Think about the jobs that existed ten years ago that don’t exist today. Now think about the jobs your child might hold that don’t exist yet. The world is changing faster than most school curriculums can keep up with and that raises a real question for every parent: what are we actually preparing our children for?
As educators it is imperative for us to look towards the future to ensure that our children have the skills to think, build, and lead. Fortunately, Dr. Montessori created a model over 100 years ago that provides a strong foundation for executive functioning skills that will help our children do just that.
The answer isn’t solely in academics or test scores. It’s something deeper: the ability to think flexibly, manage yourself, solve problems, and keep going when things get hard. These are what researchers call executive functioning skills, and they may be the most important thing a child can develop.
What Are Executive Functioning Skills?
Executive functioning refers to a set of cognitive processes, primarily working memory, inhibitory control, and cognitive flexibility, that help us coordinate thoughts and actions to reach our goals.[1] These skills also support the ability to plan, organize, emotionally regulate, and take initiative.
Unlike specific facts or formulas, these skills transfer. Research has repeatedly shown that executive functioning predicts educational outcomes above and beyond measures of intelligence or prior academic ability.[2] A child who can regulate their frustration, think through a problem from multiple angles, and manage their time doesn’t just do well in school — they’re equipped for life’s challenges and opportunities.
Why Starting Early Matters
Executive functioning skills develop rapidly in early childhood and continue maturing throughout adolescence.[3] The brain’s prefrontal cortex — the hub of executive functioning — is highly responsive to environment and experience during these years, which means the conditions we create for children genuinely matter.
Notably, research has found that working memory at age 5 is a stronger predictor of later academic performance than IQ.[4] This looks different at each level here at Greenspring. For instance, toddlers begin to count and set out plates for their peers. In Children’s House, students are building on their foundation, following complex, multi-step sequences that require them to retain detailed information. In Elementary and Adolescence, our students manage their own work journals, keeping track of where they excel and where they have room for growth. They are all, in very real ways, building new neural pathways and skills that will last a lifetime.
Scaffolding these skills early doesn’t mean pushing children before they are ready — it means creating the right environments with meaningful choice, appropriate challenges, and the freedom to learn from their mistakes.
How Montessori Builds Executive Functioning Skills
A study published in Science found that children in Montessori programs showed significantly greater gains in executive function, reading, math, vocabulary, and social problem-solving compared to peers in conventional schools.[5] A 2023 systematic review of 32 rigorous studies confirmed these findings, reporting that Montessori students showed higher executive functioning than peers in traditional schools.[6] Most recently, a national randomized controlled trial of 588 children across 24 public Montessori programs found that Montessori students scored significantly higher in executive function, reading, memory, and social understanding by the end of kindergarten.[7]
Our Guides thoughtfully look at Dr. Montessori’s curriculum to ensure that children at all levels are developing executive functioning skills such as:
Working Memory
Cognitive Flexibility
Sustained Attention
Inhibitory Control
Task Initiation
Planning
Prioritizing
Organization
Time Management
Self- awareness
Emotional Regulation
This is no small undertaking! A Young Toddler learning to return a material to its place is practicing order and self-regulation. A Lower Elementary student choosing how to spend their work cycle is practicing planning and prioritization. An Adolescent navigating a multi-week research project is practicing every executive functioning skill at once. The work looks different at every level — but the intentionality is the same.
Preparing Children for a World We Can’t Predict
Researchers have identified creativity, flexibility, self-control, and discipline as the four qualities children will most need to thrive in the future — all of which are rooted in strong executive functioning.[8] We can’t know exactly what challenges our students will face in 10, 20, or 30 years, but we can give them the inner tools to meet those challenges with confidence.
[3] Garon, N., Bryson, S. E., & Smith, I. M. (2008). Executive function in preschoolers: A review using an integrative framework. Psychological Bulletin, 134(1), 31–60.
