"A significant indicator of conceptual understanding is being able to represent mathematical situations in different ways and knowing how different representations can be useful for different purposes" (Adding It Up, 2001).
As teachers of mathematics, it will be important to create appropriate problems and be able to fluidly move between representations and evaluate their effectiveness.
| → | → | → | |||
|---|---|---|---|---|---|
| Students: | Begin with problem | Concrete* solutions | Visual solutions | Abstract solutions | Explain why |
| Teachers: | Create story problems | Model and evaluate solutions | Explain why | ||
| → | → | → | → | → | |
* We typically use visual representations to stand for concrete manipulatives.
Examples: