When I first meet with my assistants, whether we've worked together or not, I express to them that we are a team and I appreciate new ideas, trains of thought, paperwork, etc. If my assistant has an idea that will help me or help the team as a whole, I embrace it. Granted, your SM may or may not have said this during your prep time, or at your first rehearsal, but perhaps you can broach the subject with her in a gentle manner. Personally, I love learning new things from my assistants, whether they are seasoned veterans or they are fresh out of school. Everyone's ideas should always be considered - and who knows, it may be something I'd tried before but just couldn't get right on paper, but the assistant knows just how to do it. Or they've got an idea for a task and it's something I've done before, and together we find the perfect way to make that task the exact fit for our show.
If you guys have time before a rehearsal, maybe suggest getting together, before you do your preset, and ask how she feels about sharing ideas on different aspects of Stage Management. Tell her that you learned a few things from your assistant on a previous show you SM'd and you think the idea may be helpful for her. I wouldn't bring up the number of shows or whether they were professional or not, or the fact that you feel she is undereducated on the subject. Ask if there are things you and the other ASMs can do to help her out, or mention that you feel you are bearing a lot of the ASM responsibility and were wondering if you could try a particular task in a new way, that will allow the other ASMs to help you and share the work evenly.
At the end of my regular seasons, I have my ASM work as the SM for our ballet school's show. The shows she called were ones I'd done before, and I offered her my cue sheets and experiences, but I told her she should change it all to meet her needs. I was there to field her questions and help her along, but ultimately, it was her show and she was in charge. Granted, you don't have this relationship with your SM, but it can't hurt to ask if you can help. Obviously someone on your school's staff felt she could do the task, and perhaps her method is very different from yours and how you've been trained. I always feel that Stage Management Teams are just that - teams, and team members help each other out to achieve the goal we all have: a good show.
Final point: she can learn from you, and you are going to learn from her. Be a team and help each other.