Most young children first learn about math by being taught how to count to ten. “Trained” I should say. Because that’s what it is. “Teaching” a three year old to count to ten has more in common with training a chimp than it does with developing human potential.
What do you have when you can count to ten at age three (or four, or whatever)? An Italian aria. Well, for all intents and purposes. you do. Huh? The young counter is merely reciting a memorized series of sounds, no more meaningful than the non-Italian speaking opera star singing a melodic Pucini song. “Show aunt Joan how you can count to ten dear…” as if “dear” has any clue what she’s saying. As if she’s a budding mathematician. Oh, maybe “dear” can go one better – she can point to the symbols to show that she really understands what she’s saying: she knows her numbers.
No she doesn’t. The aforementioned chimp can pull this off. This is because there are no “fours” (4’s) in the world. You can’t point to a “four” and say “that is a 4” because you can’t see “four” as a unit. “Four” is a brilliant abstraction, a conceptual invention. Powerful and wonderful, yes. This is why the young child has no clue what the numbers to ten mean – they are abstractions that require a process to be formed.
Better to begin with quantity: a bunch of ones, units. That’s what you can point to. A one, a one, a one, a one…. yes, long ago a brilliant person devised the system that we use so effortlessly and created a means to hold all those ones together as an individual unit: behold the “4” in all it’s glory, and all the rest too, of course. Sorry, 4, you’re not any more special.
You’ve got to get to what’s real: build meaning. Meaning-making is what learning is supposed to be, not remembering. Remembering leads to forgetting, remember? Meaning-making leads to embedding. This is learning. This is knowledge. And so when you sing “they can’ t take that away from me”, it could be your knowledge you’re talking about, because knowledge is like that.