Recruit retired engineers as volunteers and part-time teachers. Many would find it more rewarding than their original careers. Of course, if a retired engineer replaces an unqualified teacher in the math or science classroom, the teacher's union won't be happy.
How come we can't even begin to agree on the basic facts? The hot "engineering" jobs are in developing software to lure eyeballs to websites based on novel services and premises on the front end, and to figure out ways to monetize on the back end, involving nontraditional technologies like big data analysis, and these are far from "traditional" engineering topics. The "classic" engineering jobs in the US are being taken over by Asian engineers brought over for such absurdly low wages that Asians are one of the fastest-growing poverty categories in the US. I communicate with a small group of avionics certification engineers across several countries and some of us haven't had regular work for many months. The reason we aren't recruiting new students for traditional STEM education is the jobs and wages are in the poorest condition I've seen in decades, but I suppose between the ever-lower-labor-cost industry forces and the well-heeled lobby of "educationists" (who make a nice living in the industry but can never be bothered to actually TEACH) it's always going to be necessary to "perpetuate the myth" of high-paying jobs going begging, and if we could only find someone smart enough to program that robotic entry in the high-school science fair...give me a break, folks, there's absolutely no reality in this picture!!!
Teaching math and science at the K-12 level may not need an engineer but it does need a teacher both motivated and interested in the STEM related courses. I had both great math/science teachers in school and some, well, not so great; the difference: their interest in the subject, not their pay nor their degree. All too often we are told: "We need to spend more on education" instead of "We need to engage both the students and the teachers". All too often we ignore the reality that not everyone wants to learn science/math, just like not everyone wants to learn history or geography. It takes a motivated student and an engaged teacher, not to mention parents being involved and interested. The hard facts are some students just don't want to work and some do. The reasons vary but the result is the same. Until the culture values STEM related endeavors rather than tossing a ball we will continue to have both the conversation and the battle to encourage students to pursue science/engineering degrees. One program that WORKS is FIRST (www.usfirst.org), I have had multiple kids and first hand experience coaching a team. We could use more FIRST teams in schools...
Sounds like a good plan. But how can we do that? The fact that teachers are not paid enough is an issue. Yet at the same time, there is no money to pay anyone anything more, certainly not in the public sector.
I think the biggest impediment to STEM is that we have Liberal Arts majors teaching math and science in all of our schools. Most teachers are just barely functional in these subjects. If we want better STEM interest, we need to facilitate the use of Scientists and Engineers in the education process.