Abstract Math Needs Concrete Roots

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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 that 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 intuition, no 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.

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

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