I have been tutoring for as long as I have been in school (around the age of 5) - giving me about 15 years experience with everyone from young children to graduate students.
I have a B.S. in Mathematics, with a Physics minor, with an overall GPA of 3.1 and a GPA in mathematics of 3.5, and I am currently a graduate student in mathematics.
My approach is based on problem-solving, which allows students to turn formula sheets into a way of viewing the world around them. I would rather show where a concept comes from and demonstrate its connection to previous knowledge than load a backpack with formulas whose true meaning will never be known, but there is no formula that can't be shown to be useful and well-connected to other knowledge and I work with formulas if a student finds it more helpful.
I do not sugar-coat anything, especially when the time to assess a student's performance comes - often the best thing that can happen to a student is a rigorous, seemingly-impossible obstacle course, and I do my best to challenge everyone who thinks they know anything.
I believe that mathematics is necessary for anything involving critical thinking or problem solving, as well as being a beautiful study of symmetry and patterns that anyone can enjoy, and will do whatever it takes to help a student see that.