Don't peek at the punchline
Enter at your own risk. (Image by Nino Carè)
I was working with an eighth-grader to solve a challenging math problem.
“I’ve read the solution, but I don’t understand the steps,” he said. “I don’t understand what they did.”
Solving a complex problem is like learning the rules of a complex board game: It’s much easier to understand by playing, not just reading. If you’re not engaging with the problem, the words don’t mean anything.
The answer doesn’t help you much either — the punchline of a joke means little without the setup, and reading the last page of a novel has no resonance if you didn’t spend the time investing in the story.
To get the most out of a challenging problem or an interesting question, do the work to fill in the gaps yourself before seeking the solution. This can mean covering up the next paragraph of your book with an index card, pausing the video, or taking a moment in conversation just to think. Get as far as you can on your own.
For a really juicy problem, this may take hours or days. For others, it may only take ten or fifteen seconds to make a fresh connection that helps you to understand. The important part is to take the time.
When you get stuck, you have a few choices. You can sleep on it, you can talk it out with someone else, or you can peek at the next step. Give yourself just enough to get moving again. The solution or explanation, even one sentence of it, will now be rich with useful information where it had previously appeared to be barren.
If this doesn’t happen for you, you may be trying to solve a problem that requires foundational knowledge you don’t have. Backtrack to pick up that knowledge (which may take anywhere from a few minutes to a few months) and try again.
Continue to follow this process of gradually revealing information until you have arrived at a solution that you fully understand. You’ll know that you’ve really got it when you feel the satisfaction of a key turning in a lock. If not, you may need to go back to step one (or do any necessary backtracking quests to make sure you have all the foundational skills and information needed).
Working this way is not easy or quick. Good. It is the mental equivalent of lifting a heavy weight. The intense effort and resulting discomfort makes you stronger in the long run.
Unfortunately, many of us have developed the notion that if we can’t solve a problem quickly, we are mentally deficient. We have to let go of this notion. It would be absurd to think that lifting a heavy barbell means we’re weak. Similarly, doing the intellectual heavy lifting doesn’t mean we’re unintelligent. Quite the opposite: As we do the work, we become stronger and better thinkers.
Sometimes, the urge to just “know the answer” can be nearly overpowering. But the tickle of finding out how it ends can’t compare to the thrill of getting there on your own. You can do it!