## Understanding Before Fluency

### A problem:

Despite a century of critiquing "mere memorizing", schools still routinely ask students to commit ideas to memory without understanding them.

It's not enough to remember — you have to understand.

But the inverse of that is true, too: it's not enough to understand — you have to remember.

Schools often have a hard time getting students to do both of those, and in the right order.

### Our basic plan:

When it comes to concepts that students have to struggle to understand (e.g. math formulas), imagine three stages: understanding, fluency, and automaticity.

First, help students aim for complete understanding. Help them ask a flurry of small questions about the concept, help them see different ways of representing it. Build ladders for them.

Only after students demonstrate complete understanding should they aim for fluency — the ability to explain the concept quickly.

And only after students can routinely reach fluency should they attempt automaticity — the ability to see the entire concept in their head at once.

### The goal:

Adults who understand things fully — and know when they don't.

Adults who understand the practice it takes to get concepts from understandable to useable — tools for solving larger problems.

### If you walk into a classroom, you might see:

If three kids are working on a math problem like — let's say 6 × 5 — one might be working on understanding, and drawing out five rows of six dots, then counting them: "1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15..."

Another might be working on fluency, and counting by sixes: "6, 12, 18, 24, 30."

Another might be working on automaticity, and holding all the above in her head when she reports: "6 times 5 is 30."

### specific questions:

Taking concepts in stages is crucial for math. Where else might it be helpful?

(This idea is currently in beta! If you've thoughts on how to make it better, *please *shoot an e-mail to Brandon at **schools***for***humans**@gmail.com.)

### Related elements:

Math Ladders

Deep Practice Book

### To Learn More:

Actually, I'm not sure — typically math educators advocate for a focus on memory or a focus on understanding. I'm certainly not the only person to say both is necessary, but I'm not sure who else talks about the need to systematically progress through stages.