I remember Sputnik. This is one kind of problem that can be solved by throwing money at it.
The reason is that most scientists can think of nothing they'd like more than doing more of what they are already doing: research.
Fund grad school science education with more scholarships and we'll get more students.
The only additional feature needed is pressure to get scientists, real ones, into the elementary through high school classrooms.
I'm not sure about that. In my department we've had full-ride fellowships go unfilled for lack of qualified U.S. students to fill them. They shy away from this particular field of engineering because they don't see a future in pursuing it.
So funding is one aspect of a multi-sided coin. Having qualified students who are interested in the discipline.