How can learners move from concrete models to mathematical symbols?
A mathematical representation shows a quantity or relationship through objects, drawings, tables, number lines or symbols. Materials do not create meaning by themselves: learners must connect actions with mathematical expressions. The aim is to explain connections among suitable representations, not merely increase their number.
Making connections explicit
When regrouping with base-ten blocks, explain the place value represented by each piece. Connect the same situation to a drawing and then a numerical operation. Ask which part of the model corresponds to a symbol. A representation useful for one concept may mislead for another. Fraction comparisons need a consistent whole; number lines require equal spacing. Teachers can explain what an inaccurate drawing distorts. Justification questions prevent models from becoming decoration or memorised shapes.
Reducing support flexibly
Learners comfortable with symbols may not need objects for every question, but returning to models for a new concept is not regression. Everyone need not stop using materials at the same time. Assess movement between representations and explanations of preserved relationships. Too many complex visuals at once can distract, so select simple examples. Accessibility and familiarity with materials also matter. Obtaining a correct answer with a model does not alone establish independent understanding of its symbolic expression; check that connection separately.