Arithmetic Racks or Rekenreks
The arithmetic racks (rekenrek in Dutch) are used as a model in Investigating Number Sense, Addition, and Subtraction (Grades K-3). The arithmetic rack is a calculating frame consisting of two rows of ten beads—two sets of five (one red and one white) in each row and provides a powerful model for exploring the composing and decomposing of number.
Cognitive psychologists, such as Susan Carey and Stanislaus Dehaene, have shown that even toddlers can recognize small amounts, such as two or three, as a unit and that this ability (known as "subitizing") is probably innate. Young children can do addition and subtraction with amounts of this size because they use this innate perceptual ability to see that three is one more than two. Using the arithmetic rack allows kindergarteners and first graders to build on their natural ability and use five as a unit. When the five structure is used, it can support understanding of 6 as 5+1, 8 as 5+3, or 4 as 5–1. The arithmetic rack also supports the strategies of doubles and near doubles (for example, 6+7 = 6+6+1) and making tens (for example, 9+6 = 10+5). Work with this model helps children automatize the basic facts (Treffers 1991).
Arithmetic racks can be purchased through the following web sites: