One thing I've found to work teaching 9th grade is believing in them. The other answer by ConfusedANDHungry01 is really good and touches on this but I want to say it explicitly.
I've found kids to have an understanding of what teachers are on their side and want them to succeed and what teachers care about them.
So first of all congratulations. You care - that puts you above most teachers I've run into when teaching 9th grade. Let's see what skills you can apply:
Build self efficacy.
You want to build her ability to believe she can accomplish her goals. This starts by literally saying things like:
I believe in you and your ability to do great on this topic.
And then gradually building small successes with her. Give increasingly harder assignments that are not out of reach for her and you believe she can succeed (even if initially the assignments seem small) and gradually build up her feeling of self efficacy.
Self efficacy has been (for my 9th graders) the biggest determining factor in who succeeds and who doesn't at the end of the year.
Focus on her commitment to succeed
If for example she did not do all the homework but did half of it instead of talking down to her you can say something like:
I see you've done half the homework. Thank you for dedicating time to work on the topic and doing substantial work on the questions I gave you. Can we go over the parts you didn't do and understand together what was harder about them?
Explain to her that you're on her side, ask her what she wants and why and then sit down and figure out together how to get there and plan.
Make her an active participant of the plan and have her commit to the different parts. Make sure she does not over commit (see the part about self efficacy above). Commitment and small successes create a sense of accountability.
Find interesting ways to approach the topics and use them. For example I've found project based learning on subjects that interest the students to be a great motivator and a way to cultivate curiously which people naturally have.
Remember that you have a shared goal (her success). Criticism is fine but only within that specific context. Criticism needs to be:
- Direct to the student.
- About an action and not about her. It is very important to understand that it is not your place to judge her as a person as her teacher.
- Within a context of caring about her.