I’ve noticed a pattern in the way people learn to teach math.

At first, someone is thrilled just to know how to solve a particular kind of problem and show someone else how to do it. They can teach a student how to carry out a procedure that they have learned.

The next step in the development of the aspiring teacher or tutor is to lead a student toward an understanding of a concept strong enough that the procedure becomes self-evident.

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When educators and coaches talk about the benefits of failure, we’re not talking about creating a $200 million film that’s a flop at the box office, launching a startup that uses all your life savings and runs up $100K on your credit card, or running for president and losing.

I suppose those failures build character, but those kinds of “place all your eggs in one basket” failures distract from the everyday struggles that really make the difference in our success. These are the failures in which we’re risking our self-concept and ego, as opposed to money and prestige.

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A friend of mine told me about a conversation with a business coach she had been considering working with.

The coach said to her, “I can’t believe in you more than you believe in yourself.”

Which seemed reasonable, until my friend realized that that’s actually what was seeking to hire a coach to do.

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When I was running operations at my music school, I would often get a panicked calls from one of the many teachers.

“Did you change the key?” they would ask. “I can’t get my key to work. I’ve been trying for like ten minutes — I’ve tried every key I have.”

After I reassured them that I hadn’t changed the locks without telling them, they would usually make their key work within a minute. The seemingly impenetrable mechanism would now suddenly give way. The only thing that had changed was that now they knew that they had the right key. That gave them the fortitude necessary to succeed in unlocking the door.

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If you want to learn something — anything — the content is out there.

There are books, videos, and courses galore to show you how to do whatever it is you want to do, from flower arranging to sailing to investing. Whether in person or online, there is no shortage of information and eager teachers out there.

Despite this, we don’t reach our goals. We don’t all learn how to do the things we want to. Although online course completion rates are not the best measure of whether someone is learning, most sources suggest that they hover between 5 and 15 percent. Presumably, some of these people got as much as they wanted to from the course or learned what the wanted to learn elsewhere, but for many of them, life happened. They wanted to follow through, but they didn’t.

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