metacognition

Our initial exposure to an idea shapes our intuition. And our intuition impacts how much we enjoy a subject

Don't learn by tracing: find (or invent!) those pencil structures. Seeing the pencil lines makes the idea become your own: you can modify it, combine it with others, or just appreciate it at a deeper level. And that's the joy of learning.

"The noblest pleasure is the joy of understanding." —Da Vinci

Our math vocabulary shapes what we're capable of thinking about. Multiplication and division, which eluded geniuses a few thousand years ago, are now homework for grade schoolers. All because we have better ways to think about numbers.

math is about ideas — formulas are just a way to express them. Once the central concept is clear, the equations snap into place. Here’s a strategy that has helped me:

• Step 1: Find the central theme of a math concept. This can be difficult, but try starting with its history. Where was the idea first used? What was the discoverer doing? This use may

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