What's that word?

I am filling out a job application and having some difficulty describing my job duties. I tutor a student weekly in Algebra 1. During our tutoring sessions, we go over material covered during class that she doesn’t understand. We also go further than the teacher did. I make sure that the student really understands the material - how everything connects together. How should I best word this?

For the material that she doesn’t understand, I have described that as remedial tutoring. What is(are) the word(s) to describe the more in-depth advanced learning that she does?

Perhaps you could say something like “remedial tutoring as well as consolidation of the fundamental algebraic principles”.

I love that, Cunctator. Thanks!

Sorry for the double post. I’ve decided to go with this:

Remedial tutoring of concepts covered during a ninth grade Algebra 1 class as well as in depth discussions of the material to provide the student with a more comprehensive level of understanding.

How about Analytic and Algebraic Topology of Locally Euclidean Metrisation of Infinitely Differentiable Riemannian Manifold?