There is perhaps no more important task for primary teachers than to help young children develop powerful understandings of numbers -- their meanings, their relationships to one another, and how we operate with them.
The Rekenrek has recently emerged on the U.S. mathematics education scene as perhaps the most powerful of all manipulative models for young learners. Developed by mathematics education researchers in the Netherlands (although similar models were used in ancient cultures) the Rekenrek combines various strengths of other manipulatives (e.g., number lines, base-10 blocks, counters, etc.) in one accessible tool.
The Rekenrek is comprised of two strings of ten beads each, strategically broken into two groups: five red beads, and five white beads. Readily apparent in this model is an implicit invitation for children to think in groups of five and ten. As illustrated below, the strings of red and white beads (in groups of 5) provide a visual model that encourages young learners to subitize, i.e., to build numbers based on groups of five and ten.
For example, a child might view the number 7 as one group of 5 (red), and 2 more.
Similarly, 13 might be thought of as 10, and 3 more.
Of course, there are other ways to represent these two numbers with a Rekenrek, a fact that students are eager to explore. Additionally, the Rekenrek can be used to encourage informal strategies for addition and subtraction, for example, using doubling and halving strategies, counting-on from known quantities to solve addition and subtraction problems, etc. As elaborated in the book, this model can be used to build numerous concepts, and to help students develop meaning and facility with number operations.
The Rekenrek has become a key tool for teachers in the Netherlands, one of the top performing countries in math education in the world. Learn what makes this mathematical model so compelling for young learners, and so powerful for the development of their mathematical understanding!