How Concrete Math Becomes Abstract

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A kid first learns to count with physical objects like beads or marbles, blocks.

And after enough of these examples, of counting these concrete items, the number 7 stops meaning 7 specific beads right in front of them and it starts to mean an abstract quantity.

Carrying out this counting procedure has enabled them to climb up to this abstract concept.

And that matters when they get to arithmetic, right?

I mean, to do 340 times 7, you can’t count out 2,380 beads.

And you can’t try to visualize it like that every time.

You need to work with numbers as abstract symbols.

But before you make the jump up to algebra, that next level of abstraction, you gotta do plenty of concrete procedural arithmetic to lay this concrete foundation for the even more abstract idea of a variable, a placeholder in this arithmetic.

This teaser is distilled from the following post, if you want to dive deeper: Layering: Building Structural Integrity in Knowledge .

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