Our main goal is to achieve longterm retention of material we teach. To achieve this goal, we use many techniques. We teach math in an engaging and fun way, with games and contests to get kids’ competitive juices flowing. We show them the side of math they would not typically see in a regular school, whether it is a historical perspective or a real world application. We emphasize abstract and conceptual thinking versus mechanical calculations and memorization. We want our students to “think on their feet” and do mental calculations of increasing complexity. We take effort to ensure that our learning objectives are appropriately sequenced; we always “cycle back” to old knowledge and connect it with “new knowledge”; we triangulate or look at things from many different perspectives; and we practice, practice, practice.
Below are some examples of math problems emphasizing conceptual understanding as compared with more mechanical approaches:
Typical 4th grade problems 
We prefer these 4th grade problems 
1) John bought 4 bananas and 6 apples. A banana cost $0.80 and an apple  $1.20. How much did John spend? 
1) John paid m dollars for 6 chairs and n dollars for 4 tables. What does expression n/4m/3 represent? 
2) Divide 734 by 3, find Quotient and Remainder 
2) A triangle with each side one inch in length has its vertices labeled A, B, and C (clockwise). An ant crawls along the sides of the triangle, clockwise, starting at point B. If the ant crawls 734 inches, at which point will it stop (A, B, or C)? 
3) Paul walks 20 miles with a speed of 8 miles per hour. How long will it take him to complete the journey? 
3) Paul and Jane are 16 miles apart. They start heading towards each other at the same time. Paul walks at 5 miles per hour, and Jane walks at 3 miles per hour. Also at the same time, a dog departs together with Jane and heads toward Paul. The dog runs at 8 miles per hour. As soon as the dog gets to Paul, he immediately turns around and starts running to Jane. As soon as the dog gets to Jane, he turns around and runs toward Paul, once he reaches Paul – back to Jane, and on…and on…and on. How many miles will the dog run?
(This problem is adapted from the actual Russian 4th grade math textbook; what % of US highschool students will be able to solve this problem?)


"Thank you for such a great math class! You have opened all our eyes to how much interesting, challenging, and fun math can be (even in 4th grade!). The class has been a great help for our son!"
Parent of Squared School student
