# “Thinking Mathematically” Co-teaching Student Experience

Students in Heather Bourrie’s “Thinking Mathematically” course recently had an opportunity to participate in an experiential education activity to co-plan and teach a mathematics lesson for their peers. The exercise provided students with hands-on experience facilitating mathematical thinking and also helped them to use “student solutions” which involves being responsive to student thinking in the moment.

The goal of the lesson was to support the students in learning how to anticipate elementary students’ solution strategies within the framework of “5 Practices” when conducting a math lesson.

The “5 Practices” are a framework developed by Mary Kay Stein and Margaret Schwan Smith as a guideline of how teachers can orchestrate mathematical discussions through problem solving, including:

• Anticipating: For their planned mathematical problem, teachers anticipate possible student responses by using a variety of strategies. This allows the teacher to interpret a solution that was not anticipated.
• Monitoring: The teacher identifies student strategies by visiting groups and begins documenting student solutions. The teacher may prompt student thinking and encourage students to go deeper.
• Selecting: The teacher determines which solutions will be highlighted in the discussion. The selecting is driven by the goals and objectives of the lesson.
• Sequencing: The teacher determines a specific sequence of presentation that makes pedagogical sense and will highlight student solutions in the order chosen during this phase. The order sets up the solutions to be connected in various ways in the next stage.
• Connecting: The teacher makes connections in the approaches or solutions students have used through questioning. Often other students are asked to explain their understanding of another student’s work. The student work is used to meet the goal of the lesson. The role of the teacher in this phase is to help the students make mathematical connections.

This task not only offers teacher candidates the opportunity to practice their skills in guiding a ‘consolidation’ to a lesson by using student solutions as the basis of the instruction but also challenges the traditional ways of thinking about mathematics. The course encourages a shift from binary thinking which imposes math is either right or wrong, to the idea that mathematics is thinking.

“Whether a students’ solution is ‘right or wrong’ (in a traditional sense) still tell us ‘thinking’ is occurring. So, we need to focus on thinking and moving that thinking forward, rather than focusing on labelling math ‘right or wrong’ which in effect, shuts down thinking and learning” says the course director, Heather Bourrie. She highlights the importance of making mathematics accessible for every student and hopes that the teacher candidates can bring these experiences into their classroom and encourage their own students to think of mathematics in a different way.