Previous research has shown that treating dependent effect sizes as independent inflates the variance of the mean effect size and introduces bias by giving studies with more effect sizes more weight in the meta-analysis. This article summarizes the different approaches to handling dependence that have been advocated by methodologists, some of which are more feasible to implement with education research studies than others.
Scammacca, N., Roberts, G., & Stuebing, K. (2013). Meta-analysis with complex research designs: Dealing with dependence from multiple measures and multiple group comparisons. Review of Educational Research, 20(10), 1–37. doi:10.3102/0034654313500826