Each Level of Math Is the Foundation for the Next Level of Abstraction

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Lots of students think math is confusing because it’s abstract.

Weird symbols, weird rules for pushing them around…

Can’t we just go back to 6 × 7?

But you have to remember:

Even 6 × 7 once felt the same way.

You started by counting objects: beads, blocks, marbles, etc.

At first, “6” meant six objects right in front of you.

After enough practice, it meant an abstract quantity.

Then you could work with numbers on paper.

You could calculate things like 6 × 7.

You didn’t need to count out 42 individual beads.

It’s the same with each successive level of math:

Arithmetic → Algebra → Calculus

Each one provides the foundation for the next level of abstraction.

But you have to get concrete reps.

Trying to learn calculus when you’re shaky on algebra…

Or trying to learn algebra when you’re shaky on arithmetic…

It’s like trying to learn 6 × 7 before you can even count 6 beads.

Further reading:

• The Necessity of Grinding Through Concrete Examples Before Jumping Up a Level of Abstraction
• If You Want to Learn Algebra, You Need to Have Automaticity on Basic Arithmetic

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