I have two and half years of experience tutoring math in K-12 and two years of experience as a course instructor and tutor at the University of Colorado at Boulder, from which I graduated in May 2012.
Working as a tutor, I've tutored several high school students in algebra and geometry with a few occasions doing trigonometry and calculus. I have also tutored in SAT math and discrete mathematics as well as tutored elementary and middle school math subjects such as pre-algebra and basic math.
Through my position as a teaching assistant, I've taught two terms of the first semester of calculus and one term of a college math course aimed at students who aren't pursuing math or science majors. It dealt with propositions and logic; units of physical quantities, unit conversions, and different systems of measurement; percentages; scientific notation; some business math dealing with simple and compound interest, savings plans and loan payments, and taxes; introductory statistics and probability; and linear and exponential modeling. I also led recitations sections for business calculus and pre-calculus in this position.
This is my basic style. It's flexible and it depends on how the student approaches math. That said, after tutoring students in a wide range of aptitudes, I've found that what I've written below is the general framework of a tutoring session.
I want the students I'm tutoring to get the most of out of the math classes they're taking and even possibly find the content appealing. I want the students to know why they are doing a math problem: what use they could get out of doing it besides getting a passing grade in the class. I start by asking where they feel stuck. I usually get a problem that needs to be solved although at other times it's an example in the book or some notes from class.
I like to make up a problem similar to it and do it myself, explaining the steps as I go along. Then I summarize what I did and explain how it can be applied in the same way to the problem that the students gave me. I'll ask them to tell me what the steps for solving the problem are, too. Then I give them another similar problem, still different from the one they initially gave me, and ask them to do it. If they can do it correctly, great!
However, most people don't get it the first time, so it helps to explain the step where they are having trouble. In this case, I stop them when they make a mistake and then explain to them what to do instead at that point. I give smaller exercises specific to the step where they are having trouble to have them master this step that they don't know how to complete until they do complete it. Once this happens, then I let the students finish the problem or repeat this until the problem is complete.
I hope this answers your questions. As for availability, I am free in the evenings during the weekdays and am also free during the weekends.
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Bryan's subjects
Discrete Math
In discrete mathematics, I have tutored in set theory and set operations such as set unions, intersections, power set of a set, Cartesian product of sets. I have tutored in countability and noncountability and explained Cantor's diagonalization argument. I have used Zorn's lemma several times in proofs and am familiar with Russell's paradox. I have tutored in propositions and logic -- truth tables, logical equivalence, explaining the truth table for the conditionals, etc. I am familiar with basic...
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Differential Equations
I took a class in introductory differential equations as well as a graduate level class in differential dynamical systems and chaos, which required the former class as a prerequisite.
Linear Algebra
I took, and got an A in both undergraduate and graduate level linear algebra.
MATLAB
I have used MATLAB to make scripts, among plenty of other things, that give approximate solutions to the Laplace equation, do polynomial interpolation, Gaussian (and other forms of) quadrature, as well as scripts for generating graphs -- both 2D and 3D. I have used MATLAB to make scripts for algorithms in number theory as well.
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