big, From my experience working in inner city schools, ( Brownsville, Brooklyn NY,) teachers need to be trained more in behavior management. One of the problems used to be that new teachers pretty much had to teach in the worst schools, since the more experienced teachers could bump them from their positions in the better neighborhoods. I don't know if that is still true.
By far the most difficult challenge was to get parents involved in their child's education. Most of the parents of my students had bad experiences in the school system, and had little interest in their child's education. Homework was rarely if ever done. Gangs and violence in the schools was another big problem. Drugs were an ever present, and if a kid is high, he or she isn't going to learn well. " Close the gap was the war cry ", but no real solution was found as far as I could see. Perhaps teaching trades and occupations could help keep kids in school.

buffalo, The Supreme Court correctly ruled that school prayer was unconstitutional. This is not anti-Christian, it is pro freedom of religion. As far as corporal punishment is concerned, study after study has shown that it is extremely harmful to the psychological growth of children. It is true for all mammals including kids.
As far as " marxist " teachers unions are concerned, I was a representative to my local chapter of the NEA for about ten years. I can't speak for the other large teacher's union, but we spent the large majority of our representative assembly discussing how we could help kids learn. Only secondarily did we talk about how we could improve our salary, and/or benefits. Twenty percent of new teachers quit within the first five years because the compensation was way to small to earn a descent living, and pay back school loans. When I retired, I had a doctorate in special education, and thirty three years of successful teaching experience. I wanted to substitute teach for a few years, but the pay the county offered made it not worth my while. Can you imagine the pay if I wanted to continue working in an area like finance with those credentials? If people want better teachers, they will have to attract better college graduates. That means higher pay and better benefits!
The voucher system would only take needed funds from public schools. If you want to send your child to a religious school, good for you, but you need to pay for it, and not ask other tax payers to help you out.