The Montessori method of teaching math to Lower Elementary students is revolutionary.  The curriculum takes the children from manipulating the concrete materials, to doing math in the abstract form with pencil and paper.  Each work is sequenced so that the child builds upon a concept learned in the previous work.  The child is taught division using the stamp game, so the concept of HOW division works is established first—the child can SEE how they are dividing up one number by another number, by manipulating the concrete material.  It is only after the concrete materials are introduced and learned that the child moves to the abstract, computing in their head or using pencil and paper only.  

One of the most interesting facets of this curriculum is the variety of materials available to learn the same concept.  For example, addition, one of the first and most basic concepts taught in Lower Elementary Math, is usually initially taught using the golden beads, then using the stamp game, then the snake game and so on, until the process is completely understood.  All of these materials provide the child the opportunity to learn addition.  The same is true for subtraction, multiplication and division—there are several works that can be used for the same process until it is completely understood.  Multiplication can be taught with the stamp game, then the bead frame, then the checkerboard, then the golden bead frame, each work adding a concept (such as an additional digit).  If one particular work doesn’t capture the attention of a student, there surely is one that will.  Fingercharts are used to aid in memorization of math facts, and makes what is usually a tedious duty, fun!  Fractions and decimals also have specific, concrete works to guide the children in grasping these difficult concepts.  The geometry materials, which include, but are certainly not limited to; the exploration and study of lines, angles and shapes, capture the attention of the children easily.  

In the math curriculum, the child is given an isolated item to learn, one concept at a time so as to not overwhelm—to help the child maintain order and learn in a progressive fashion.  If a child has not mastered one work, another one using the same concept is offered, so that by the time they are ready for the next step, success is ensured, which in turn makes the child feel happy, and proud of him or herself.