[4] Alloway, T. P., & Alloway, R. G. (2010). Investigating the predictive roles of working memory and IQ in academic attainment. Journal of Experimental Child Psychology, 106(1), 20–29. Cited in: Promoting Executive Function Skills in Preschoolers. Frontiers in Psychology (2021). https://doi.org/10.3389/fpsyg.2021.720225
[6] Randolph, J. J., Bryson, A., Menon, L., Henderson, D. K., Kureethara Manuel, A., Michaels, S., Rosenstein, D. L. W., McPherson, W., O’Grady, R., & Lillard, A. S. (2023). Montessori education’s impact on academic and nonacademic outcomes: A systematic review. Campbell Systematic Reviews, 19, e1330. https://doi.org/10.1002/cl2.1330
[7] Lillard, A. S., et al. (2025). A national randomized controlled trial of the impact of public Montessori preschool at the end of kindergarten. Proceedings of the National Academy of Sciences. https://doi.org/10.1073/pnas.2506130122
[8] Diamond, A., & Lee, K. (2011). Interventions shown to aid executive function development in children 4–12 years old. Science, 333(6045), 959–964. https://pmc.ncbi.nlm.nih.gov/articles/PMC3159917/
Rich oral language is a building block for strong literacy
Learning to be – this is every toddler’s goal. It is both simple and richly complex. Between the ages of 2 and 3, the child is newly aware of possessing their own identity separate from their family, and they are ready to truly be that person, with full independence.
A critical element of this self-realization is the ability to communicate. The toddler is beginning to understand conversational language and they are working to express their own thoughts, experiences, and feelings. They are yearning to label every object in their environment and know every detail of the work they find in the classroom. They are reaching for the words to seek help effectively in moments of struggle. In the Montessori method, we approach the toddler’s sensitive period for learning oral language strategically to help ignite their understanding of language and the world.
Developing Skills in the Toddler Classrooms:
Attention
Auditory memory
Indirect preparation for written language
Self-confidence with increased vocabulary
Early conversation is essential for child development
One of the most crucial elements of a toddler’s journey in language is conversation. In Montessori, we believe that the most powerful way to learn a skill is through practice, and conversations provide the ultimate “learning by doing” experience. The conversations that toddlers have with adults in the classroom provide them with richness – the knowledge that they are respected and seen, they feel valued for their opinions and feelings, and an opportunity to practice articulation with someone who can echo words back to them with exact pronunciation. These conversations provide them with a model of conversational etiquette and flow. It is through conversation that the young child learns the confidence to express their heart. Through this process, toddlers learn the functions of conversation—conflict resolution, self-expression, storytelling, clarification, and so on. In the Montessori classroom, we aim to converse with children throughout the morning—upon arrival, between a child’s tasks in the work cycle, and especially at the snack table. Any item in the room, event in our day, or thought from a child becomes a worthy and captivating topic.
Directive vs Expressive Language
Conversations between adults and children are spontaneous and natural in our Toddler classrooms, with the adults focusing on receptive and expressive language. Receptive language refers to what children can understand, such as following directions. Expressive language refers to what they can communicate with words and/or gestures. Adults minimize directive language (e.g., “Put your shoes here. Sit down. Wipe your nose.”) to provide space for meaningful, rich conversation.
The gift of music
We also use poems and songs to introduce new language to children. Rhythm and cadence can help children hear words more clearly. Poetry and music can also bring concepts to the child’s mind in a manner that connects them with his heart. We often give toddlers the option to sing or review poetry as a group, and these activities are available in the classroom for individual work or lessons.
With all these language tools in his belt, the toddler is ready to take on the world and build himself into the world citizen that he was meant to be. He will take with him all his accurate knowledge, confident self-expression, and the songs in his heart, and will approach the world with compassion and curiosity.
Speak clearly and truthfully to the child
Accurate language is another crucial tool for building a toddler into an effective communicator. Children create themselves from the tools they are given, so it is fundamentally important to communicate with children clearly and accurately. As we model speech, we enunciate as precisely as possible, and echo back correct pronunciation of the child’s mispronounced words in natural conversation. Beyond enunciation, we strive to give the child exact names for the elements of his environment and a detailed understanding of his world. In our Montessori environments, we provide children with exact names for every item in our environment, and for each of its parts. Baskets on the shelfs contain unique pictures and objects, exposing the children to new and interesting things.
