I'm team teaching ESL to some students. The woman I'm working with is a wants to teach the students in a way that she's used to teaching. I'm convinced that a strategy I recently learned about would be the ideal method to teach these students with. I even have a plan laid out on how to incorporate this method in the lessons. Last week I mentioned storying to my co-teacher, but she is not familiar with the method I mentioned. On top of that, she's older than me. Here in South Korea, suggesting something to someone older than you is especially frowned upon. What would you suggest I do?

That's a tough one....you might want to get her to sit down and talk with you....explain that you would like to try your new ideas....if it doesn't work, you could go back to her old method. Speak to her respectfully, and let her know that you value your experience.
I've been teaching a long time, and sometimes when a newbie suggests an idea...my first reaction is to reject it....but I have learned some fresh new ideas from people who just came into teaching....we 'old' ones just need a little push to convince us to try it.