When I worked in a book manufacturing plant, a pre-press technician unintentionally left a small piece of tape on a sheet of film before a printing plate was exposed. 

I happened to overhear the resulting discussion between two managers. "You're going to fire him, right?" one said.

"No," the employee's manager said. "That would be a waste of the $100,000 lesson he just learned."

If asked, most people will likely say they learn more from their mistakes. And while the manager's response sounds like leadership-speak, science agrees. According to a 2016 study published in Annual Review of Psychology, the bigger the error we make -- and the more confident we were about being right -- the more likely we are to learn.

As the researchers write:

Interestingly, the beneficial effects are particularly salient when individuals strongly believe that their error is correct:

Errors committed with high confidence are corrected more readily than low-confidence errors.

That outcome is partly due to the fact that getting something wrong is, in itself, more memorable.

Which is why the best way to study isn't to reread; the best way to study is to quiz yourself. If you test yourself and answer incorrectly, not only are you more likely to remember the right answer after you look it up, you'll also remember that you didn't remember.

In short, remembering that you didn't remember helps reinforce the lesson.

So does thinking about thinking, a process psychologists call metacognition. Where mistakes are concerned, that means considering the actions that led to a mistake. Reviewing the thought process that led to an error. Reflecting on the reasoning that led you to feel so confident that you were right.

Thinking about the thought process that led to a mistake not only makes you less likely to commit that mistake again, it will also help you make better decisions in the future.

The pre-press tech was supposed to ensure no stray pieces of tape were on the film. He clearly didn't -- a clear, obvious error, one most managers would have handled in a way that boiled down to, "Don't let that happen again."

And that probably would have worked.

But that would have wasted an opportunity for deeper learning. By asking the employee why he thought it happened -- what his normal process was, what things could cause that process to be interrupted, what assumptions he made about how other employees did their jobs -- he uncovered a few broader issues that needed to be corrected. 

And turned what could have just been a mistake to avoid in the future into a developmental opportunity.

None of which means you should hope your employees make huge mistakes. But it does mean allowing room for trial and eventual error. As the researchers write:

If the goal is optimal performance in high-stakes situations, it may be worthwhile to allow and even encourage [people] to commit and correct errors while they are in low-stakes learning situations, rather than to assiduously avoid errors at all costs.

Because no employee knows everything you need them to know. (You and I don't know everything we need to know.)

Nor does every startup. As Elon Musk says, "The difference in a startup that is successful and one that is not is the successful one recognizes mistakes and fixes them very quickly, and the unsuccessful one tries to avoid mistakes."

Or as Bill Gates says, "Once you embrace unpleasant news not as negative but as evidence of a need for change, you aren't defeated by it. You're learning from it. It's all in how you approach failures."

That's why we're all more likely to learn when we're given the latitude to make occasional mistakes -- and then encouraged to think not just about avoiding that mistake in the future, but to consider what caused us to make it in the first place.

Because we're all going to make mistakes.

What matters is how we respond -- and whether we learn -- when we inevitably do mess up.