Pre-school aged children have natural mathematical minds. They have the capacity to reason, to calculate, and to estimate. They are intensely conscious of quantity – counting skips on the way to school or the steps going up a hill. The concrete Montessori mathematical materials allow these sensorial explorers to begin their mathematical journey from the concrete to abstract through manipulation, experimentation and exploration.   Here are five reasons why we love Montessori Maths!    1. Child-Centric Approach / Individualised Learning In Montessori, we adopt an individualised learning approach where learning progresses according to each individual child’s pace. Children have the freedom to choose (but of course, within boundaries!) to work on any activity that they would love to do. This makes learning enjoyable. Moreover, with the individualised learning approach, children are not pressured to meet a certain learning benchmark, ensuring that they fully grasp a concept before moving on to another!  2. Concrete Materials Dr. Maria Montessori believed that children learn by using their senses – whatever they touch, they learn. Children learn Mathematics through tactile experience such as the Sandpaper Numerals where it has a tactile texture. Likewise, rods, spindles and beads are some of the concrete tools used to symbolise mathematical abstractions. The child does not merely learn to count, she understands the concept of ‘how many’ because she holds the amount in her hands.  Learning through the usage of concrete materials create a strong foundation for children. The child is able to perform the operation of addition, subtraction, multiplication, and division in increasing complexity as part of a natural progression. 3. Concrete to Abstract Approach As the child progresses, she continues to gather from her environment but in a different way. Her inner drive now is to give order to the impressions. She takes the concrete experiences and turns them into more abstract ideas. Her concrete work in the earlier stage literally laid the foundation for complex abstract ideas and thinking. A prime example of this approach can be seen when the child is working on the Number Rods and Cards. After mastering the Number Rods, the child will be introduced to the Number Cards where she proceeds to match the numerals to the corresponding rods. This one-to-one correspondence allows the child to grasp the value of quantity behind each number. 4. Sensorial Exploration In a Montessori classroom, Sensorial activities are as vital as numbers and counting. They allow exploration and experimentation on the part of the child and because they are easily explored, they encouraged children to spend a great amount of time in this exploration. Through working on the many Sensorial activities, children learn several mathematical concepts such as size, length, height, volume, visual discrimination and more! The child develops her mathematical mind through this process of materialised abstraction. The exactness of relationships between the materials makes for the development of a concrete understanding of gradation and order. For instance, the building of Knobless Cylinders requires more than just hand-eye coordination. It involves the child’s ability to be able to identify which cylinder is bigger or smaller. 5. Control of Error Montessori values independence, confidence and self-reliance. This is one of the reasons why Montessori materials were made to be precise. One of such material is the Spindle Box where children learn to associate numerals (0 to 9) with loose quantities (spindles). There are exactly 45 spindles. When a child is done working with the Spindle Box and should there be any short or leftover, the child will know if something went wrong. At the end of the activity, there should be no spindles left, or any shortages. These precise-made materials are more than just enhancing the child’s academic abilities. It helps to promote their social-emotional development as well. Children learn independence and self-reliance as they are able to self-correct themselves. This also helps to boost their confidence as they are able to learn independently without the teacher’s intervention.  

Dr. Maria Montessori and her work were both greatly impacted by the World Wars. In 1939 Dr. Montessori herself was barred from returning to Europe from India when World War II began, and she remained there for the duration of the war. The devastation of both wars affected her greatly and she saw education as the answer to preventing such hostility between people. She believed children must learn about the world–both its physical and political landscape– in order for peace to be a reality in their lifetimes. This took shape as the fifth subject of the Montessori curriculum: Cultural Studies. Today at House on the Hill our children learn from Dr. Montessori’s curriculum as well as from one another. We are a diverse community where both teachers and students are engaged in daily cultural exchange, working towards a peaceful future.  The Culture Curriculum  The cultural curriculum includes both political and physical geography. With interactive land and water form trays children learn the names and shapes of archipelagos, straights, peninsulas, isthmuses, and more. There are maps and globes that show physical land features as well as political demarcations. Children learn where in the world different countries are, flags of different nations, and even which animals are found in that part of the world.  The cultural materials are always available to children to explore, and they are often a mere starting point for discussion with children about life in different parts of the world. Different land features impact people’s lives, for instance living on an island is different from living in the middle of a continent! Climate is also a part of the conversation and we talk about how life is affected in colder, wetter, drier, or hotter parts of the Earth.  The Next Generation  As Early Childhood educators, we are often asked about why we have chosen this profession. For most of us, it is because we understand our children to be the future, and we want them to have and to build the best future possible. As Dr. Montessori said, “The child is both a hope and a promise for mankind” (Education and Peace). Educating the future is no small task! In addition to wanting our children to understand the world around them, we must also teach them to be valuable participants in it.  Various aspects of Montessori education combine to teach skills that go beyond academics. Mixed-age, vertical learning teaches leadership and patience. Having just one of each material in the classroom teaches sharing and kindness. Individual pacing and instruction allow children to grow their curiosity and love learning. The care we expect for our classroom environment grows to be a care for the Earth’s environment. These are only the tip of the iceberg; every day our work is to help children grow into kind, responsible, and curious members of the world.  Our Community  Dr. Montessori may never have imagined classrooms as diverse as ours when she first began her schools in Italy. Across our three campuses, we have children representing dozens of nationalities, languages and cultures. Our teachers and staff also hail from places within and beyond Singapore! We take special care to incorporate cultural activities throughout the year.  Our Mandarin Lao Shi incorporate their various cultures into their teachings, giving our children first hand experience of not only the language but the myriad of traditions from China. For our Lunar New Year celebrations, they lead children in calligraphy, food preparation, and song and dance!  Learning about Deepavali/Diwali in class Each year we celebrate different holidays from various traditions. For example, we’ve had Easter, Christmas, Deepavali and Halloween over the years. We read stories, play games, and do crafts that help children understand the festival and their friends who celebrate it.  Dr. Montessori said, “Education is the best weapon for peace.” (Dr. Montessori, 1937 lecture in Copenhagen). At House on the Hill we are working each day to impart values and critical thinking skills to our children that will help them be socially conscious citizens who make Dr. Montessori’s dream of peace a reality.  

