Our program is made of many levels, so that students progress from learning simple tools and techniques of a math detective to understanding how to solve very hard problems in notoriously challenging areas of math, such as combinatorics and geometry.
The adventure starts in Level 0. We introduce the kids to the basic tools of a math detective – finding clues in math problems, organizing what you know, understanding and using tables, using visualization, and so on. We start learning important math terminology and how to decipher a problem when the student does not know some words. We do that while working through a variety of fun topics, such as making and counting coin combinations, made-up operations, simple cryptarithms, logic puzzles, and problems on a number line. We also introduce some interesting number patterns and discuss large numbers around us – always a hit among the kids.
In Level 1, we continue to introduce the fundamental ideas of analytical reasoning. The difficult math problems are often only hard because their solution requires many steps. Trying to connect the clues given in the problem to what one must find is impossible at first. We teach students to focus on the clues and what more they can discover from them, one step at a time, until the answer “miraculously” appears. This is done through learning many of the same topics that we introduced in Level 0, but to a greater depth. For example, while in Level 0 students learn simple logic puzzles, in Level 1 we work through harder ones involving indirect clues. This reflects our approach in general, where we study the same topics at various levels, and show kids that there is always more fun in math as you learn more and dig deeper. For instance, cryptarithms make their appearance in Levels 0 through 3.
Students in Level 0 and Level 1 participate in Continental Math League (CML) contest and Math Kangaroo contest. Some of the top students in Level 1 could be invited to participate in the Math League contest for fourth graders.
By the time students arrive to Level 2, typically in fourth grade, they are ready to face real math challenges and explore pre-algebra patterns in numbers. We avoid over-using algebra at this age, rather we focus on solving math puzzles without algebra, but start introducing algebraic ways of presenting our solutions.
The math problems at those levels turn into multi-step puzzles. Our main focus is on number theory, logic, and introductory topics in geometry. We investigate divisibility rules and factorization, prime numbers, perfect numbers, and amicable numbers, study advanced logic puzzles and cryptarithms, learn how to count sub-shapes in 2-D figures and understand 3-D solids made of simple cubes, and explore infinitely beautiful patterns in Fibonacci numbers and Pythagorean triples.
Students in Level 2 and Level 3 participate in a variety of age- and skill-appropriate contests. Those include CML, Math Kangaroo, Math League, and Math Olympiads for Elementary and Middle Schools (MOEMS) Division E. Some of the top students in Level 3 could be invited to participate in the AMC-8 contest. Many students also compete in math contests on their school teams.
At this point most students have entered middle school and are expected to have completed pre-Algebra and are ready for more algebra-based challenges. The topics in our curriculum focus on four main areas: combinatorics and probabilities, exponents and sequences, geometry, and number theory. These areas have proven hardest for students to master and usually are the difference between the top students in math competitions, such as MathCounts and AMC-8/10. We make a concentrated effort to help students truly embrace and understand these difficult topics. We firmly believe that you cannot “teach” advanced mathematical topics – they must be “learned” through discovery. One must develop a sense for them, a feeling that comes from “inside”. And so we go through a variety of topics and have students work in groups to discover the solutions for themselves, with some “nudging” from us. We help students discover and prove important theorems of geometry, find patterns in combinatorics problems, and develop intuitive sense for the number theory.
In the process, we explore many interesting areas of math, e.g. graph theory, consider the wide world of numbers, and introduce the role of infinity in math. This is also the time when students are ready to appreciate the beauty of algebra and so we use algebra more extensively. Most of the time, we show algebraic way as one of alternative approaches.
Students participate in many advanced math contests. Our teams compete in MOEMS Divisions E and M, AMC-8, and Math League Algebra I contest. Many students also join math teams at their schools and compete in numerous contests. Our program goes a long way to help prepare middle school students to successfully represent their school in the math contests.