Math tutoring is focused on working problems, learning formulas, and preparing for tests. These are all important, but they are not enough.
Mentoring is about working with each individual in a way that works for that person; it's about relationships. Solving math problems is absolutely essential to doing well in math, but if a student is apathetic or fearful about math, he or she isn't going to be open to learning math. That's why mentoring is so important.
In my practice I work to help students turn around beliefs about math at the same time that we are working on problems. They think we're just doing homework, but over time they start to see that math isn't as boring or intimidating or difficult as they used to think.
One of the most important things I can do to help a student is to get to know him or her. I learn about their interests, what they're afraid of, what motivates them, what makes them smile. Every one of my students knows that I am genuinely interested in his or her well-being.
My approach is based on what I call The Three E's: Enthusiasm, Engagement, and Encouragement. They are the backdrop of every session. They make the difference between just doing math problems and making real progress toward better grades and greater confidence.
After several sessions with a 5th grader, my student's mom wrote me to say, "We have seen such a turnaround in her attitude and abilities that sometimes we have to "double-take" her to make sure it's really her!" That's what mentoring can do!