Numbers can be scary, or numbers can be fun. All too often, a child's first serious encounter with mathematics is on a sheet of paper in a workbook in a school where there have been neither preparatory exercises nor introductions as to just what exactly "quantity" is, why it matters, and what it is that numbers and their manipulations are based on. Of all the truly creative human abstractions, the development of number systems and calculation was fundamental to much of what we preserve of ancient civilizations. Before mathematics there were no monumental buildings, no sciences, and little commerce. In a Montessori classroom, every child recreates in miniature the processes of discovery that brought the ancients to an understanding of counting, measurement, and spatial relationships. The Montessori student likewise re-constructs the rationale for "place notation," from binary systems (convenient now for computers) to the Arabic numerals and decimal systems devised long ago and still used to represent the numerical abstractions of calculation.

Montessori materials simplify the natural absorption of number concepts because they are ingeniously designed to focus the senses on concrete notions of smaller and larger, longer, and shorter, more and less and so forth, They are fascinating by themselves, yet they inspire the child to physically place them in a certain order that reveals mathematical relationships. They variously demonstrate the progression in regular countable steps of units, of size and measure. There are Montessori materials that concretize in a strikingly obvious manner such things as the theorem attributed to Pythagoras about right triangles.

The children start by learning about quantity using many different tactile examples. Next they encounter the symbols for quantity. Using their senses they take in the shape and texture of numbers. Finally they associate the number symbols with what they experience to have a particular quantity. They learn the numbers from 1 to 10 with colored number rods graduated to represent each successive quantity.

Sandpaper number symbols are physically matched to the appropriate rods. Golden bead material accelerates the manipulation of numbers in the decimal system of notation and renders them real by the concrete physical handling of one bead, strings of ten, squares of a hundred, and cubes of one thousand beads. The children count other materials in single groups, squares, and cubes of 2's through 9's. Other materials introduce addition, subtraction, multiplication, division, and fractions.