Representing

Students represent mathematical ideas and relationships and model situations using tools, pictures, diagrams, graphs, tables, numbers, words, and symbols. Teachers recognize and value the varied representations students begin learning with, as each student may have different prior access to and experiences with mathematics. While encouraging student engagement and affirming the validity of their representations, teachers help students reflect on the appropriateness of their representations and refine them. Teachers support students as they make connections among various representations that are relevant to both the student and the audience they are communicating with, so that all students can develop a deeper understanding of mathematical concepts and relationships. All students are supported as they use the different representations appropriately and as needed to model situations, solve problems, and communicate their thinking.
(Ontario Elementary Math Curriculum, 2020)

Instructional Strategies

• Model various ways to demonstrate understanding.

• Introduce new concepts using concrete materials.

• Pose questions that require students to use different representations as they are working at each level of conceptual development – concrete --> visual --> symbolic – continually revisiting each stage to make connections.

• Allow individual students the time they need to solidify their understanding at each conceptual stage.

Prompting Questions

• Explain why you chose this representation.

• How could you represent this idea algebraically? graphically?

• In what other way(s) can you represent this problem?

• How you can represent this situation more efficiently?