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The Montessori Curriculum: 

Mathematics

“Actually, a child has only a sensible appreciation of these proportions, but his mind is trained on the basic data that prepares the way for mathematics.”

-Maria Montessori 

The ancient philosopher, Pascal, said, “Man’s mind is mathematical by nature and that knowledge and process (how we understand things) comes from accurate observation.” The child is an observer. The child is an explorer. The child is a thinker. The child is a discoverer. The child is an inventor. The child is an intellectual being filled with potential and promise, moving through life with the mission of perfecting the self and mastering the world. From his/her earliest days, the child’s mind absorbs the environment, making connections, processing, reasoning, and analyzing. As the child grows in age and wisdom this mind refines and sharpens. The reasoning, processing and analyzing become more conscious and the mathematical mind is awakened. 

Mathematics is essentially a science of structure, order and relationships. It includes logical reasoning and quantitative analysis. It helps to understand and reveal the natural world. Galileo said, “Mathematics is the alphabet with which God has written the universe.” Mathematics as a science evolved with the human race. As ancient humans became more conscious of the world and more aware of their faculties of intellect, they mastered the world around them and began to understand the organization and forces of the universe. Mathematics was a serendipity, an accidental or unexpected discovery of something good. The same is true for the child in the Montessori environment. Mathematics becomes a natural discovery of the order and structure of the universe, based on a concrete understanding of the world and evolving into an abstract means of understanding and organizing the world. 

Maria Montessori believed that the child possesses the ability, even at a young age, to begin the process of reasoning and analysis for mathematics. The basis of mathematics actually begins in practical life, with the emphasis on order and process. This helps the child to refine and develop those essential building blocks that will allow the reasoning mind to work and make inner connections. The sensorial curriculum also helps to train the child’s mind to notice and differentiate between size, shape, and dimension. It enables the child to think conceptually and systematically thus building the concepts that will lead to abstract thought and analysis. 

The Montessori Math Curriculum, like all other curriculum areas, follows a logical, systematic sequence of order. It follows the needs of the child at each level and provides not only the needed skills, but also supports the mathematical potential within each child so that mathematics becomes one strand of an integrated, holistic curriculum to reveal the creative spirit within.

Preprimary

In the preprimary environment, the mathematics curriculum begins with concepts of quantity and symbol for numbers 1-10. Quantity is explored first followed by symbol. Sets of ten are introduced, initially as an established whole with the numerical rods and then as individual parts of a whole with materials such as the spindle boxes and cards and counters. These concepts of 1-10 are expanded into the decimal system, where the child sees the relationship of units, tens, hundreds, and thousands in the composition of numerals and quantities. The golden bead material aesthetically attracts the child, but also gives the child a concrete view of the decimal system and the growth of numbers. This foundation paves the way for the introduction of the operations (addition, subtraction, multiplication and division). These operations are investigated with a variety of materials, engaging the senses and giving concrete understanding of quantity and the relationship of numbers. The materials aid in an understanding of how the process works in each operation, as well as helping with memorization of basic facts. At the same time the child is introduced to materials involving linear counting, showing the growth of numbers in teens and tens, as well as applying the knowledge of squares and cubes. As the child grows in confidence and ability the materials change, becoming less concrete and more abstract, allowing the child’s mind to move to higher levels of thinking and understanding.

Elementary

The solid foundation of mathematical concepts in the preprimary environment enables the elementary child to continue this exploration of mathematics as a discovery of truths and an opening of understanding. The experience in elementary is one of helping the child to continue to move from the concrete to the abstract and continuously build the mathematical mind. The math curriculum is multi-dimensional and material-rich with an emphasis on problem solving and working through the steps of how mathematics works. Many of the same materials from preprimary continue to be used in the elementary environment. They remain concrete in form so that the mathematical concept becomes clear and through time is “imprinted” on the intellect. As mastery of skills occurs the materials become less concrete and more abstract. Manipulation of a three dimensional material is followed with two-dimensional representations such as drawing a diagram to show what is happening. The goal is to build skills for the final step of abstraction, using just numbers to work through the math. The basic mathematical operations continue to be honed and mastered. Fractions and decimals are also introduced as well as mathematical applications such as measurement, money, time, and graphing. Project work is also introduced in elementary. This allows for cross curricular connections between math and science or math and history. It also helps to develop independence, leadership, and life skills.

