“Can you help me with this problem?” Adam asked. His math book was open in front of him.

I looked at the problem. I thought about the work that Adam has been doing over the past week. Really hard work from a challenging, well-written math textbook. Work that, at times, brought tears. He had already tackled two dozen problems like this one.

“I can help in a different way,” I said. “Do you think you can let go of the need to do every single problem in the book?”

I frequently draw on my experience as a music teacher to solve problems in other subjects.

In music, the effectiveness of various learning strategies and tactics can be quickly and easily heard. Therefore, as I experimented, it became obvious which ones to keep using.

One of the most straightforward of these was simple repetition. But the key, I discovered, was to repeat something until you saw results, compressing your effort into a short period of time.

It’s really hard to admit when things aren’t working. Often, we would rather have the illusion that we’re making progress than face the brutal truth that we’re spinning our wheels and getting nowhere. Change is hard, being wrong is hard, and acknowledging sunk costs is especially hard. But simply trying harder won’t fix it.

There are ways to reframe the circumstances so that backtracking or review is less painful. The reality is that there are plenty of times when it looks like we’re going backward, but we’re really advancing in our knowledge and ability.