Learners learn to communicate mathematically through problem solving.
In a Grade 11 Pre-Calculus class, a teacher noticed that it was hard for learners to engage consistently. Learners would take down notes and try to apply strategies learned from examples given in class to their practice. It promoted a rigidity in math learning, leaning too heavily on algorithms instead of promoting mental resilience and problem solving.
One day, the teacher welcomed learners into class with playing cards that were used to sort the learners into randomized groups of three. Within these groups, learners assigned roles to themselves: the scribe, the communicator, and the inquirer. The scribe was the learner with the writing utensil and was the only one who was allowed to write. The communicator was the learner who would explain the solution at the end once they had solved it as a group. The inquirer was the learner who could ask the teacher questions. Each group was given a whiteboard.
All groups were given the same challenge question found in a University of Waterloo math contest. Bound by their roles, learners worked together within their groups of three to find a solution. After each group found a solution, the groups’ communicators took turns presenting their solutions to the entire class. At the end, the whole class needed to come to a consensus as to what the correct answer was, without the help of the teacher. When the class came to a consensus, having co-constructed their understanding of the mathematical concepts, the teacher either confirmed the solution as correct or encouraged more conversations if it was not correct. Learners sometimes needed to adjust their thinking to understand the context of the question.
Assigning roles was an important part of this process. Oftentimes, learners would express their emotions—specifically, insecurity—about being in charge of various aspects of the groups’ communications. As everyone had a specific role, each person was forced to express themselves, often revealing that each group member saw the problems in a way that was different from the others.
If the question was correct, then a new question was given and the learners would change roles within their group. The process would repeat to fit the span of the class.
Over time, learners had more confidence in communicating their ideas to their classmates. They were able to think on their feet in a problem-solving situation more comfortably and with more ease. They also began to value their own contributions and the contributions of others, which made room for natural mathematical conversations.
*These descriptors represent the dimensions of global competencies in mathematics.
