I believe part of the problem with public schooling today is that we used to force all women into the teaching and nursing professions, which meant that very bright women, barred from professional careers, became teachers. I would not go back for the world. Another major problem is that 11% of students go to private schools and "[e]ighty percent of political contributions come from the wealthiest one-quarter of 1 percent of the population." If there is significant overlap, it means that most of the people who fund US politics have no direct concern with public education.
In order to teach better, I believe the school year should be shredded and reorganized. Another major benefit will accrue to students who can jump ahead or fall behind. I'm thinking classes should be three and four weeks long. When the Marine Corps had to teach its anti-academic "students" the particulars of their military jobs, they taught them in modules of 1 to 2 weeks, eight hours a day. I am thinking to make sure English, Math and Physical Education are taught for an hour each day, meaning it would be about a half day for the module class. Students would, just like now, get 5 minutes an hour, to stretch their legs. Now that time is used between classes, here it would not. When I was in first grade, a student was held back. He peed himself. If a student is held back from his "Vocabulary 1" class they will still advance with their peers in all other fields, and some way down the line will repeat Vocab1 when their peers go to Vocab2. Students who "skip" grades are usually better at math or english. Being able to skip ahead much less than a whole year, for example skipping Addition2, will make that transition smoother.
In order to increase parental involvement, each classroom will be video recorded and available online, live during the day, to parents. This is slightly fascistic, but legally they are just kids.
This argument is for all the libertarians and free-marketeers out there. If the average wage for teachers is lower than the average wage, won't we inevitably bring education levels down? The average teacher wage should be at least as high as the average wage. People don't often think of teachers as part of government, but a popular government(elections, juries) simply will not work if popular ignorance prevails.
The last suggestion is the most well known. Class sizes need to be much smaller.