The Power of Imagination in Mathematics

I have been reading and thinking a lot about the power of imagination in learning — specifically, learning mathematics. In this and successive blog posts, I will discuss one role imagination plays in helping children form number sense.

Merriam-Webster’s definition for imagine: “to form a mental image of (something not present),” is what I mean when I use various forms of the word in this blog post. To clarify slightly, by not using the root word image in the definition, we look to the Cambridge Dictionary: “to form or have a mental picture or idea of something.”

Constructing a Unit to Count

Babies begin acting on things around them in a perceptual, sensorimotor world. They look at things, put them in their mouth, grasp them, et cetera. Everything is new, but not permanent. We might call this cognizing. When a thing is out of sight, there’s no indication that the child knows where it is. We can see examples of this in peek-a-boo.

Child @ 5 months

In the preceding video, the look on the child’s face indicates that she is familiar with the other person, but that she doesn’t know where the other person went when hidden. We might call this re-cognizing. Again, there’s no permanence in space or time. Later on, when a child begins to imagine things they have seen before (forming an object concept), the child will look for and anticipate the person that is hidden. We might call this imagining.

Even though this video may break your heart, we can see the child anticipating the return of her dad, looking toward where he is and reaching to pull away the cloth. It seems that the child is imagining her dad while he is hidden, because the beardless person that emerges from under the cloth is not who she anticipated.

Soon, children become experts at imagining where something went even when it is not in sight. They have formed a permanent object that they can imagine at any time without prompting, such as the brothers in the following video.

Children also begin using plural language, which may indicate that they recognize more than one object that they put into the same category. When the child sees the plurality of objects, the child may want to know how many there are and form the goal to count them. The child then has the potential to count each object because each object has now, to them, become a unit item that they can work with.

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

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