication to look for (see rubric here):
- precise – relevant choice of method that has accurate calculations
- clear – logical organization that is easy to follow and requires little inferencing
- cohesive – reasoned argument held together through explanations, diagrams etc.
- elaborate – justification of ideas and strategies with sufficient detail
- appropriate – proper use of mathematical terminology, symbolic notations etc.