Adolescent Program

The mathematics program in middle school transitions the child to prepare for high school math. The sensorial math materials used in elementary are no longer necessary, as the mathematical mind now functions abstractly and an emphasis on algebraic thinking and reasoning becomes important. The math program is more “traditional” in nature with the curriculum following a math textbook. There are essentially two “tracks” for mathematics in middle school. There is an “on-level” track which has a student taking 7th level math their first year and 8th level math their second year. The “advanced” track has students taking pre-algebra their first year and Algebra I their second year. This allows for various levels of math to be accommodated and ensures that students leave GSCM with a solid foundation of basic math skills. Even though the math now is more abstract, there is still a measure of concreteness as real-life applications are made when possible. Students spend time outdoors measuring and collecting data. Students build roller coasters and calculate speed, trajectory, and rate. Students sew geometric pillows to demonstrate reflection and rotation. In addition, math skills are utilized during gardening and workshop as part of ErdKinder. Math careers are explored in micro-economy as well as such topics as budgeting and banking.

“The mathematical mind is a mind which is especially interested in mathematics. Instead of finding mathematics idiotic and absurd, it finds them interesting and absorbing. It is a fact that most of the children in our Montessori Schools do achieve great enthusiasm in doing mathematics. It is the preparation of their minds which enables them to derive this pleasure.”

-Maria Montessori

The Montessori Curriculum:

Sensorial

“The training and sharpening of the senses has the obvious advantage of enlarging the field of perception and of offering an even more solid foundation for intellectual growth. The intellect builds up its store of practical ideas through contact with, and exploration of its environment. Without such concepts the intellect would lack precision and inspiration in its abstract operations”

-Maria Montessori 

Throughout history, humans have pondered the question of “What is the essence of humanity?”—What makes us unique and defines our nature?  One of the most comprehensive and researched explanations comes from Mortimer Adler in his book Intellect.  In this book, Adler explains that we, as humans, possess a “spiritual” intellect, which allows us to think conceptually.  This ability of conceptual thought separates us from the other primates, whose highest power is perceptual thought.  He states:  “Only in man does mind rise above matter or over matter, by virtue of man’s having a mind that has intellectual as well as sensitive powers, conceptual as well as perceptual thought, the power to think about what is perceived and totally imperceptible.”

Humans possess this spiritual quality and the potential for conceptual thought at the moment of conception.  However, the manifestation of the ability to think conceptually comes as part of a natural growth and development. Maria Montessori, being both a scientist and a philosopher, realized the intricate connection between mind and body.  She observed that man’s spiritual powers are exercised and connected to the material world through the physical body, particularly the senses.  She observed, in children, a natural tendency to explore and investigate the physical world, as the tangible means of perfecting and forming the self, the personality, and the intellect. 

Montessori advocated a “training of the senses” for the young child, as was utilized by the educators Itard and Sequin.  She recognized that the concrete experiences of the senses were the foundation of and the critical link to the development of the human intellect and abstract thought.  

This belief supported the philosophical maxim of Aristotle:  “There is nothing in the intellect which was not first in the senses, but it exists in the intellect in a different mode from the senses.’

Montessori’s goal with sensorial education was not to measure the senses of the child, but rather to exercise and develop them so that the child can build up and store a mentality and a personality to think conceptually, systematically observe the world, and adapt to that world as an individual within a greater community.  This essential work of the child is the essence of humanity.  Thus, the child virtually innovates humanity.  The child is a being unlike any other that absorbs the whole of his/her world and fits it together into a human personality that sustains and supports civilization. However, the child can only develop these capacities to their highest potential if the child’s environment provides the means and structure necessary for the rational and orderly acquisition of the sense stimuli.

