First-class investigative reporting by Diane Ravitch revealed that when schools seem to have overcome poverty and have achieved "stunning results," it is usually "the result of statistical legerdemain," and that "the only miracle at these schools was a triumph of public relations." (Waiting for a School Miracle, http://www.nytimes.com/2011/06/01/opinion/01ravitch.html).
The media and politicians are slow learners (see eg Jonathan Alter's remarks on Ravitch's column. Alter focuses on two small details but ignores the other cases, past and present; http://www.bloomberg.com/news/2011-06-03/don-t-believe-critics-education-reform-works-jonathan-alter.html). Gerald Bracey regularly reported cases like this years ago, and I contributed an analysis as well. We both concluded that there were very very few cases in which schools in high-poverty areas achieved high scores on tests.
Individual cases of overcoming poverty are rare as well. When individuals do succeed despite poverty, they often give credit to the fact that they became voracious readers: Access to books is rare in high-poverty communities, but they found a way to get access to books, and gave reading the credit for their school success (I describe some cases, including Geoffrey Canada, in Krashen, 2011). Oddly, providing access to books through support for school libraries and librarians does not seem to be a feature of school "reform" these days.
Bracey, G. 2007. It's being done. Oh really? http://www.huffingtonpost.com/gerald-bracey/its-being-done-oh-really_b_63067.html
Krashen, S. 2002. Don’t trust Ed Trust. Substance 27 (6): 3. (http://sdkrashen.com/index.php?cat=7)
Krashen, S. 2011. Protecting students against the effects of poverty: Libraries (New England Reading Association Journal) http://sdkrashen.com/