Dr. Maria Montessori believed that the child's mind is mathematical and based on the order and intuitive understanding found in the development of the senses. She felt that it was essential to expose children to numbers and their symbols at a young age because they are at a sensitive period for repeating tasks over and over again. The repetition is necessary for a child for him to internalize these mathematical concepts.
Preparation for math happens way before he enters the math area in the Practical Life and Sensorial areas. There he develops healthy work habits and concepts such as qualities, form, quantity, dimensions, change, and distance. The sensorial materials help refine the child's idea of differences and similarities, and the concepts of less than, the same as, and more than. The practical life exercises introduce the child skills required in math by many aspects such as pouring between two jugs to the more complex ones like measuring dry ingredients with measuring cups.
The child also needs to learn one to one correspondence and gain a sense of order before he can concentrate and finish a task and work independently to achieve success.
The child learns mathematical principals and foundations by developing the association between concrete and abstract and simple to complex, and that's how Dr. Montessori designed all materials, including math. When we first introduce the child to the new content, we present him with concrete quality, so he can feel it and have a sensory experience of it. When the child masters it, he can then move on to the abstract symbols. Not until he knows both can he be expected to associate the concrete and abstract together.
Math in the Montessori environment has five groups:
The Basic Five - Number Rods, Sandpaper Numerals, Number Rods, and Sandpaper Numerals together, Spindle Box, Numerals and counters and the Memory Game
Intro to the decimal system and base ten system - the child gains a real experience of units, tens, hundreds, and thousands represented by the Golden Beads material and learns how to combine them in the four basic operations of addition, subtraction, multiplication, and division. We use The Stamp Game and the Dot Game as an addition to the Golden Beads to reinforce and refind those skills.
In the third group, we teach the child the use of Ten, Teen, and the Hundred boards. The second and third group work well together and should be combined to reinforce counting skills by units, linear and skip counting.
In the fourth group are the basic facts of addition, subtraction, multiplication, and division. To introduce these, we use Positive and Negative Snake Game, Addition and Subtraction Strip Board, Division and Multiplication Charts, and the Short Bead Stair exercises.
Group five introduces the fractions using the Fraction Skittles and Insets.