MATHEMATICS:
Maria Montessori believed that the child possesses a mathematical mind. This is based on order and perception found in the development of the senses. The child progresses from the use of concrete material to the abstraction of math concepts. Children learn about numbers, simple and complex addition, subtraction, multiplication, division, exchanging, and fractions.
Students are introduced to numbers at age 2, learning the numbers and number symbols one to ten, the red and blue rods, sandpaper numerals, association of number rods and numerals, spindle boxes, cards and counters, counting, sight recognition, concept of odd and even. Introduction to the decimal system begins at age 3 or 4. Units, tens, hundreds, thousands are represented by specially prepared concrete learning materials that show the decimal hierarchy in three-dimensional form. The objective is to develop the concept first.
Linear counting
addition, subtraction using the Golden Beads and other manipulatives
Concepts of dynamic addition and subtraction
Memorization of the basic math facts ( not through drill, but through no fail practice)
Skip counting with the chains of the squares of the numbers zero to ten
Skip counting with the chains of the cubes of the numbers zero to ten
Beginning the "passage to abstraction," the child begins to solve problems with paper and pencil while working with the concrete materials
The study of fractions begins with very concrete materials
Solving word problems, and determining arithmetic procedures in real situations becomes a major focus
Money concrete to abstract; real life problems
Reinforcing application of all mathematical skills to practical problems
Data gathering, graph reading
Sensorial exploration of plane and solid figures, children learn to recognize the names and basic shapes of plane and solid geometry