Additionally, true stories give toddlers a unique learning opportunity. They provide details about the world the child would not otherwise have, as well as an understanding of the concepts of beginning, middle, and end. These stories help children understand how life happens in the real world – an understanding that they desperately crave. We also gift children with the opportunity to tell their own stories. Nothing is more beautiful than hearing the story about his baby sister that he is bouncing in to tell us. Storytelling is a daily part of our community life, and anything can serve as inspiration, from our family and friends to our breakfast.
Toddlers have a need to understand the world, and part of that is learning to differentiate between facts and opinions. In our classroom, we introduce both concepts on a daily basis. We let the child know that the details provided in lessons are facts, and ask them what they think of pictures in books. We help them understand the difference between those true details learned in lessons and the opinions that are expressed.
Learn more about our Toddler Program
Our Toddler Montessori Program serves children ages 18 months to 3 years at Greenspring Montessori School. Click here to learn more.
Whether you are first beginning your Montessori journey with your toddler or you have been involved with the Montessori community for years, having an independent child at home may be a goal of yours. This blog post will walk you through age-appropriate activities for your children at home. In school and at home, it is important for your child to be doing work that is challenging and meaningful. Even as a young toddler, it means so much when they know their work is helping others and they are contributing to their community. As your child gets older, they can do progressively harder tasks around the house. Just remember this Montessori philosophy – let your child try to do for themselves, and resist the urges to swoop in and correct what they’ve done. As they practice, they will get better and feel good about how they have helped.
Household Contributions by Age
Contributions for 2-3 year olds
Dust off end tables, TV stands, and wherever else they can reach safely
Help set table
Clear dishes from the table
Help cook
Put clothes in a hamper
Pick up toys
Wipe up small spills
Sweep and mop floors
Wash windows
Water plants
Feed pets
Contributions for 4-6 year olds
Make bed
Fold laundry
Put their own clothes away
Help put groceries away
Set and clear table
Begin making simple meals (eggs, oatmeal)
Learn to use the stove
Make own snack
Wash dishes or empty the dishwasher
Sweep and mop floors
Vacuum small rooms
Assist with raking the yard
Empty trash and recycling
Contributions for 7-9 year olds
Cook more complicated meals, such as a pancakes or scrambled eggs
Plan menus
Pack own school lunches
Load/unload the dishwasher
Wash dishes
Walk the dog
Train pets
Clean their bedroom
Use the washer and dryer
Sort and fold laundry
Fill the bird feeder
Sewing projects
Contributions for 10+ year olds
Clean the bathroom sink, tub, and counters
Fully clean the kitchen
Cook full meals
Take out trash and recycling
Wash and vacuum the car
Mow the lawn
Ironing
Use tools to fix things around the house
Plan and lead outings
For more information on household contributions for your child, please take a look at these articles:
A group of Lower Elementary students share their work with their classmates.
Montessori Mastery: A Learning Process for Life
Students are best motivated to learn when they work on something of their own choosing, at their own pace, and until they determine that they know. But is this realistic in the classroom setting? Can we really expect students to know what they want to pursue, stick with it, and then demonstrate mastery?
Many of us who grew up with a conventional school education had a very different experience: the teacher would enter the classroom with the day’s lessons all planned to be delivered in defined blocks of time within the boundaries of the regular school day hours. The next day was more of the same. Everyone would receive the same lessons at the same time, regardless of interest, readiness, or need for practice to solidify newly presented material. Content was presented in a prescribed curriculum administered by adults. Various quizzes and tests were given within a specified time period to determine whether or not newly presented material was understood. Regardless of the test results, the curriculum moved forward.
One major problem with this approach is that it does not take into account the students. Not all students are interested in the same thing at the same time, nor are they always ready for the same work because they are in the same class. There is a growing body of research that confirms the significant role that choice plays in student motivation and learning. Sue Grossman Ph.D. states strongly in her article, “Offering Children Choices: Encouraging Autonomy and Learning While Minimizing Conflicts,” that, “giving children choices throughout the day is beneficial, even crucial to their development.”
So, how do we change the system?
