What is your background in math?
I was attracted to math and science back in high school, and I always liked how there are objectively “right” and “wrong” answers. I majored in electrical engineering in college (with a minor in economics), and I studied a fair amount of calculus, statistics, and discrete math. I was able to keep up with my engineering peers on differential/difference equations, and I took on Laplace and Z-transforms with confidence. After college, I decided to pursue a PhD in plasma physics, and I branched into applied mathematics and applied physics. At this point in my life, I identify myself more as a physicist than a pure mathematician. However, I do a lot of work on numerical methods and modeling, and I spend most of my days worrying about either complex discrete math or really intimidating partial differential equations.
Can you tell us about your experience in math in high school and college?
I always had an aptitude for mental math, and it actually got me into a bit of trouble back in high school. I would often get the right answer, but I never took the time to show my work. I did poorly on my first big algebra test freshman year of high school; I made a few simple mistakes like flipping negative signs or dropping coefficients. Under normal circumstances, I probably would have gotten something like an A-, but without partial credit, my grade dropped to a C. I spoke with my teacher afterwards, and she was nice enough to let me do some extra credit to recover the grade a bit. Still, ever since then, I’ve be hyper-vigilant about showing my work.
College was an interesting transition. I continued to do well in all of my math classes, but I had to get used to getting graded on a curve. It’s always a little weird to get a 70/100 on a test and still get an A in the end. The other adjustment was that you really have to go out and seek advisors on your own. Unless you take an active role in hunting down professors and talking to them, it’s easy to become just another face in a 100-person lecture hall. My strategy was always to do my homework early and to go to office hours with questions. While they won’t give you all the answers, professors are usually more than happy to help you work through the problems. It seems really simple, but it’s something that most students neglect to do, and it kept me well ahead of the curve.
How did you study for math?
Whenever I study for a test, I start by going through all my old homework and notes. Most teachers like to give test problems that are similar to their homework problems, just with an added little twist, like an extra term or a negative coefficient. It’s not always enough to get you a guaranteed A, but I would always redo questions that I got wrong or felt unsure about. I also recommend changing the numbers a little bit and retrying a couple questions from each homework assignment.
After I go through my homework and review my notes, I try to think of the worst problem that a teacher could reasonably ask. It may seem silly, but the process of actually coming up with a good test question requires you to understand “What have I been learning?”, “How could I test that knowledge?”, and “How could I demonstrate that knowledge on a test?”. Back in college, my roommate and I actually made a game out of trying to stump the other person with increasingly difficult questions.
When did you start tutoring?
I started tutoring during my senior year in high school, back in early 2005. As part of my senior project, I volunteered for 10 hours a week with local non-profit called Summerbridge. The name is deceiving; they provide year-round coaching and tutoring for young people in underserved communities. I applied for the position on a whim, but they took a chance on me, and I quickly found myself working a few hours a week in their Cambridge office, teaching basic algebra to a few amazing middle school students.
I continued to volunteer as a math tutor early in college, working mostly with younger students. Later on in college, I tutored math, physics, and the occasional math-heavy economics course (like microeconomics or econometrics). It started out with just helping out friends here and there, but I developed a good reputation over time and connected with other students through word of mouth. I’ve done quite a bit of one-on-one tutoring since then, and, after gaining all of that experience, I started working with New York branch of Signet Education (then known as Harvard Square Tutors) in 2011.
How do you describe your approach?
I’m a big believer in making students recognize their own mistakes and correct their own work. Rather than saying to them, “This is wrong, and here is the right solution,” I ask them to double-check their answers and only then give a gentle nudge in the right direction. It’s hard to have a tutor looking over your shoulder all the time, and students who learn to take their time and correct their own work will perform much better when they take that big test and make mistakes on their own.
I also try to make a connection between abstract math and real-world applications. Not everybody is able to find the “beauty” in mathematics, but a little bit of social, historical, or practical context can go a long way. A topic like exponential growth and compound interest becomes a lot more interesting if you tie it into credit cards or the writings of Thomas Malthus on population growth. At the end of the day, you will still need to work through dozens of problems, but understanding why a topic is worthwhile can make the whole process a lot more palatable.
In your opinion and experience, what three things can lead to success in math?
- Show your work, even if you aren’t being graded on it. It forces you to slow down and really think about what you are doing, which can prevent careless errors. It’s good advice whether you are in high school, grad school, or taking a standardized test.
- Practice! Practice! Practice! When it comes right down to it, nothing prepares you better for a big test than working through a few dozen practice problems. While it’s time consuming, there is no substitute for old-fashioned work and repetition.
- Don’t be afraid to ask questions. Math is cumulative, and almost every topic builds on the one before it. If you feel like you don’t understand something or are falling behind, speak up (or crack open the textbook and read up)! There is good chance that the topic will come up again down the road, and clarifying things earlier rather than later will save you lots of time and stress.
What do you for work when you’re not tutoring?
When I’m not tutoring, I do research in the plasma physics lab at Columbia University. I’ve been working on my PhD for the past four years and am in the process of writing my thesis. Most people don’t know a whole lot about plasma, but it’s basically just a fancy name for ionized gasses (high school textbooks might mention that it is the “fourth state of matter”). Right now, our work is aimed at developing fusion reactors, and it’s actually a pretty exciting field.
What do you do for fun?
I spend a lot of free time watching movies with friends, either in theaters or on Netflix. I also try to take in some culture by visiting museums around New York. I like to cook, and recently I’ve been getting into fermented foods. In the past couple of years, I’ve started making cheese, olives, beer, beef jerky, pickles, and a few other goodies. My other big hobby is computers and gaming. I built my first desktop when I was 13, and I’m always buying new components and tinkering around. I don’t have a lot of time for games anymore, but I still buy the popular games and play for an hour or two on the weekends.
Why do you like tutoring math?
I’ve always been a big believer in the importance of math literacy and science education. Even if you don’t use math professionally, the ability to understand and analyze problems in a quantitative fashion is profoundly empowering. A solid understanding of mathematics will demystify mortgage rates, the national debt, actuarial tables, or why “the house always wins.” On a personal level, it helps individuals balance a checkbook, understand political discourse, and make informed choices about their personal health and wellbeing. Beyond test scores and good grades, my hope is that my students will walk away a little wiser and with a greater appreciation for just how powerful that knowledge can be.
Can You Tell Us About a Memorable Tutoring Experience?
One time, a college junior came to me for help solving sets of ordinary differential equations (as part of a course on control systems). No matter how hard he tried, he just couldn’t get the right answers in the end. We sat down and started worked through all the various steps. He had no trouble writing out the equations, setting up the space state variables, and doing 99% of the problem. He was able to do all the hard work and convert the problem into a simple matrix equation “Ax=B”, but he had no idea how to get rid of the matrix on the left-hand side! The best idea he could come up with was trying to divide one matrix by the other. To this day I still have no idea how he did it, but he had managed to work his way through high school and most of college (along with quite a few advanced math courses) without ever really understanding matrix algebra. We spent the next few days doing a crash course on linear algebra and matrix manipulation. After that, he was right on track, and he went on to get an A in the class.