This is a very popular meme in tech circles, based mainly on John Ogbu's work, but if you actually look at the literature in the area, the results are all over the place. Roland Fryer at Harvard is a proponent of the "acting white" theory, but even he didn't agree with Ogbu and he had to "adjust" the definition of acting white to show a trend: http://www.economics.harvard.edu/faculty/fryer/files/Empiric...
Tyson et al found that reduced academic achievement was generally for a variety of reasons ("fear of not doing well academically" being the biggest) and not "acting white": http://www.tc.columbia.edu/students/see/events/Darity_et_al_...
Cook and Ludwig as well found that "acting white" was not much of a factor in academic perforamnce: http://onlinelibrary.wiley.com/doi/10.1002/%28SICI%291520-66...
Erika Fisher: "According to the students themselves, their lack of academic success is not seen by them as a way to be anti-White or proBlack by any means. .. When asked how they felt about the high-achieving students, underachievers claimed to respect their determination and commitment to academics. They cite individual personality differences rather than a racial or ethnic divide as the cause of the achievement disparity between the groups." http://findarticles.com/p/articles/mi_qa3626/is_200507/ai_n1...