I've been tutoring for a long time. While in college, I periodically tutored high school students in the sciences as well as other college students in my major (physics). After graduation I held weekly individual tutoring sessions with local high school students, teaching everything from English to college math. I went to Caltech, so math and science are my specialty, but I'm a decent writer as well, having just graduated from law school in 2012. High school subjects that I've personally taught include algebra 1, geometry, algebra 2, trigonometry, calculus, biology, chemistry, physics, grammar, and composition. I've also taught college subjects, including advanced calculus, differential equations, group theory, and several topics in physics (relativity, quantum mechanics, and classical mechanics).
Besides teaching high school subjects I have also tutored for the SAT and ACT. My standardized test experience includes high scores on the SAT, ACT and LSAT, as well as one of the highest scores on the bar exam's multi-state multiple choice section in July 2012.
As to methods, I like to teach by working through problems. It's worked for me, and I find it works for my students. When I teach math for example, I make up a series of problems on whatever subject I'm teaching, ranging from simple to complex. Some students learn just by working through those, but most of the time I have to guide them, at least in the beginning. By the end most aren't having trouble any more. The best way to give someone confidence on a test is to teach them a little more than they're expected to know, so my complex problems are usually harder than the ones in a textbook. It can be challenging, but in the end my students' grades always improve, and I like to think I have something to do with that.
Every student I've tutored has been more than satisfied with my work. When I tutored after college, my business slowly expanded based purely on referrals and word of mouth. I think a personal relationship between myself and my clients is very important for learning to take place. Many a student has gotten bad scores simply because their teachers failed to engage them in a subject. I try to show students the motivation behind topics, the magic in the math, besides helping them nail down the nitty gritty. A passion for learning is a hard thing to impart, but it's essential for success in college and beyond. I do everything I can to share that passion with my students.
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