What are some things that the 5th graders learned during their No Talking experience?

One lesson that the children learn in their "No Talking" experience is the power of solidarity.
The fifth graders begin to understand the power they possess when they stick together.  After Dave and Lynsey initially issue their challenge, the kids take sides.  While there are challenges, they begin to understand the need to act in the name of their side.  They also begin to realize the power they wield because they stand with one another in their vow of silence. They understand how much power they wield over the adults in the school.  For example, in their solidarity to remain silent, they transform the lunchroom and the playground during recess.  Part of why Mrs. Hiatt reacts the way she does is because she is unable to formulate an effective response to the strong display of unity that the children demonstrate.  This is shown when Dave recognizes that he could not remember the last time "an adult apologized to him."  In their pledge to stand with one another, the children have learned the importance of collective identity.  The fact that there is no winner at the end of the contest underscores that the students have learned the power of solidarity as a result of their experience.