Math

Curricula

Grades 2-3

We start with concepts of numbers and the real number line, concentrating on the sets of natural numbers, whole numbers, and integers. We build computational skills and intuitive understanding of major properties of operations (commutative, associative, distributive). We go into set theory, Venn diagrams, concepts of variable and simple equations, word problems, and the overall language of math.

Grades 4-5

We go deeper into the concepts of the second and third grade programs. We work to enhance and increase an assortment of computational skills, placing further attention on the concepts of variables, constants, algebraic terms and expressions, concepts of fractions, decimal arithmetic. We teach equations as logical statements, and emphasize the skills of communicating through math, all the while developing logical and abstract thinking and personal reasoning skills.

Grades 6-9

We concentrate on further enhancing abstract thinking, problem solving skills, understanding of the basics of algebra and geometry. Throughout all of these programs, we focus on developing computational skills, avoiding the use of calculators when possible. Programs in this group include fundamental combinations and probabilities, identical transformations and major algebraic identities, data analysis, and some basic SAT-I related strategies. The more advanced programs in this group include properties of functions, theory of quadratic expressions, inequalities, and other conceptually fundamental topics of elementary algebra and geometry. The goal is to develop a taste for the process, and an ability to relate different mathematical objects to each other.

Grades 10-12

We provide different programs for this group based on the goals and levels of the students. Although we continue to teach all fundamental topics of elementary math, the concentration is on SAT preparation. There are advanced groups that targets SAT-II, 2C, and there are more general programs designed for SAT-I, and SAT-II, 1C. Along with thorough insight into math concepts and skills required for these tests, we make sure that each student is equipped with SAT-specific strategies and knows the most efficient approach to getting the best result.

Our teaching philosophy

by Alexander Shilmover (M.S. in Math from Moscow State University, lifelong experience teaching Math)

Our math programs are designed to fill the gap between the requirements reflected in the recommendations of the Curriculum and Evaluation Standards for School Mathematics made by the National Council of Teachers of Mathematics (NCTM) in 1989, and the existing practices in most of public schools. Some of the shortcomings of current practices are the tendencies to focus on the acquisition of memorization skills; to cover many topics superficially; and to be highly repetitive without in-depth learning.

Nearly every subject has a shadow, or imitation. One can learn imitation history – kings and dates without the slightest idea of the motives behind it all; or imitation literature – stacks of notes on Shakespeare’s phrases, yet a complete lack of power to enjoy Shakespeare. Many traditional programs and textbooks reflect disconnected orientation, focusing on the end results, omitting the important notion of the process, the association between different topics and concepts.

The result is often a feeling of dissatisfaction and even a fear of math, a notion that mathematicians are a race apart, and a feeling by the students that they will never be able to understand math. We are convinced that these perceptions do not lie in the nature of the subject, but, rather, are caused by the poor tradition of teaching math.

The fear of mathematics is a tradition handed down from the days when the majority of teachers knew little about human nature and nothing about the nature of mathematics at all.
— Walter Sawyer

So, what do we emphasize in our programs? We emphasize mathematics as a language; mathematical reasoning and proof, which includes true comprehension of the differences between theorems and definitions; and, ultimately, the ability to draw logical conclusions, making and testing scientific conjectures. When a student realizes that he actually deals with the same phenomena when he looks at things from various perspectives, the fear of math is replaced with the pleasure that comes with deep understanding.

To master anything requires effort. But it does not require unpleasant effort, drudgery. The main task of any teacher is to make a subject interesting.
— Walter Sawyer

We are passionate about teaching our students to communicate and express mathematical ideas coherently. We want to instill the ability in each and every student to listen to himself or herself, to become aware of the way he or she is thinking. We emphasize the idea that math is a language, and therefore, using verbal and symbolic ways, each person learns to express it.

Our Russian background and the traditions of the Department of Mathematics and Mechanics of Moscow University is reflected somewhat in the school curriculum and the selection of permanent and guest teachers, but the philosophy of the school is defined in the first part of this proposal and is very much in the spirit of the new approach developed in the Curriculum and Evaluation Standards for school mathematics, and MCAS requirements.