My background: I have a PhD in physics from NCSU and am working on some product development and theoretical hydrodynamics projects.
Over the years, I have tutored students from middle school through college in physics and mathematics. In addition, I have tutored lower-level chemistry and statistics. This last year about half of my clients were doing AP-Calc or physics and much of my daytime work was with students from UNC in undergrad classes in physics ranging from quantum to analytical mechanics and math up to differential equations and real analysis. I am lucky to actually have my own tutor now in to form or a retired math professor from UNC (Dr. Mike Schlessinger) who is mentoring me in algebraic geometry (always my weakest subject). Learning should be a lifelong passion and those of us who teach had better keep doing it.
I have gradually become the local go-to guy for help with AoPS and math olympiad curriculum and (my favorite) young gifted/driven/inspired (whatever word suits you) students who are searching for their own path in mathematics and are far ahead of or off the course curricula of the local schools.
My counselling background has helped me develop my style for working with gifted students who are not challenged by the material and with capable students who have fallen behind. I focus on watching and listening to their work and interests and tailoring problems that focus on their (usually surprisingly few) fundamental weaknesses and misunderstandings. This approach, combined with giving them confidence and comfort in what they do know usually does the trick. I will not keep a student if I am not helping them improve. I understand that trying to coach your child in addition to all the other parental roles can get to be too much. Let me help make algebra or calculus be one less thing they are annoyed at with you.
I am currently hearing a lot about the COMMON CORE curriculum. Many students and parents are out-of-their minds frustrated with it. I think the details of the implementation of this is part of the problem. While we don’t control this we can seek the kind of connections with a child’s interests to make the acquisition of these skills more natural and ward off cynicism. This is the biggest danger for many children; a feeling that what they are doing has no value or meaning.
I have worked for a GRE/SAT testing service and one of my current students is seeing me for SAT prep. The GRE has significantly evolved and I have a lot of problem solving speed up tricks that work for all multiple choice tests. There really is no substitute for good problem solving skills and familiarity with the material. I remember when I first took calculus I thought I had learned so much. Eventually I realized I only learned about 5 things in the first semester. The rest was applications and special cases. Most things seem like that. Standardized testing has promoted teaching of “tricks” to get answers instead of a basic understanding of math. You will forget the tricks. You won’t forget the look of the whole forest once you really see it.
Note: for some interesting thoughts and history on common core see this article: http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html