How to fix the public school system: teach philosophy. Philosophy can be taught in a completely "secular" way according to even the strictest understanding of that term.
It would also greatly help our Catholic schools as well.
Start in about 4th or 5th grade. One class a year on the history of thought and thinking. Most kids sit around asking the serious questions of life around 3rd-4th-5th grade anyways, and most of them don't know that their questions are the same questions that many great thinkers have been writing about and working on (and even "asnwering") for millennia.
When I was in the seminary learning philosophy, I regularly thought:
1) This is AMAZING!
2) These were the same questions I was thinking through and wrestling with since 3rd grade.