A study coming out of my alma mater, University of Illinois, concludes that public school students perform better in math on standardized tests than students from private schools. Check out a Science News article outlining the results.
This is a comprehensive study that used data from 270,000 4th and 8th grade students from 10,000 schools, so the results are significant with little in the way of statistical uncertainties. The researchers looked at five factors to see which correlated more positively to achievement. Those factors are parental involvement, school size, class size, teacher certification and instructional practices.
School size and parental involvement did not correlate significantly with achievement. However, small class sizes do correlate positively with achievement, and small class sizes are more prevalent in private schools. Certainly, the general public perception of private vs public schools is that everything private tends to be better, with the possible exceptions of the elite, wealthy public schools (such as a New Trier or Stevenson in the Chicago area) or magnet schools in urban areas, such as Walter Payton Prep in Chicago. But typically the strerotype is private is better in general.
So if small class size is more typical of private schools, how can public schools end up doing better than private in mathematics? It lies in the quality of the teachers and in the trend to adopt research-based, modern curriculum. Many private schools apparently still adopt traditional "back to basics" methods of learning mathematics, built around rote memorization and 'drill and kill' problems. Newer curricula are built around understanding concepts, problem solving and applications of math. Private schools also do not require or are mandated to have certified teachers, and tend to offer smaller salaries that are not competitive for top teachers. The research suggests these are the two driving forces that lead to better achievement, at least in mathematics.
Like anything else, though, there are outstanding private and public schools, and there are other schools that are in dire straits. This is an interesting study that not only concludes something that goes against common perceptions, but I think it more importantly gives insights into factors that make for better learning experiences for students. The evidence that curriculum and teacher certification and expertise are significant drivers for learning supports efforts among school districts for robust and focused staff development programs and collaborative efforts between universities and school systems for continual development and improvement of data-driven/research-based curricula. One other piece of this puzzle is, in my opinion, using cognitive science research in larger capacities with the development of curriculum as well as in-class practices, where we provide more ideal environments for students that are literally targeted at students' brains, and how our brains make the inner connections that lead to learning. This includes understanding differences between male and female brains and how they are 'wired,' where genders learn differently. There is still much to do, and hopefully both public (where 90% of our children go) and private schools use such research to better educate our children.