The title "teaching science" has a double meaning. Science needs to be taught more, and earlier, to American children in particular, and we also need to use science to improve teaching.
Far too often, a teacher enters into a school with a few methods that have been passed down without scientific analysis. They then settle into a rut that does not change, regardless of effect. We need to bring Scientific Management to teaching. Teaching can be optimized just like any other process. This is not to say that individual teachers should be robots, but they should be compelled to use methods that work better. This requires a lot of leeway for teachers and administrators to see if a particular teaching method is more effectual for a given educator, but that's what all Scientific Management features, in an ideal world.
People seem to think that Science and its cousin Math are advanced topics that are only fit for a small segment of students, and they only should be introduced at a relatively advanced level of schooling. Both of those principles are disastrously wrong. Everyone should have a basic knowledge of how science works, and anyone can learn it.
If science were better known, we wouldn't have nearly as many parasites on gullibility, our psychics, homeopaths, astrologers, mediums (media?), ghost hunters, and so on would have to move into industries that actually create value.
There's no reason younger children can't learn the basics of Math and Science. If a kindergartner can learn that "The cow goes 'Moo'", then there's no reason that they can't learn that the red line (below) is the radius of a circle.