Mental Tollbooths

(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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Imagine having to stop at a toll booth every few hundred feet.
You can still reach your destination, technically.
But every stop breaks your momentum, slows you down, and forces you to pay before you can keep moving.

That’s what algebra feels like when multiplication facts are not automatic.

The student’s supposed to be solving equations, transforming both sides, simplifying expressions.
Instead they get stuck on factoring.
What are all the factors of 48? Is it a perfect square?

The student isn’t just doing algebra.
They’re doing algebra while constantly stopping to multiply numbers.

Each stop takes another payment of the student’s limited attention.
It increases the chance they’ll make an arithmetic mistake.
And then they have to reorient themselves afterwards.
What was I even doing? Where am I?

That’s why multiplication facts need to be automatic.
That’s the only way the student is going to be able to focus their limited attention on the algebra ahead of them.

Here are the 100% manually-written long-forms that this teaser is distilled from, if you want to dive deeper:

• If You Want to Learn Algebra, You Need to Have Automaticity on Basic Arithmetic
• What Happens When Students Don’t Know Their Math Facts

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