Kathryn Lindholm-Leary is a professor emerita at San Jose State University, and has completed numerous studies on bilingualism and academic achievement in children from dual immersion (DI) programs.
The research of Lindholm-Leary is also frequently cited in support of DI programs (http://www.lindholm-leary.com/). Her work has included program evaluation for many DI programs in the United States. Here are just a few of her works that may be useful:
Lindholm-Leary, K. (2000). Biliteracy for a Global Society: An Idea Book on Dual Language Education.
Lindholm-Leary, K., & Adelson-Rodriguez, N. (2015). Research & Resources for English Learner Achievement. STARlight, 12. downloaded from http://www.elresearch.org/downloads/12/Starlight_NRodriguez_English_BW.pdf
Lindholm-Leary, K., & Hernández, A. (2011). Achievement and language proficiency of Latino students in dual language programmes: Native English speakers, fluent English/previous ELLs, and current ELLs. Journal of Multilingual and Multicultural Development, 32(6), 531-545.