I have over 30 years of experience as a tutor and lecturer in mathematics and physics, both before and after I completed my physics & biology BA at UC Berkeley and my physics PhD at the University of Illinois. I am available for tutoring at middle school, high school, and college levels. My students feel comfortable telling me what they didn't get in class or from their textbook, and so we are able to address those issues right away. I like to first establish the knowledge base of my stud... [more]
Before we jump into Algebra, I make sure that my client has mastered pre-algebra subjects. Many students entering algebra need work on arithmetic with fractions, how to calculate least common denominators, etc. I very often start by showing my student how to write out the prime factorization of the integers from 1 to 50, and then having the student continue, as a homework exercise, from 51 to 100.
I have found it to be critical to be sure that the student has mastered skills from Algebra 1 before going forward. My first session thus usually involves some diagnosis of which skills the student needs help with before going on to Algebra 2. A firm base on which to build is required.
I have been teaching and tutoring math for years, and the student feedbacks on my Wyzant profile indicate that my methods are very effective. I invite you to read those student feedbacks. I use active learning techniques so that my students learn by doing, not only by listening to me or watching me solve problems. As can be seen from the feedbacks, these techniques often result in markedly improved performance and confidence for my students. I sometimes share my decades of experiences in physics research and biomedical instrumentation engineering in order to tell my students some of the direct applications of the math and physics that I teach them.
It is often necessary to brush up on arithmetic and algebra while concurrently working on geometry. I do such review on an as-needed basis. An essential part of that review is supervised practice of techniques.
I have loved physics, and the teaching of physics, since attending Lowell High School in San Francisco. My undergraduate major at University of California at Berkeley was Physics & Biology. In addition to my experience teaching physics as a grad student at SF State and the University of Illinois, I've taught physics courses at University of San Francisco and College of San Mateo.
It is critical, before going into pre-algebra, that students have a firm command of arithmetic. My experience is that many such students have troubles adding and subtracting fractions, and my first task with such students is to make sure that they have mastery of that kind of calculation.
Much of my work with precalculus students has consisted of a thorough review of trigonometry, finite and infinite series and sequences, and analytic geometry. My approach is always to be sure that the basics are mastered before attempting more advanced topics (e.g., students need to have mastered the graphical properties of linear functions before working on quadratic ones (hyperbolas, ellipses, parabolas).
Since so many homework and exam problems in trig involve multiples of 30 and 45 degrees, I show all my students how to derive all the trig functions for those angles based on only two facts that need to be memorized: sine 30 degrees= 1/2, and tangent 45 degrees=1. It's nice to go into an exam knowing that one can derive all those trig function values based on just two memorized facts.
The key to studying for the SAT Math section is to get an SAT practice book and work on as many problems as possible. Those practice books contain the right mix of geometry, algebra, probability, etc. I usually work through such books with my SAT math students, giving them supplemental information in those areas where they need extra help.
The GRE math questions are by no means simple, and they cover the gamut of geometry, algebra, number theory, and applications of all of the above. I have found that working from a GRE test preparation book is the most effective way to gain experience with how to handle GRE-type math questions. As necessary, I supplement the content of such prep books with explanations of concepts that are often confusing to students (e.g., that the square root function does NOT distribute over addition, as some students think).
I have helped several people with the math section of the ASVAB test, but do not consider myself qualified to teach the rest of the test, certainly not the mechanical aspects of the subject. I have found that my ASVAB test prep manual has superb word problems for doing math, and I share them with my ASVAB (math) students.
I prepare my students for ISEE by working problems from ISEE prep books together with them, focusing on those subjects with which the student has the greatest difficulty. For example, one of my current lower level ISEE students needs much remedial work in arithmetic, but is already very good at reading comprehension. For both vocabulary and for mathematics preparation, I find that flash cards are a very useful tool for my students.