Montessori is intentionally and appreciably different than conventional models of education. Montessori is a developmentally based approach, in which choice has always been a critical element in our work with students. We cannot force a student to learn. We can create an environment, rich with resources and hands-on materials, that encourages autonomy and independence. We can offer lessons, observe students, and work with them to ensure their progress. We can model, demonstrate, establish and maintain high expectations for engagement and accountability. Ultimately, it is the students who takes ownership of and responsibility for their own learning.
In the words of Dr. Maria Montessori, “Education is a natural process carried out by the human individual, and is acquired not by listening to words, but by experiences in the environment.”
Guiding a class of curious young students, each of whom is making individual choices about what he or she is working on, is no easy feat! How do we support individual interests and pursuits while also ensuring that skills are practiced and expectations for high quality, polished work permeate? We have at our disposal a deep understanding of the developmental needs of the students, uninterrupted work periods where we are available to provide lessons, observe practice, meet with individuals, and offer an abundance of beautiful, engaging materials with which to engage students.
Breaking down the process
A key technique we utilize to present information to students is called the three period lesson. Regardless of the content being introduced, this framework supports on-going work for individuals and groups of students as they move from observation to active manipulation and application, and finally to deep understanding and mastery.
Ms. Shweta gives a lesson to a Children’s House student on a short bead chain.
The first period: An introduction
During the first period, the Guide presents a new skill, idea, or story to a student. Depending on the developmental needs of the student this presentation may be short and precise: “This is blue.” It may be a naming period where vocabulary is introduced. For older students the first period may be the sharing of an impressionistic story such as The Story of the Universe, where just enough information is conveyed to inspire wonder and awe, and the story itself becomes the springboard for further exploration. This first period is presented in such a way that the students leave curious, excited, and motivated to engage with the work. A Toddler works independently, exploring types of insects—an example of the second period of the lesson.
Second period: Thorough investigation
The length of time a student spends manipulating, exploring, questioning, and repeating newly presented lessons is not determined by the Guide, but rather by the interest and drive of the student. This period of deep engagement is known as the second period of the lesson. It is the longest and most important part of any lesson. Students are not rushed to complete a task or to prove they have mastered a new skill. Instead, students are encouraged to become thoroughly immersed in their work. For younger students, this usually involves repetition until new skills and concepts are internalized. A student may sort, match, name, and paint with all shades of “blue.” Older students may choose to explore the three states of matter, gravity, the composition of the earth, or formation of mountains after hearing The Story of the Universe. When students freely choose topics that interest them, motivation comes from within and kindles their natural desire to learn. They are learning for learning’s sake, and their drive is ignited.
Curiosity begins with questions and is fed by on-going investigation, discovery, and the sharing of ideas. As older students dive into self-chosen research topics, they rarely work in isolation. Learning is infectious! Students not only enjoy sharing what they are learning, but also invite critical feedback from their peers as they bring their research to completion. Learning to give and receive feedback supports whole-class collaboration. Students encourage one another by giving descriptive feedback that is kind, specific, and helpful. Engaging in the critique process often inspires multiple revisions, encourages further opportunities for developing listening and speaking skills, builds student confidence, and leads to amazing polished work. There are no limits when students share, exchange ideas, and support each other. Expectations for deep engagement and high quality product are modeled and reinforced by peers with the overarching goal being the creation of beautiful work.
Two Adolescent students teach a group of Children’s House students how food scraps are used to make compost.
Third Period: Demonstration of Knowledge
So, how do we know when the students know? Third period activity is unmistakable with young students. They show us they know by spontaneously teaching their peers! Newly acquired skills are applied directly in daily activity, whether it is to identify the color blue or by helping a classmate put on her jacket. For older students the third period is manifest in myriad ways. Students know when they are ready to present their work. They have spent time revising and practicing, speaking clearly, making eye contact, fielding questions from an audience, and graciously receiving feedback. They have become “experts” in their topic. Presentations may include a skit, a song or poem, a video, or a model built to scale.
