Concrete Skills Build Abstract Understanding

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People often say that kids should learn the concept before they do the procedure, and sometimes that’s true, but other times it’s concrete procedural practice that actually builds the abstract understanding.

It goes both ways.

The concepts and the procedures, they’re mutually reinforcing.

Alternating rungs up this ladder.

For instance, 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 seven stops meaning seven specific beads right in front of em 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 seven, you can’t count out 2,380 beads.

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.

And this pattern keeps on going throughout math.

Every layer of concrete skills gives your brain something to build the next level of abstraction on.

This teaser is distilled from the following posts, if you want to dive deeper:

• Layering: Building Structural Integrity in Knowledge
• The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction

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