Chinese parents do organize and teach classes outside of the public schools, and where we live, the subjects have included Chinese language, art, contest math, English, and chess (the last two taught by outside instructors). The classes are held at a local elementary school and are open to everyone. Since many Chinese parents are mathematicians, scientists, and engineers, there are some highly qualified math teachers -- I have sit in on some math classes.
This is very much like it is in our area. One particular school district has a very organized Chinese group. They attend the same church but are spread over several different elementary and middle schools. They have a rented store front in a small strip type mall. They love to start the kids as young as you can they stress respect and hard work. You have to complete a series of math test to be considered. They have high numbers of kids who compete in the top at national competitions middle school and high school. Chemistry Olympiad, USAJMO, USAMO, Mandelbrot, ARML and others. My son has participated in summer and weekend classes mostly in competition math, science and chemistry bowl and olympiad type prep.
They are very inclusive with 25 or 30 showing up at each class 2 times a week. There are very few to just 1 or 2 non-Chinese people who a regularly participate. This is not at all uncommon in their culture.
