steps to develop mathematical reasoning and computation using: 1) manipulatives to experience the reality of math, 2) imagery and language to concretize that reality in the sensory system, and 3) computation to apply math to problem solving. On Cloud Nine® manipulatives serve two purposes: 1) to concretize numbers and mathematical concepts, and 2) to serve as a base for establishing imagery.
When asked to add the numbers 3 + 2, children who are drawing on their vault of images may see 3 apples and 2 more oranges to show 5 pieces of fruit. Others may draw on an image of a number line and place their mental finger on the 3 as a starting point. The “+” tells them to move forward and the “2” indicates how many places. They know the answer because they can “see it” in their mind’s eye. These children may look up as they access their images