Three Basic Connections in gecKo mathematics

1. Focus on the Inverse Relationship

   The student is neither a docile recipient of facts nor the starting point, the center, and the end.

   John Dewey

   gecKo math, like the Korean national curriculum, looks at addition and subtraction as inverse relationships. In other words, from the very beginning, children are taught addition and subtraction at the same time. Instead of separating the concepts, the children learn that addition and subtraction are the inverse of each other and that once they can do one procedure, they already know the other.

   For example, children learn from the beginning that 2 and 1 can be merged to make 3. At the same time they learn that 3 can be separated into 2 and 1. A similar inverse relationship is presented in multiplication and division.

   Sample Inverse Relationship Lesson
   For interactive show use the arrow buttons on slides.

2. Focus on the Base 10 Decimal System

   Children are taught to focus on the base 10 system from the beginning of their study of mathematics. Children learn all the combinations that make ten. Then they learn how to add and subtract, to regroup and borrow, by counting up to, or down to, ten.

   For example, if a student is adding 6 + 8, the child knows that 8 only needs 2 more to get to 10. He then adds the remainder of what was left after the 2 was taken out of 6 (4) to make 14.

   Sample Base 10 Lesson
   For interactive show use the arrow buttons on slides.

3. Multiple Models and Strategies

   Instead of children doing 20 problems in class as they may do in other curricula, children using gecKo mathematics may look at only one problem in class. The teacher may then present the problem in many different ways to make sure every child knows exactly how an answer can be reached.

   For example, children will learn how to add 2 numbers by first showing with their fingers how many groups of tens and how many single units it takes to make the number. Then they will solve the problem using counters and other manipulatives. They will learn to add it horizontally. Finally, the problem will be presented on a number line and children will be presented with a vertical algorithm.

   Sample Lesson with Multiple Models

   At all grade levels operations are modeled on the number line in more and more complex ways, providing consistency in conceptualization across grade levels.

   Sample Number Lines Across Grade Levels
   For interactive show use the arrow buttons on slides.