 ### Mathematics

The study of mathematics is a reflection of the human tendencies for investigation and orientation, for order and classification, of reasoning and making judgments, and for calculating and measuring. In the Montessori Children’s House, when mathematical concepts are first presented to children, they are embodied in concrete materials.

Mathematics in the Children’s House builds on and extends the exercises of practical life and the exercises of the senses, as well as the many mathematical experiences children encounter incidentally in their daily lives.

Montessori’s mathematical materials enable children to begin abstract concept formation as they develop operational thought. Children use sensorial materials to isolate concepts such as size, form, weight, and volume, eventually internalizing the abstract concept each represents. The Practical Life materials help children develop the ability to concentrate on explicit sequences, and it helps them become confident in their ability to make judgments. These skills are essential to the construction of their mathematical mind.

The Mathematics curriculum for three to six year olds is organized around these objectives:

• Acquisition of the concepts of number and quantity, including zero.
• Development of number theory including counting sequences and odd/even numbers
• Understanding of the concept of place value
• Development of a vocabulary of mathematical terms
• Introduction to basic operations
• Introduction to memorization of math facts
• Naturalistic data collection and representation
• Mathematical problem solving
• Understanding of measurable attributes
• Introduction to geometric shapes and solids

As they work with the exercises of the senses, children are making judgments in relation to distance, dimension, graduation, identity, similarity and sequence. Building on the foundation, the Montessori mathematics materials introduce children to:

• counting (from 1 to 10, 10, 90, linear 1 to 100 and 1000, and skip-counting as an introduction to multiplication)
• place value to four digits
• number operations (addition, subtraction, multiplication, division)

The base ten number system is represented for children in concrete form using golden beads organized so they vary simultaneously in quantity, size, mass, and geometric shape. Children are also given the corresponding symbol for each quantity. In this way, children experience relations between the hierarchies of the system in multliple ways. Using this material in active and enjoyable games, children learn to add, subtract, multiply and divide. This material supports the heightened sensitivity for number children tend to experience around the age of four.

Children work through the Montessori mathematics exercises and games in a supported and incremental way. Students progress through the mathematics curriculum following their own interests, so not all children complete the activities in the same sequence or in the same timeframe.

Read an Overview of Montessori Mathematics >>