Encoding Affordances with Correspondences
I was recently intrigued with my daughter’s stacking toy. The objective is to build the tallest tower using all of the boxes. The sizes of the boxes increase along with their corresponding labeled number, starting with one and stopping at ten. It’s intended to teach concepts like numbers and ordering amongst others. The natural correspondence between numbers/physical size and the stackable boxes created an affordance for learning.
Numbers require one level of abstraction from the world. We all in time become quite familiar with numeric operators like addition or multiplication but to a toddler, numbers don’t represent much more than perhaps labels. But something interesting happens when we “program” or encode size into each box that corresponds with a strictly increasing number. Whatever the child learns by playing with the boxes becomes transferrable to their understanding about numbers. What’s more fascinating is the learning process is encoded in such a way as to be visually self-correcting.
My daughter’s first attempt at stacking the boxes meant randomly picking up a box and placing it on top of another. She would soon discover that if she hadn’t stacked them in strictly decreasing order, she had left over boxes. She would then scan the tower and find where the missing box should be placed relative to the largest box from the base and repeat this process until none were left. Of course the fun part was pushing the tower over, but it was teaching her something about numbers, ordering, and dependencies. There was a fittingness between attempting to stack the boxes and learning about numeric ordering that was embedded in the objects and objective.
For those interested in the mathematics, see: https://en.wikipedia.org/wiki/Measure_(mathematics)
If your curious to see where this kind of thinking can take you, see: https://graphicallinearalgebra.net/2017/04/24/why-string-diagrams/
https://www.math3ma.com/blog/matrices-as-tensor-network-diagrams
