I agree with you on health care. Since my father is in the military I get government health care. In Virginia, it's great, but up here in New York it blows. So a lot of my beleifs are based on personal experience.
As for education I disagree. I beleive that the national government should take it away from the states. A reason why I beleive in small government is because I think that government hand-me outs hinder human potential. But education enhances that potential. Instead of hindering potential why not have the government take part in enhancing it.
The problem with our education system, and again this is from personal experience, is that the states are teaching different things. In one state you have schools teaching children Spanish or French in seventh grade, in another you have schools teaching no foreign language. In one state you have one grade teaching one class in one grade and in another, the same one in a different grade. We need to have all schools teach the same things at the same time periods. We need to get more rigorous in our educational system.
Another problem is that many students are simply not motivated. We need to get students motivated to work in school.
Also the final problem is that we rely on too much on test scores. We need to focus on the skills in science, math, history, etc. Not test scores.