what approaches does the author use to problem solve, to figure things out?

Paley first outlines the problem itself. She explains the phrase "you can't play", and then spells out the way in which the phrase creates social hierarchy. Afterward, she begins writing a story with her class, a story that highlights the pain of rejection the "phrase" causes..... a story that she adds to everyday. The title of the book is "You Can't Say You Can't Play".

Paley then involved the older grades, approaching them one grade at a time. The older students, who range from first to fifth grade, didn't immediately embrace the rule, and weren't in favor of having it applied to themselves. Over time, however, Paley found that the rule became self-enforcing..... that the students began monitor themselves, invent their own methods for applying the rule, and overcame challenges they faced along the way.

In the end, Paley notes that the rule brought improvements.