All of
Ian’s current tutoring subjects are listed at the left. You
can read more about
Ian’s qualifications in specific subjects below.
Algebra 1
In most school systems, Algebra 1 begins the separation of students into the differently paced math tracks, only the fastest of which culminates in AP Calculus senior year. Re-instilling confidence and competence in a student who is struggling in Algebra 1 pays dividends down the line, and not just in other math classes, but required classes for science, engineering, and medical degrees.
As a former chemistry professor, I observed first hand how much difficulty with basic algebra translated into difficulty in Chemistry. In many cases, these were students who had probably managed to achieve a C or B in Algebra by "getting through it" but generally did not expect to need it again. My teaching style is to stress the importance of algebra with word problems and real world examples, both as a core skill and a motivational tool.
I recently (03/2013) passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12) with the maximum scores in each category.
Algebra 2
Algebra II extends and continues the techniques of problem solving and graphing introduced in Algebra I. It generally includes a variety of new functions (exponentials, logarithms, polynomials, trigonometric), as well as an introduction to complex numbers and matrices.
Although my educational background is in Chemistry, my other undergraduate major was Applied Math, and I have used much of the subject matter from Algebra II in my own career as well as science tutoring. I recently (03/2013) passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12, including Algebra II) with the maximum scores in each category.
Calculus
Although my primary educational passion has been the physical sciences, I decided to add Applied Mathematics as a second major in college because of my strong interest in the field. I first encountered Calculus in my AP course in high school, but I continued to take advanced classes in the subject throughout my undergraduate education.
Calculus is an especially practical field of mathematics that lends itself to real world problems, and it is a tool I have continued to use throughout my scientific career. My teaching philosophy for mathematics in general, and Calculus in particular, emphasizes two key skills: First understanding the meaning behind the equations and symbols with examples and word problems that relate a math problem to a real world description. Second is to learn systematic approaches to simplifying the purely mathematical problem and getting to the answer. The second skill is more obviously useful in a quiz or exam situation, but the first skill is vital to retaining the knowledge you've gained and developing an intuition for the subject.
I recently (03/2013) passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12) with the maximum scores in each category.
Chemistry
I have a Ph.D. in physical chemistry, and taught general and physical chemistry at the college level before leaving for a job in industry.
Having taught this subject as a college professor and as a graduate student I have numerous resources to call upon. Depending on what works best for your learning style, I can tailor tutoring sessions to follow along and reinforce your classroom lessons, or we can identify problem areas and focus exclusively on those.
I recently (03/2013) passed the Chemsitry subject test (number 012) of the Massachusetts Test for Educator Licensing (MTEL) with the maximum scores in each category.
Geometry
Geometry can seem like an unusual step in the traditional middle and high school mathematics track, coming between algebra I and algebra II. Although elements of continuity do exist (emphasis on ratios is Geometry is very algebra intensive, and the first introduction to trigonometry often starts in geometry), Geometry stands apart from the other traditional math courses with its emphasis on visualization and formal proofs, and the problem solving strategies are often more open ended. Strong algebra students are sometimes surprised find themselves struggling in a math class for the first time.
It is critical to adjust to this new type of math problem, as both the rigor of justifying each step as well as the frequent occurrence of multiple equally valid approaches mimics the type of creative technical problems modern S.T.E.M. workers encounter.
I recently (03/2013) passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12) with the maximum scores in each category.
MATLAB
I've used MATLAB extensively in my research career and am very familiar with the base package, as well as the image processing toolbox and the Graphical User Interface Development Environment (GUIDE). Depending on your needs I can offer a startup lesson for a new user (Basic command line analysis, script and function coding, and plotting data), code consulting to improve performance (memory management, vectorization, efficient use of data types), and any other help needed.
Physical Science
Physical Science is often the first high school level science class students take and the first science class with a strong math emphasis. Topics such as measurement error, graphing data and significant figures are general skills that apply to many other more specific subjects like chemistry, physics and biology. My background in chemistry teaching and scientific research provided me experience covering these topics with students as well as applying them to problems in the real world.
Physics
I have a Ph.D. in physical chemistry, which encompasses aspects of both chemistry and physics. I am well versed in the various subjects of beginning physics (mechanics, electromagnetism and optics).
The basic concepts are the same at the high school and college freshmen levels, with the college class typically covering a few more topics and requiring calculus as a prerequisite. I can teach you problem solving skills for both levels, and equally important, help you learn to appreciate physics as a way to explain the observable world and not just a series of riddles and algebra problems.
Precalculus
In addition to the obvious precursors to differential calculus such as limits and series/sequences, precalculus covers a variety of subjects with far ranging applications, from analytic geometry and polar coordinates to linear algebra and methods of solving large scale systems of equations. A significant challenge some students face is motivational; topics like imaginary numbers seem completely disconnected from the real world and hard to justify the effort it takes to understand them. My science background helps here, and I can often find examples of techniques I have used in my career despite not knowing the application when I was in high school.
Although my educational background is in chemistry, my second major in college was applied mathematics. I recently passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12, including algebra II) with the highest scores in each category.
Trigonometry
Trigonometry is the study of angles and associated functions. The typical high school trigonometry curriculum focuses on the basics with examples of triangles, circles and function periodicity, but this only touches on the wide applications for trigonometry to the multidimensional world. From the interactions of non-parallel forces to understanding the nature of light and sound waves, a solid grasp of the fundamentals of trigonometry is critical to any study of science or engineering, as well as the mathematics classes that follow it.
Although my doctorate is in Chemistry, my second undergraduate major was Applied Math, and I have used much of the subject matter from trigonometry in my own career as well as science tutoring. I recently (03/2013) passed the Massachusetts Test for Educator Licensing (MTEL) subject 09 test (which covers the standard math curriculum from grades 8 - 12, including trigonometry) with the maximum scores in each category.