Kindergarten Montessori Mathematics

The Montessori math materials; through concrete manipulative materials allow the child to internalize the concepts of number, symbol, sequence, operations, and memorization of basic facts. This is a concrete experience in the Montessori classroom.

Special materials such as spindle boxes and bead bars allow the child to see what “nothing” or zero looks like, or to see that multiplying 5x5 can be done with 5 bars of 5 beads each. Development of the concept of the four basic mathematical operations: addition, subtraction, division, and multiplication through work with the Montessori Golden Bead Material. The child builds numbers with the bead material and performs mathematical operations concretely. Work with this material over a long period is critical to the full understanding of abstract mathematics for all but a few exceptional children. This process develops a much deeper understanding of mathematics.

Introduction to the decimal system - Units, tens, hundreds, thousands are represented by specially prepared concrete learning materials that show the decimal hierarchy in three dimensional form: units = single beads, tens = a bar of 10 units, hundreds = 10 ten bars fastened together into a square, thousands = a cube ten units long ten units wide and ten units high. The children learn to first recognize the quantities, then to form numbers with the bead or cube materials through 9,999 and to read them back, to read and write numerals up to 9,999, and to exchange equivalent quantities of units for tens, tens for hundreds, etc. Linear Counting: learning the number facts to ten (what numbers make ten, basic addition up to ten); learning the teens (11 = one ten + one unit), counting by tens (34 = three tens + four units) to one hundred.

Montessori math develops of the concept of "dynamic" addition and subtraction through the manipulation of the concrete math materials. Addition and subtraction where exchanging and regrouping of numbers is necessary) Memorization of the basic math facts: adding and subtracting numbers under 10 without the aid of the concrete materials. Development of further abstract understanding of addition, subtraction, division, and multiplication with large numbers through the Stamp Game (a manipulative system that represents the decimal system as color-keyed "stamps") and the Small and Large Bead Frames (color-coded abacuses). Skip counting with the chains of the squares of the numbers from zero to ten: i.e., counting to 25 by 5's, to 36 by 6's, etc. Children develop a first understanding of the concept of the "square" of a number. Skip counting with the chains of the cubes of the numbers zero to ten: i.e., counting to 1,000 by ones or tens. They also develop the first understanding of the concept of a "cube" of a number.

Beginning the "passage to abstraction," the child begins to solve problems with paper and pencil while working with the concrete materials. Eventually, the materials are no longer needed. Children develop concepts of long multiplication and division through concrete work with the bead and cube materials. Development of more abstract understanding of "short" division through more advanced manipulative materials (Division Board). Sensorial exploration of plane and solid figures at the Pre-primary level the children learn to recognize the names and basic shapes of plane and solid geometry through manipulation of special wooden geometric insets. They then learn to order them by size or degree.