You Have to Build the Concrete Understanding First

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Abstract math is not the problem.

Proofs are not the problem.

The problem is throwing students into abstraction before they understand anything concrete.

That’s how the math becomes meaningless symbol pushing.

Definitions.

Theorems.

Proofs.

More theorems.

More proofs…

But no intuition.

No examples.

No real grip on the objects.

That’s backwards.

You have to build the concrete understanding FIRST.

Solve lots of problems.

Work through different examples.

Make the calculations instinctive.

Then the abstraction actually means something to you.

A theorem can compress dozens of examples into one idea.

But if you haven’t worked through the examples…

Then you have no idea what it’s compressing.

That’s why you need the concrete foundation.

Further reading: The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction .

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