There is no system that is better than the other, but some major differences I have noticed is that German schools emphasize discipline and rubric-based work more than American schools. Of course, I only have this experience, but from talking to my friends teaching at other schools in Germany, they feel the same way. Once I got used to this style of education, it made it easier to adjust.
As a teaching assistant, I help the English teachers with their classes and sometimes teach my own lessons. So far, I've taught lessons on Columbus Day, voter suppression and Halloween (really a wide range of topics!). I am so grateful that my school gives me lots of freedom to decide what I want to do my lessons on.
Outside of school, I have tried to integrate into the community as much as I can. Again, this also turned out to be extremely difficult, especially since Chemnitz is a small city and I feel more comfortable in large capital cities. I am lucky to have four wonderful German roommates, which have definitely helped my German. In the two months I've been here, I've noticed my German improve greatly. Sometimes I get tripped up when speaking English to my American friends because my brain operates all day in German!
One goal I'd like to set for myself is to stay in Chemnitz more on the weekends. It's very tempting to leave because I don't work Fridays and I know many people living in other cities in Germany. I know, however, in order to truly integrate into the city, you have to spend most of your time there! I've challenged myself to stay in Chemnitz at least three of the four weekends in November.
In the next weeks, I hope to sign up for volunteering.