The final facet of the third period for older students is reflection. Students analyze the learning process from start to finish: “What went well?” “What were the challenges and how did I learn from them?” “What would I do differently next time?” Self-reflection inspires ownership of learning. Students are accountable to themselves. They not only begin to understand themselves as learners, but also how to tackle obstacles, work with others, accept feedback, and build the muscle they need to continue learning. John Dewey went as far as to say that “We do not learn from experience…we learn from reflecting on experience.”
Two Children’s House students explore the different types of leaf shapes, veins, and margins.
At Greenspring Montessori, students are encouraged to dive into their work wholeheartedly—to make mistakes, and to learn from them. “That’s how learning in a Montessori classroom works – not by memorization, or simply listening to a teacher at the front of a classroom, but by doing.” (threetree.org)
Yes, we do expect students to know what they want to pursue, stick with it, and then demonstrate mastery. They demonstrate this every day, with gusto and an insatiable appetite for more!
As emerging adults, it is crucial that adolescents learn and grow in an environment that matches their development as well as gives insight into the time in which we live; we must improve each individual to improve society.
Dr. Montessori calls the Erdkinder the “school of experience in the elements of social life” where work is an introduction to both nature and civilization and provides a limitless field of scientific and historical studies. Adolescents work through experiences on the land: growing crops and caring for animals. They also run a shop where they buy and sell produce and handmade items, promoting personal craftsmanship over mass production. This allows them to fully engage with the two main independences indicative of this developmental stage: social and economic. The shop becomes a general meeting place for their extended community where they take responsibility for the corresponding financial and moral obligations associated with running their own business.
Adolescents volunteer with Real Food Farm in Baltimore City, growing fresh produce for communities in need.
An Adolescent organized a service project to clean up the Jones Falls waterways.
Throughout their educational studies, they meet with experts from various fields as they study the earth and living things, human progress and the building up of civilization, and the history of humanity. They will build a library of atlases, primary documents, and other resources that highlight the connection between peoples and cultures throughout time. They explore scientific progress in biology and chemistry through individual or small group projects that are related to the land whenever possible. All curriculum areas are interrelated and these connections are consciously discussed. This also includes self-expression: music, language, and the arts and the development of the personality that entails ethics, mathematics, and modern languages.
Adolescents learn water conservation from indigenous farmers in Arizona for their Spring Odyssey.
Adolescents clear brush on an Arizona farm.
Adolescents are brought closer together by their work on the land throughout the year.
Within this framework, the moral and physical care of the students is also a priority as they face difficult physical and emotional transitions. They must be provided with work that is in the open air of nature, promoting plentiful and nourishing food that is their own produce whenever possible. A space that allows them to peacefully reflect and meditate when the psychological characteristic of decreased attention takes hold. They learn about nutrition and how to properly care for themselves as they discuss health and wellness topics with adult role models that guide them towards informed decision-making. There is a division of labor, which leads to a genuine cooperative community. They are diplomatic in their acceptance of other’s points of view through Socratic discussions.
Adolescents learn about the Chesapeake Bay watershed while fishing and living on a boat for their Fall Odyssey.
Work on the land provides natural consequences unmatched by any other environment. The plethora of studies inspired by the land also provides a true understanding for the range of careers available today; our wide and thorough education grows their professional interests so that they can take part in the science and technological applications being used to understand and solve the complex problems of our times. The land also provides the right type of freedom where they act on individual initiative within clear limits and rules that results in the self-discipline necessary for success. Our students will know how to put things right: how to adjust a machine, mend a broken window, build a shed, forge a path, and that most importantly, that they can be self-sufficient.
An Adolescent makes field notes on a Maryland native plant garden.
Schools today do not offer this essential balance of manual and intellectual work, leaving adolescents unprepared for taking an active role in society. Our environment acknowledges that these two kinds of work complete each other and are equally essential to a civilized existence and is designed to balance them so adolescents gain a clear understanding of the society for which they are about to join, one that demands a personality of character that adapts quickly and easily.
In order to emerge into the final plane of development, maturity, adolescents must be made to feel capable of succeeding in life by their own efforts and merits. Montessori reminds us that when adolescents’ needs are met within this framework, they can then provide humanity with the clues and hope for future progress.
