WEBVTT

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Hi, I remember teaching interest theory during

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my first year at Drake University. And while

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I was explaining the force of interest, my mind

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suddenly went blank. Fortunately, one of my students,

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Terrence, understood exactly where I was headed

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and he did help me out. It was a little bit humbling

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to ask. Now, one of the most difficult sentences

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to say in mathematics is also one of the most

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important. I do not understand. It is easy to

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treat those words like an admission of failure,

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because it is easy to worry that they will make

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us look unprepared or maybe incapable. But in

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my experience, the opposite is true. The people

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who learn the most are often the ones who are

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willing to admit when they're confused. Actually,

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if you think you already understand something,

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you may stop asking questions. But the moment

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you say, I do not understand this yet, you've

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identified exactly where learning can begin.

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Mathematics has a way of exposing false confidence.

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You can read a proof and think it makes perfect

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sense. And then you can try to reproduce it on

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your own and realize you only recognize the explanation.

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You did not truly understand it. I find that

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I truly understand an idea when I can apply it

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to a new setting or maybe build it from first

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principles. So here are some standard questions

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that I ask. Why is this assumption necessary?

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Where did this equation come from? Or my favorite,

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can I program this idea or build a spreadsheet

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that models the concept? Questions like these

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lead to a much deeper understanding than simply

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asking what is the next step. I've also discovered

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that one of the best ways to test my own understanding

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is to teach the idea to someone else. The moment

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I struggle to explain it clearly, I know I've

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found a gap in my own thinking. And there's another

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benefit to admitting that you do not understand.

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you give someone else permission to do the same.

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Often you are not the only person who is confused.

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You are simply the first person with the humility

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to say it. So do not measure your progress by

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how rarely you are confused. Measure it by what

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you do when you are confused. Do you pretend

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to understand or do you become curious? In the

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end, humility chooses curiosity.