The Sensorial Area is an integral part of the pre primary environment. Although it is not a specific area in elementary or adolescence, sensorial education continues specifically in the math and geometry areas, expanding the child’s mental capacities, building the mathematical mind, and inviting the child into reason, verbal expression, and interconnections. 

Preprimary

The Sensorial Area is visually striking in the preprimary environment. Many iconic Montessori materials are featured: pink tower, brown stair, knobbed cylinders, color tablets, geometric solids, etc. The materials and lessons are designed to engage the child’s five senses and help the child discriminate, classify, clarify, and understand the outside world. The sensorial materials are divided into six categories: size, form, color, tactile, gustatory, olfactory, and auditory. The sensorial materials isolate one quality at a time, so that the child can focus his/her attention and hone in on one skill at a time. This is called isolation of difficulty, which encourages focus and concentration. In addition, the sensorial materials have an internal control of error. The material is designed to show the child when an error is made, so that the child self-corrects and continues to develop independence and self-motivation for learning. The sensorial materials are beautifully constructed, usually from wood, which attracts the child and instills an appreciation for beauty.

Elementary

The sensorial foundation of the preprimary environment trains the child’s mind and body to access and appreciate both the Math and Geometry curriculum in elementary. Whereas the Sensorial Area of the preprimary environment strove to train the child’s visual sense to recognize and categorize shape and form, the Geometry Area of the Elementary Environment strives to bring that sense of shape and form into a conscious level, thus training the child to use his/her growing Mathematical Mind to order, name, classify, and identify the world of reality—both natural and man-made. The didactic materials are still used in order to draw the child into the reality and continue to form that impression and “point of departure” for abstract thought.  However, in the elementary Mathematical and Geometry Areas, the child’s imagination is now drawn upon, and questioning and problem solving occupy a large majority of the child’s time and attention.  The materials draw upon the imagination and become an impression of higher realities and abstract thought. 

Adolescent Program

Following their unit on Transformational Geometry, 8th level students apply the concepts by designing and sewing a keepsake pillow.  First, they choose a shape that can be slid, rotated or reflected and create a template.  Next, shapes are cut out of colorful fabric and carefully sewn onto a larger pillowcase-sized fabric.  Finally, the entire case is sewn closed around a pillow form.  Creating this pillow is a reminder of the lessons and their classmates, and a way to bond and participate in the age-old tradition of a sewing bee. Not only does this reinforce mathematical and geometric skills, it ties in practical life for the adolescent. They create a useful product with their own hand. 

“A child who works spontaneously and for a long period of time with this material not only strengthens his reasoning powers and his character, but acquires higher and clearer cognitions, which increase his mental capacity.  In his succeeding spontaneous flights into the abstract he will show ability for surprising progress”

-Maria Montessori

The Montessori Curriculum: 

Practical Life

“Through practical exercises…the children develop a true “social feeling,” for they are working in the environment of the community in which they live, without concerning themselves as to whether it is for their own, or for the common good.”

-Maria Montessori 

Maria Montessori often described her approach to education as a “help to life.” She recognized that education is not about the mere transmission of knowledge, but rather a means to aid the child in the formation of self and bring about the transformation of the world within the context of family and community. Montessori designed an area of curriculum called “exercises of practical life.”  These were activities and materials designed to put the child in touch with the environment and refine those movements and skills that are essential to the establishment of culture and the building of relationships within the community. 

The activities of daily life are what sustain us as a human community, build our cultural norms, connect us with our environment, and continue to evolve us as a human society. They not only enable us to meet basic human needs, but also build the foundation for the human personality. The young child has an absorbent mind that takes in the environment and enables the child to build his/her intellect, control the will, refine movements, and recreate behavior patterns of the community. As the child grows, the absorbent mind develops into the mathematical mind, one that is capable of reason and higher order thinking. Exercises of practical life at this stage highlight how the human person lives and works within the social constructs of society. The child becomes part of the ongoing human narrative, the progressive incarnation of God’s plan for humankind and the establishment of the Kingdom of God. 

