Mastering the MathRack
Rationale for Using the MathRack with Students
It is always important to have a rationale for the methods we employ when teaching
mathematics to young children. Using manipulatives without a rich understanding
of the potential – and the possible pitfalls – of the tools can not only limit their
effectiveness, but in some cases interrupt the natural and desired development of
mathematical thinking among young children. The following information is intended to provide you with a brief summary of the theory that underlies the use of the MathRack.
The MathRack helps young children to see numbers as groups (e.g., groups of 5, groups of 10, “doubles”, etc.), rather than having to count every object in every set.
For the purposes of helping young children develop number sense through the use of the MathRack, we might best think of subitizing as the ability to instantly recognize particular groupings of objects within a larger grouping without having to count each individual element. The MathRack helps children build on their natural capacity to subitize in order to recognize quantities up to 10 (and beyond for more advanced students) without depending on the routine of counting. In the example below, the child uses the structure of the MathRack (5s and 10s) to subitize... to see 8 as a group of 5 and three more, without having to count any individual beads.
Decomposition: Part, Part, Whole
Once children are able to subitize, it is only a matter of time before they will be able to do more complex decomposition of numbers, a concept that is essential for children to understand if they are to complete operations on numbers with meaning. The MathRack is instrumental in setting the stage for conceptual understanding of decomposition as it relates particularly to the operations.
Anchoring in Groups of 5 and 10
The MathRack can be thought of as a dynamic 10-frame model. Since 10 does play such a large role in our numeration system, and because 10 may be found by combining two groups of 5, it is imperative that we help children develop powerful relationships for each number between 1-20 to the important anchors of 5 and 10.
Informal Strategies: Doubling, Halving, One/Two More, One/Two Less
The MathRack can aid in the development of informal strategies for addition and subtraction that are essential for later work with larger two and three-digit numbers. Students learn strategies like doubling and halving (and the associated number facts, e.g., 6 + 6 = 12) as well as the notion of “adding on” by ones and twos. With the Rekenrek, children quickly associate numbers in relation to each other. For example, seven can be seen as “2 less than 9” or, “one more than 6.”