“The hand is the pathway to the brain.” – Dr. Maria Montessori
It may be hard for some parents to believe, but all children have the ability to really enjoy learning math. In Montessori classrooms, mathematics are introduced to children at 3 to 6 years old, enabling the child to form positive associations with numbers to be carried on throughout life. Scientific research supports that the key to developing this positive relationship early is to provide the child with hands-on experiences [source – https://www.hand2mind.com/resources/why-teach-math-with-manipulatives]. Dr. Maria Montessori demonstrated that if a child has access to concrete mathematical materials in their early years, they can come to their own understanding of the concept much faster than if introduced in an abstract form at a later age.
Think back to your own experience as a young student. Most of us learned math in school by memorizing the steps required to solve a problem. For example, when learning to “borrow” in subtraction, we learned to slash through one number and write another number above it, add a tiny number one in front of the number to its right, and then continue with the problem. Many of us learned how to do this without ever really understanding why we were doing it or what it meant. Yet for Montessori students, those mathematical symbols represent very concrete ideas that they have physically manipulated; they fully understand what they mean, how they work, and why.
At a certain point in development, usually around the age of 4, the child enters the sensitive period for numbers, and the child’s mathematical nature awakens. She graduates from purely sensory explorations to interest in specific measuring and counting. Once begun, the child progresses through the math materials sequentially. Montessori materials are scientifically designed to meet the child where they are, allowing for independent exploration. The materials are made to be self-correcting, allowing the child to learn as they go.
So, what are some of the essential Montessori materials for learning math? Here are a few of our favorites:
The Pink Tower
One of the first materials a child encounters in the Children’s House classroom at 3 years old is the Pink Tower. While this material may look like basic building blocks of conventional preschools, it is designed very specifically to introduce the child to the quantity of ten as well as basic experiences of order, sequence, coordination, and precision.
The smallest cube measures 1 centimeter cubed, and the largest is 10 centimeter cubed. In this way, the Pink Tower introduces the concept of base ten, which is also present in other sensorial materials such as the Brown Stair. When beginning the activity, the child carefully takes each cube, one by one, to their work mat. As the child builds the tower from biggest to smallest, they are able to work independently to determine the right order. If they place a cube out of order, they will quickly discover the tower doesn’t look quite right. This control of error is present in all Montessori materials and allows for the child’s self-discovery.
The Red Rods
The Red Rods are comprised of 10 wooden rods differing in length. The smallest rod is 10 centimeters long, and the largest rod is 100 centimeters, with each rod increasing by increments of 10 centimeters in length. The shape, weight, and color of this material is alluring to the child, drawing them in to learn more.
The Red Rods are introduced to children at around 3 years of age after they have become familiar with the initial sensorial materials in the classroom, including the Pink Tower, Brown Stairs, and Knobbed Cylinders.Moving the Red Rods allows the child to perceive the differences in length and weight. The child also expands upon their basic language of mathematics by discussing length, size, and order.
The Number Rods
Children are naturally drawn to the Number Rods after mastering the Red Rods. They are the same dimensions as the Red Rods, however, each 10 centimeters alternates between red and blue, showing the visual representation of each unit. The child is introduced to the number symbols and they learn to associate quantity and symbol.
With this work, the child is not simply memorizing 1-10 to recite back. They are learning that each quantity is a separate entity, known as one to one correspondence.
The Golden Beads
The presentation of The Golden Beads gives a visual and a very concrete experience of the decimal system and place value. With this material, the child learns the terminology of units, then tens, hundreds, and thousands. The child can literally feel the heft of the thousand square and see visually the relationship between the unit bead and the thousand cube.
The use of tangible materials allows the child to tap into mathematical concepts much earlier than in a conventional education setting. By physically exchanging (ie, carrying ten ten bars to the shelf and trading it for a hundred square), students as young as four quickly learn that ten tens are equal to one hundred. Montessori students discover that the “square” of a number (10 squared = 100) is literally the shape of a square and the “cube” of a number (10 cubed = 1,000) is literally a cube.
The Bank Game
Once a child is able to build a visual representation of a number, the Golden Beads are used to add, subtract, multiply, and divide numbers into the thousands. When students start using this material, one subtraction problem may take 20 minutes! But because it’s physical, social, and interactive, it doesn’t feel like work.