Practical life is a cornerstone of the Montessori environment. It provides the means for the child to develop the core foundations of the inner self, as well as the structure to live and work within the community. Practical life could be called the foundation of life, culture, and community. 

Preprimary

Practical life in the preprimary level focuses on developing order, concentration, coordination, and independence. It includes such exercises as spooning, washing, pouring, and sewing. These works help develop both large and small motor skills as well as the interior skills of a centered self, capable of working and focusing for various periods of time. The young child is in a sensitive period for “real” activities that build essential skills and enable one to gain more and more independence and self awareness. Practical life activities are categorized into the following areas: Care of Self, Care of the Environment, Control of Movement, and Grace and Courtesy. These lay the foundation for the work cycle and all academic skills.

Elementary

Practical life in the elementary level moves from individual activities of building skills to all the “practical” procedures that help the community function daily: caring for the environment, community service, designing schedules, maintaining schedules, organizing materials.  Some of the same activities from preprimary can be extended with more skill development such as quilting, knitting, cooking, etc. They can also be part of larger cultural projects.  

Elementary students are becoming more aware of social constructs and the ways in which a community functions. 

For this reason lessons of grace and courtesy are extended  and more complex social skills are often directly taught, modeled, and practiced. This often happens “in the moment” or as part of a social/emotional curriculum. 

Adolescent Program

Practical life in the adolescent environment expands further to include ErdKinder, committee work, farm chores, and class trips. Montessori believed that the adolescent is again in a sensitive period for “real” work that contributes to the community and begins to develop life skills in the transition to adulthood. They help to valorize the individual and begin the process of discernment of one’s vocation and specialized skills. 

ErdKinder includes experiences with woodworking, gardening, and microeconomics. The adolescents across these groups work together to help organize and run a school store that gives experience in running a business and maintaining an economy. Committee work gives the adolescent an opportunity to make choices and practice leadership and cooperation not only within the middle school, but also to the school and greater community.

“Everything must be taught, and everything must be connected with life; but this does not mean that the actions which children have learned to perform and to integrate with their practical lives should be suppressed or directed by us in every detail. This integration of his actions is one of the highest efforts that a child can make.”

-Maria Montessori

The Montessori Curriculum

Revealing the True Child

“It is not true that I invented what is called the Montessori Method. I have studied the child, I have taken what the child has given me and expressed it, and that is what is called the Montessori Method.”

-Maria Montessori 

Maria Montessori, with her scientific perspective on the world, and her passion for social change and the advancement of humanity, recognized the unique spiritual and educational  hunger of the child and set about to discover the true nature of the child. She took a unique stance before the child, the role of prophet and servant. She stood before the child and heard the call to listen deeply and share God’s message to the world–to help the world understand and recognize the child as the creator of man and at the same time to help the child understand the world as an ordered cosmos, revealing God’s love for humankind and one’s cosmic task to be a steward of creation and a citizen of the world.

Maria Montessori, therefore, advocated a cultural, cosmic education for the child.  She advocated an education that gave the child a vision of the unity of all Creation as an expression of God’s light and love. She wanted an education that not only gave the child a vision of the whole universe, but also gave the child the framework with which to build his/her personality.  Her goal was not the transmission of facts, but rather the holistic development of the individual.  She viewed education as the means of developing the potential human being within.  Every human being has a need and desire to be part of the human family and be integrated into his/her own culture.  All of life is a continuous acquisition of culture based on life experience.  It is a continual revelation of the “there-ness” of God in all of Creation and the presence that God has had and continues to have in the ongoing creation of the world.

“This plan of cosmic education…is no new idea, for it has been the natural plan wherever there has been education in the real sense of the word…Let us give the child a vision of the whole universe…an imposing reality and the answer to all questions.  We shall walk together on this path of life, for all things are part of the universe, and are connected with each other to form one whole unity.  This idea helps the mind of the child to become fixed, to stop wandering in an aimless quest for knowledge.  He is satisfied, having found the universal center of self with all things.”

-Maria Montessori