Carl Sagan spoke fluently between biology and geology and astrophysics and physics. If you move fluently across those boundaries, you realize that science is everywhere; science is not something you can step around or sweep under the rug.
It may be that our cosmic curiosity... is a genetically-encoded force that we illuminate when we look up and wonder.
I would teach how science works as much as I would teach what science knows. I would assert (given that essentially, everyone will learn to read) that science literacy is the most important kind of literacy they can take into the 21st century. I would undervalue grades based on knowing things and find ways to reward curiosity. In the end, it's the people who are curious who change the world.
... there is no shame in not knowing. The problem arises when irrational thought and attendant behavior fill the vacuum left by ignorance.
My view is that if your philosophy is not unsettled daily then you are blind to all the universe has to offer.
As the area of our knowledge grows, so too does the perimeter of our ignorance.