Children are given real-life examples of math problems, such as dividing a sum between their peers. This is a way to introduce them to solving increasingly complex problems while still maintaining a playful approach. A five year old may learn to divide 6,540 three ways to share with their peers.
The Stamp Game
When a student is ready to progress to a new challenge, either in Children’s House or during Lower Elementary, they are introduced to the Stamp Game. Instead of holding a large cube that actually shows the relative size of one thousand as they did with the Golden Beads, they use a representational material. These small square stamps are all the same size, but are differentiated only by their color and number label represent units, tens, hundreds, and thousands. Like the Golden Beads, the Stamp Game material is used to teach all four operations, with children adding, subtracting, multiplying, and dividing into the thousands. The Stamp Game is still hands-on, but slightly more abstract that the Golden Beads.
Since the elementary age child now craves variety more than repetition, other hands-on materials, such as the Bead Frame, Checkerboard, and Racks and Tubes are also introduced for computing all four operations.
The Trinomial Cube
The Binomial and Trinomial Cubes are three-dimensional puzzles that are introduced to children at age 3 or 4. The Trinomial Cube is made up of 27 color-coded blocks which fit together in a very specific way. Assembling the puzzle uses the child’s fine motor skills and requires the ability to observe the different characteristics of each block. Like other Montessori materials, the Cube is self-correcting. When it is assembled properly, it forms a cube that fits back into the wooden box. While the primary aim of the Trinomial Cube is to build a puzzle, children only later discover that it is a concrete representation of the algebraic formula, (a+b+c)³. You may recognize this formula from your own school days, but very few of us had the opportunity to interact with it in such a hands-on material. Through this process of discovery, children are able to grasp a deeper understanding of mathematical concepts.
Moving into Mathematical Abstraction
When the student is ready, they are shown how to record their work with the materials on paper. The paper is used to record the process completed with the concrete materials.
Having started with the Golden Beads, moved on to the Stamp Game, and then the Bead Frame, Checkerboard, and Racks and Tubes, at some point during this progression through the materials, the child experiences an “Aha!” moment and is able to “see” the answer without using the materials. The student understands the process so well, she can see the materials and can compute the answer in her mind. This moment is always thrilling to observe. The student feels pride and a sense of accomplishment that can not be matched by any lecture or quiz.
These are just a few of the many Montessori materials that are utilized daily in the classroom. By laying the foundation in the 3-6 year classrooms, Montessori students are able to understand mathematical concepts earlier and utilize problem-solving skills with more complicated math in high school and beyond.
To learn more about Mathematics materials in the Montessori classroom, take a look at this webinar from Greenspring Children’s House Guides, Lydia Farmer and Emily Shattuck – The Magic of Children’s House.
One of the first materials a child encounters in the Children’s House classroom at 3 years old is the Pink Tower. While this material may look like basic building blocks of conventional preschools, it is designed very specifically to introduce the child to the quantity of ten as well as basic experiences of order, sequence, coordination, and precision. 
The Red Rods are comprised of 10 wooden rods differing in length. The smallest rod is 10 centimeters long, and the largest rod is 100 centimeters, with each rod increasing by increments of 10 centimeters in length. The shape, weight, and color of this material is alluring to the child, drawing them in to learn more. 
Children are naturally drawn to the Number Rods after mastering the Red Rods. They are the same dimensions as the Red Rods, however, each 10 centimeters alternates between red and blue, showing the visual representation of each unit. The child is introduced to the number symbols and they learn to associate quantity and symbol.
The presentation of The Golden Beads gives a visual and a very concrete experience of the decimal system and place value. With this material, the child learns the terminology of units, then tens, hundreds, and thousands. The child can literally feel the heft of the thousand square and see visually the relationship between the unit bead and the thousand cube.
Once a child is able to build a visual representation of a number, the Golden Beads are used to add, subtract, multiply, and divide numbers into the thousands. When students start using this material, one subtraction problem may take 20 minutes! But because it’s physical, social, and interactive, it doesn’t feel like work.
