Montessori Math Materials and Curriculum for all Age Groups

The highest form of pure thought is in mathematics. ~Plato

Maria Montessori believed that human intelligence is no longer based on natural intelligence, but on mathematical intelligence. Humans have moved beyond the innate survival instincts of early humans and moved toward an analytical awareness of the world. Math is more than math facts and computations. It deals with shape, space, patterns, symbols and the relationships found therein.

Montessori education is unique in that it prepares a child for learning to think mathematically from the youngest of ages. Montessori materials are designed to help children succeed in becoming confident, intelligent adults with a passion for life long learning. Continue reading to learn more about Montessori education and the mathematical mind.

Montessori Math Materials and Curriculum for all Age Groups

Mathematics: Birth to Age Three
Learning about patterns occurs in utero: the cycles of day and night, activity and inactivity, the patterns of the mother and the family. The developing child also hears the patterns of speech and music around him. Music is thought to enhance the development of the mathematical mind due to the fact that the neural pathways of learning music are very similar to those for mathematics and may help with the mylinization of those neural pathways.

Montessori observed that humans tend to be attracted to order. After birth, consistency with routines and activities such as feeding, bedtimes, bathing and playing help the child establish an early sense of order and sequence. Babies learn to think logically and know what to expect. Deviations from the expected order can cause confusion and cause upset. This early tendency towards mathematics causes the child to observe others and to compare, contrast, and classify objects in his environment. Consistency helps the child make sense of the world around him. Using clear, precise language also helps develop the mathematical mind. As children are beginning to order their world, we use mathematical terms such as big, small, more, some, few, many, to help them learn to quantify.

Mathematics: The Preschool Years
Although preschool students have had several years working with numbers and mathematical concepts, children do not immediately begin working with the math materials in the Montessori preschool environment. Instead, the child is indirectly prepared for later mathematical works through the Montessori Practical Life and Sensorial activities where she develops the fundamental abilities necessary for higher level mathematical concepts: discrimination, recognizing similiarities and differences, constructing and comparing a pattern or series, finding relationships, and understanding terminology.

Many of the Montessori Sensorial materials are based on the concept of 10, which helps children visualize and comprehend our decimal system. By understanding the decimal system and place value, the child is introduced to geometry: a point (Golden Bead) is a unit, a line (Golden Bead 10-bar) is 10, a plane or square (Golden Bead 100-square), and a cube (Golden Bead 1000-cube) is 1000. With this understanding, Montessori preschool/kindergarten students are able to add and multiply to form larger numbers and subtract and divide to make smaller quantities. Because they first experienced these concepts through their senses, Montessori students are able to understand the true nature of the operations.

Mathematics: Elementary
Children inherently like working with math materials because they correspond to the logical way our brains work. Montessori wanted to ensure that each child is presented with materials that correspond both to the child’s interest as well as their developmental needs. Through self-exploration with the Montessori didactic materials, the mathematical abstraction becomes apparent to the child. Montessori students are not simply memorizing facts and rules but absorbing the knowledge and making it their own.

Elementary-aged children are both imaginative and able to reason. They are able to create mental pictures and manipulate images in their minds. Montessori math materials help children form these mental pictures as the work to internalize concepts and skills. No longer satisfied to repeat activities for the sake of repetition, the elementary child requires materials which provide repetition but with more variety.

As the Montessori elementary student moves closer and closer to abstraction, the need for prolonged use of materials decreases. All Montessori math lessons are presented first with the materials, but the upper elementary child quickly moves from concrete materials to abstraction. It is in this stage where practical application of mathematics is key. Montessori elementary students enjoy learning how math fits in the grand scheme of the cosmos. This includes studying ancient mathematicians such as Euclid, Pythagoras, Archimedes and Eratosthenes. They enjoy math puzzles such as The Sieve of Eratosthenes and Fibonacci sequences. They want to measure, construct, and recreate objects and recipes. They use their imaginations and their excitement to test theories in the Montessori environment. They are proud and astonished when they are able to solve complex mathematical algorithms such as square and cube root without the use of modern technology.

The Montessori environment is full of materials and lessons which inspire students to fully develop their mathematical minds. Unlike traditional schools, math is not feared in the Montessori environment. Concepts are internalized, not merely memorized. Children understand and master concepts before moving ahead in the Montessori curriculum. They are allowed opportunity to fully explore and understand on their own time rather on than on the timelines of others.

As much as possible, NAMC’s web blog reflects the Montessori curriculum as provided in its teacher training programs. We realize and respect that Montessori schools are unique and may vary their schedules and offerings in accordance with the needs of their individual communities. We hope that our readers will find our articles useful and inspiring as a contribution to the global Montessori community.
© North American Montessori Center - originally posted in its entirety at Montessori Teacher Training on Wednesday, April 21, 2010.