In 1850 what did most northern states done to improve education?

Not much. Educational reform really didn't take place until the 1900's. Teddy Roosevelt really got involved in educational reform. In a speech he talked about the "laggards" in the schools. Schools everywhere still were segregated and it won't be until the Brown Supreme Court decision that intergration will be enforced. The idea of vouchers came from the southern schools to stop the intergration in the schools. They would only issue vouchers to white students. It really wasn't until the 1984 book Schools Without Risk that the reform movement took a giant step forward. So, 1850 schools were pretty much the same as they had been in 1750. Many children didn't attend school and those who did left after only a few years. Teachers were untrained and not highly regarded and Horace Mann was working to establish "common schools " inspired by European models of public education. In the south schools barely existed and northern schools varied depending on the area. No organized system of public education existed in 1850.