"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:

- Number sense (Atkins, 2011) ~ notice how different representations are used