Standing by.

Does she have a boss? Our boss is supposed to observe her this week.

Can you as the senior team member speak to someone "of au-tho-rah-tay" whose and tell them these mistakes she's making? Sure, I can pass it up the ladder. Let her "argue" with someone else? Not really, she is arguing the day to day classroom decisions that we make at our team meetings. It sounds like she's causing trouble, making more work for herself, for you, detracting from the environment for the kids. Correct imho. Avoiding conflict isn't a bad thing. Unless it's your responsibility to train her, tell the people whose job it is to make sure she's doing the right things and let them deal with the conflict. It isn't explicitly my responsibility. She arrived with skills and training, unfortunately her attitudes are in conflict with my personal vision of what is appropriate. My previous administrator would have been behind me 100%, it is time to find out what our brand new administrator thinks.

Why would she listen to you anyhow? It has always been my practice when entering a new organization to adopt the culture of the place unless it somehow ineffective. Just for sparring practice? Apparently. Or to learn from you? Hopefully. If her "affect" is having a negative impact in the classroom, who should compel her to change it? People can only change themselves. I cannot change her.

It has been my unfortunate experience that teachers who place great stakes on the compliant behaviour of the children in their class are compensating for their underperformance in other areas. "Look how well i have taught the kids to follow my direction. Therefore it cannot possibly be my fault that their math skills are below average as I am clearly capable of instructing them"

Of course this snippet is of no help to you whatsoever, sorry.

Do you think she's compensating in this way? Could that and the argumentative thing both be covers for her fears that she is inadequate? And if so, do you think maybe finding and praising areas that she is good at/has a better approach to might redirect her? Just like you would do with the kids......