Recent economics graduate living in China
It sounds like you would be interested in the work of Development Media International. Their work was well-evaluated, and they are a recommended charity by GiveWell and TheLifeYouCanSave.
Development Media International runs large-scale media campaigns in low-income countries via radio, television, and mobile video. They work with local broadcasters to create informative and engaging programming that focuses on maternal and child health, nutrition, hygiene and sanitation, sexual reproductive health, and early childhood development.
Also, you may want to consider the fact that some of the most cost-effective interventions on improving general education may seems to have little to do with education itself.
Take deworming program as an example, deworming was probably the most cost-effective method of improving school participation! At a cost of $3.50 US dollars per additional year of school, it's certainly far more effective than many conventional programs like teacher-training, or providing school uniforms etc. (For a better explanation, check out this TED talk).Relating to your interest in education for girls, another research found that women who received deworming treatment as girls are approximately one quarter more likely to have attended secondary school, halving the gender gap.
While it might be difficult to find charities working directily in education that are as effective as GiveWell's recommended charities, effective health interventions can improve education greatly. Although the eductaional effect of other health programs are not as well-studied as that of deworming, I think it would be reasonable to expect some most effective health programs to bring similar benefits.
If you would like to improve education of poor people, you should also consider donating to effective charites working on global health.