I was a bio major (she said defensively) - something you reference with not a little cynicism, and frankly, you need to know it stood me well when I became a stage manager - it's really important to understand that experience in other fields actually is a good thing for us, esp from the sciences. Part of my bio training was looking at the same problem from many different angles, meaning I walked in the theater doors ready to try/suggest stuff outside the envelope. Protocol is teachable, while vision isn't always.
FYI, when I hand my assistant (or anyone) a script, it's just the script. Only once have I rec'd or handed in a binder, and that was a company that provided those items. If I don't know something, I would rather say "I don't know" or "maybe" than guess. Those are valid answers.
BUT - and this is more important - if she is your SM, you need to adapt to her. I agree w Missliz, if you have things to discuss ask her to step aside with you, but do it from the perspective of how to work well together, what you bring to the table that can support her, rather than what you can teach her. The attitude is "We learn from each other; We are a team; Here's what I can do to make your life easier, if that's ok with you." You have no idea what she's dealing with from producers/designers. Your complaint that she doesn't use GO for cues or take blocking notes or tape the floor are all things she can learn, but if you are her ASM it is NOT your place to be her teacher. And your sitting in judgment and complaining allows no room for change to happen. Go ahead and do what you know needs to be done, but do it with a gracious spirit and without expecting anything - incluiding being used - because it will help your own sanity. You never know where that can lead. A friend got her big break that way, because as ASM she did the paperwork for her own sanity and when things happened that needed a paper trail, she was able to produce it with no judgment or nose-thumbing - and got hired to replace the SM the next show.
Is this a college or high school situation? There may be a teacher who can help. If this is community theater, just make sure you are the consummate pro when you are there, whether you are SM or ASM, always smiling, always saying "yes" and helping solve problems. Folks will learn to trust you and how things are traditionally done will spread.
GOOD LUCK (break a pencil) -