The Power of Imagination in Mathematics (Part 2)

My previous blog post dealt with how the power of imagination in object experiences helps children be able to form units to be counted. This time, we will take a look at how the power of imagination in counting helps children be able to form an abstract concept of number.

Constructing a Counting Sequence

Once children have become aware of permanent objects and have “pluralized” those objects, the child can begin to count. If children form the goal to count, they must have some access to the standard number word sequence (SNWS) to count correctly. Here are some examples of children who do not yet have a standard NWS:

With multiple experiences of counting different items in different contexts (objects, movements, sounds, patterns, etc.), and with the help of imagination, children will eventually be able to count imagined items. At first, they will need a recent experience with the items to be able to imagine them.

With time, repetition, and variety, children will begin imagining those previous experiences of counting items without needing to see them recently.

By using their imagination, they will be able to do the counting activity in thought by using substitutes for the imagined perceptual items. Substitutes may include imagined spatial patterns, finger counting, movement, tempo, or just number words. The child will make connections among the various representations. Their imagination is becoming the bridge between perceptual counting and the abstract understanding of number.

After many experiences, children can imagine the result of a counting activity and take the result as given without actually counting perceptually OR by counting through imagination. At this point, children will spontaneously do what we commonly know as count-on. Counting-on should not be taught as a procedure, but as a result of multiple and various experiences counting in the imagination. Counting-on might look like this:

There are many more video examples I could have shown you from our work, including many in classroom activity contexts. It is amazing to see these same mental constructions happen in play contexts, but for the purposes of this blog post, these video examples isolate most of the sound and the action.

With appropriate mathematical activities, the imagination of children helps them move from being counters that need perceptual items to being counters that can count in the imagination to then understanding the abstract concept of number.

At this point, children can truly count-on at a conceptual level. So, from birth to being able to understand the abstract concept, imagination plays a critical part in a child’s construction of number.

In what other ways might imagination benefit learning, either in mathematics or otherwise?