international experience needed to get into international ed program?

[blithe]

Hi everyone! I have been working in education for 5 years ranging from teaching to program development in urban education. I am interested in making the transition into international education due to some of my traveling experiences. Informal experiences have led me to become interested in international education, but I don't have any formal work experiences internationally. My question is how critical is it to have international experience if you apply to an international edu program (whether MA or PhD/EdD)? If it helps, I also speak three languages, wrote an honors thesis for my undergrad, and is Teach for America alum. I'm seriously considering Harvard and Stanford's program. If you know what they are looking for, your inputs are greatly appreciated! Thanks!