I’m not sure if I should teach her using the syllabus ahead of her school topics or if I should go along with the school work and allow her to be more confident in topics she is already learning. The problem with teaching ahead is she will not be very interested and I feel like it may be too advanced for her.
Tutoring ahead helps a student’s confidence a great deal. Especially if you teach them something that is coming up in class really soon – when they get to it in the classroom it will serve as an inbuilt revision and builds the student’s ego since they know stuff that others in the class don’t. All of a sudden other students will notice that she knows the answers and may start asking her for advice; that would really boost her ego.
To prevent the possibility of her getting bored you must explain the benefits of going ahead. Being “smarter” than all her friends should definitely appeal to her, perhaps you are jumping the gun in your assumption she will be uninterested. You can always try this and gauge interest levels, gauge the difficulty level etc and refine your direction. If it’s not working well you can take a step back. Exploring ways to tailor tuition with each student will really help them while doing lots for your mentoring skills.
If you are to go ahead of the class then make sure the student is ready for it. You shouldn’t go ahead if the student is drastically struggling with current content and has countless gaps in knowledge. That would be overwhelming. At the same time, if you do go ahead, chose relevant content. Chose topics which are relevant to the current school topic, harder versions of the current school topic or general topics which a pillars in mathematics. For example, arithmetic and algebra. Don’t chose content which is irrelevant, won’t be relevant for a long time or is in your opinion WAY too hard.
Also consider that if you do not go ahead and chose to stay on par with the class the student may still get bored. If the student is on top of current school work and not feeling challenged by it then she will eventually get bored. The challenge of going ahead can also serve as a strong motivator for students, especially competitive ones.
If you are still unsure, you should discuss the option of going ahead with the student AND with the parents. Explain the advantages and disadvantages of taking that path.
Ideally each tutoring session should include covering gaps, current work, and future work.