Mathematical Representation and Thinking Engine | How Learners Work with Mathematics

Mathematics can be represented in words, diagrams, tables, graphs, physical models and symbols. A learner may understand an idea in one form and struggle when it appears in another.

Changing representation can reveal the Mathematics

• Use a diagram when symbols feel opaque.
• Use a table to expose a changing relationship.
• Use a graph to make behaviour visible.
• Return from a picture to symbols once the relationship is understood.
• Ask the learner to explain why two representations show the same idea.

Representation is not decoration. It is part of mathematical thinking. Good teaching helps students move between representations rather than becoming dependent on only one.

Detailed internal representation-selection and reasoning rules are kept private.