Abstract Math Needs Concrete Roots

(Note: This is an AI-assisted teaser for my prior manual writing. If you like it and want to read more details about this topic/perspective, then check out my 100% manually-written blog and books!)

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Abstract math is not the problem. Proofs are not the problem.

Those are not really the primary reason why math gets hard.

The biggest reason why math gets hard is:

Students are thrown into abstraction before they even understand anything concretely.

When that happens, the math just turns into symbol pushing.

Definitions, theorems, proofs, more theorems, more proofs.

But no concrete examples, no real grip on the objects.

There’s nothing to hold onto, nothing to grasp, and it’s backwards.

Build the concrete understanding first, make the calculations instinctive, and then the abstraction actually means something.

Here's the 100% manually-written long-form that this teaser is distilled from, if you want to dive deeper: The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction .

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