Jeffrey’s current tutoring subjects are listed at the left. You
can read more about
Jeffrey’s qualifications in specific subjects below.
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.
It is essential when teaching calculus to make full use of graphs, even when problems can be solved exclusively with equations. There is frequent confusion between a function and its derivative function, and this confusion can be remedied only by lots of practice with graphs.
Calculus classes now include some physics, particularly the physics of trajectories. As a physicist, I am especially well prepared to help students with such physics-based problems.
Elementary math is a fabulous opportunity to lay down a firm foundation for more advanced mathematics. Indeed, much of my time teaching advanced math is remedial work concerning concepts that students should have gotten in elementary math, such as how to do arithmetic with fractions, which operations permit the distributive property (and which don't!), etc.
As is true at all levels, it is especially important at the elementary level to teach concepts in terms of concepts already known by the student. Elementary science is best taught not in terms of abstractions but rather in terms of phenomena with which the student has already had direct experience.
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 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.
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).
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.
A key to good writing is economy and simplicity. Many of the SAT questions, however, also concern outright grammar errors (e.g., mixups of subjective vs. objectives cases). Extensive practice of SAT prep questions serves well to review such errors and learn from them.
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.