The fact is that, compared to that of all other first world countries, the American mathematical education system lies a stone's throw from dead last in the world. Even much poorer countries, such as those of Asia and Eastern Europe, routinely outscore America by terrific margins on international assessment tests. When average or even struggling math students immigrate to America from these countries, they usually find that they know most of the material that is being taught in their classes and that they have suddenly become "gifted" in math. And math education in America has been getting worse for the last 50 years! This problem begins with deep and fundamental flaws in our educational philosophy.
I believe that one-size-fits-all classroom lecture-style math education is inefficient, ineffective, and outdated. My long term career goal is to develop the "K2 Learning System," a software package which will function like a world-class private math tutor and provide a truly first rate math education to everyone for nearly free. I have spent years planning the development of this software and am currently working with a programmer and a designer to implement it. It will soon be available as an exciting free bonus to all of my students. Prior to beginning the development of my own software, I went out of my way to work for two different math education software-development companies to gain the knowledge and experience necessary for my own project. I have also studied successful approaches to teaching math that are used around the world, and particularly in three of the world's front-running countries in math education: Russia, Hungary, and Japan. I was born into and have the largest amount of personal experience with the Russian approach, while I have actively searched out exposure to Hungarian and Japanese methods.
I am originally from Russia and come from a strongly mathematically-oriented family. Alongside my school math education, I was raised from a young age with Russian teaching methods and text books. One person who I have in particular been influenced by is my aunt, Larissa Itina, who has dedicated her life to elementary math education. She has written numerous Russian elementary school mathematical textbooks, winning many prestigious awards for her work. Some of her books are still in use in countries of the former Soviet Union. Today, she runs the successful Studio of Engaging Learning in Boston, MA. In college, I also studied math for a semester in Moscow under some of the top Russian mathematicians. From the Russian approach, I have come to believe that math should be natural, methodical, and intuitive, rather than mysterious and memorization-based.
I also studied math for a semester in Budapest, Hungary, where I was exposed to the Hungarian approach to math education. I found it to be effective, intuitive, quite enjoyable, and less strenuous than the Russian approach. Lastly, I spent a year working as a Kumon instructor and solutions manual editor at the premier Kumon center in the Midwest. The Kumon method is an extremely effective method of learning math, which was first developed in Japan in 1954. It is basically a program that trains students to do math in a very orderly, drill-based fashion and makes certain that students have become adequately competent in each necessary prerequisite technique before moving on to the next technique. The method regularly produces such impressive results as 6th grade students capable of performing well on the AP Calculus exam. Unfortunately, owing to its dry, mechanical style, students usually don't enjoy the program at all (most of the time, dropping out) and, while their computational abilities are great, their intuitive understanding of math and how to apply it is poor.
My experience learning math and conducting mathematical research with some of the most prodigal students and top professors in the United States, has also been invaluable to me. In high school, I attended three summer math programs, Power Math, Mathcamp, and Hampshire College Summer Studies in Mathematics. In college, I was a counselor for Power Math, attended East Tennessee State University's Research Experience for Undergraduates in Mathematics, performed two years of mathematical research with professors from Washington University in St. Louis and the University of Nebraska-Omaha, and presented my research at three mathematical conferences. Working with and learning from a variety of successful mathematicians in a variety of contexts has helped me to discover and decompose the approaches that these people take to learning math and solving (sometimes extremely challenging) math problems. These approaches, as well as my own have been the inspiration for the component of the K2 Learning System which is dedicated strictly to teaching students how to "think mathematically."
Outside of my mathematical education, I have actively developed and continue to develop my own techniques for teaching and learning math. When learning math, an essential part of my approach was always to ask myself, "how can I be expected to come up with this solution/proof in a straightforward, methodical, and most importantly, intuitive manner." It was never good enough just to memorize a technique for solving a particular type of problem or to understand the proof of a theorem. I had to really understand where it came from and how it fit into the big picture. When teaching concepts to students, these, rather than just cook-book formulas, are the kinds of explanations that I try to give them. And they have been tremendously effective. I also use an approach dubbed “Mathemantics” by Dr. John Konvalina (see my References section). "Mathemantics" is all about learning to smoothly translate between math and English and, among other things, is the cure to students' troubles with word problems.
I tailor my teaching for each of my students to their abilities, goals, and interests. My students make and regularly review a “formula sheet” containing important formulas and concepts that they learn in our lessons. My students also keep a list of problems/techniques that they students have had trouble with in the past and regularly review them until they have a solid grasp of these techniques. I waste as little time as possible discussing concepts that students already know, try to teach new concepts as quickly and efficiently as possible, and adjust the pace of our lessons to be as fast as the student can keep up with. Finally, if necessary, I give homework assignments that are carefully adjusted to my students’ needs. My overall goal is to help each student achieve the most improvement with the least amount of effort, both in the short- and long-run.
I attribute to combinations of the above my success in learning math, performing mathematical research, math competitions, and most of all, teaching math to others. As a result of my approach, students find that they learn math faster, understand it on a deeper level, can generalize concepts to a wider range of problems, and remember it much longer. Have a look at my references section to see what others have to say about my teaching!