Dr. Maria Montessori believed in the holistic education of the child, and she created a curriculum that followed children’s natural development in five key areas: mathematics, sensorial, language, culture, and practical life. Mathematics and sensorial development are often discussed together because sensorial materials help develop a child’s mathematical mind. The mathematical mind is what makes Montessori’s method of teaching mathematics uniquely effective. Instead of expecting children to only memorize sequences or processes, we teach children to understand and appreciate the logic and beauty of mathematics through hands-on materials and exploration at their own pace. They learn numeration, geometry, arithmetic, and even algebra with a firmer foundational understanding of the concepts than if they had just memorized facts.  What exactly is the mathematical mind? Dr. Montessori believed that all children have mathematical tendencies and can enjoy mathematical study and work. Children like order, exactness and orientation, and they are also capable of imaginative, abstract thought. Montessori materials incorporate these traits into their design, allowing the child to manipulate materials to create order and exactness, and to create a concrete basis for abstract thought.  Mathematics begins long before children can count. Dr. Montessori knew that children learned best through sensory engagement, so she created a whole curriculum for sensorial development. Sensorial materials develop the mathematical mind by introducing children to concepts such as shape, size, dimension, sequence, order, precision, and even mathematical language.  These materials include: The Pink Tower  This classic material is made of 10 cubes. The smallest of which measures 1 cm cubed and the largest is 10 cm cubed. In this way children are exposed to the concept of base ten, which is also taught through Brown Stair. As children work with these base ten materials they can practice language such equal to, bigger than, and smaller than.  Red Rods  Children begin with the red rods, learning visual discrimination of length and how to order from smallest to greatest. The next step is the number rods, a mathematics material which are the same length as the red rods but with the element of quantity. Now children are adding degree to their understanding of order.  Binomial Cube  One of the most unique Montessori materials is the binomial cube. It is a box containing two cubes and six prisms of specific colors. The direct aim is to solve the puzzle and correctly put the blocks in the box, but children are indirectly learning the concept of (a + b)³, wherein each block represents a term in the algebraic expression. Children in Montessori primary schools will revisit this material when they begin algebra.    At about age four children enter the sensitive period for numbers. It is no longer enough to know the relative length or amount of something, they want to know the exact measurement! All mathematical learning begins with the concrete before it moves to the abstract and progresses through natural stages. Children must learn to associate numbers with quantity before they can begin addition and subtraction!  Children start to work with materials such as: Spindle Box  After learning numbers using the sandpaper numbers, and quantity with the number rods, children will learn to combine these two concepts. The spindle box is one of the first introductions to matching quantity and symbol, or number. The spindles that they count represent the concrete quantity, while 0 – 9 painted on each box represent the abstract numbers. This material also introduces the concept of zero. After counting all the spindles and placing them correctly, there will be no more spindles for the box labeled “0”. This is a hands-on way for children to discover and understand the concept of zero on their own.  This is quickly demonstrated in this video clip:  Decimal System  Children are introduced to units, tens, hundredths and thousandths with beautiful beaded materials. Units are represented by a single bead, tens by a bar of ten beads, hundredths by a square of one hundred beads, and thousandths by a cube of one thousand beads. This is a tangible way for children to learn about the decimal system. They will use these materials to physically represent abstract numbers and to do functions such as addition and subtraction.  As children master concepts they will begin to introduce more abstract work–writing and doing paper calculations– and will at times move away from the materials and return when learning new concepts. Because of these materials children have a robust understanding of mathematics that will help them in all future studies. 

A Montessori classroom stands out not just in how it functions, but also in how it looks. While it may differ greatly from traditional classrooms, a quick image search or a scroll through #montessoriclassroom reveals something remarkable—Montessori classrooms around the world share a distinct, recognisable aesthetic. At the heart of this consistency is the prepared environment: a thoughtfully arranged space that promotes independence and supports meaningful learning. Central to this environment are the building blocks of Montessori materials, originally developed by Dr. Maria Montessori in the early 20th century. Still used today at House on the Hill, these materials have stood the test of time. So, what makes them so enduring, so purposeful, and so perfectly designed for a child’s development? At House on the Hill, we proudly use Nienhuis Montessori materials exclusively. Albert Nienhuis was one of Dr. Maria Montessori’s original collaborators, and in 1929, he founded Nienhuis Montessori to craft materials that faithfully reflected her vision and high standards. Today, Nienhuis is internationally recognised as the benchmark for quality in Montessori materials. We value these materials for three key aspects of their design: their educational purpose, their intentional method of use, and their aesthetic appeal and enduring craftsmanship. They are the Montessori building blocks. Purpose: Foster Independent Learning Along a Child’s Natural Path of Development Montessori materials are designed with what’s known as “control of error”—a built-in feature that allows children to spot and correct their own mistakes independently, without needing teacher intervention. Each material also focuses on isolating a single concept, such as size, shape, or colour. This helps children fully grasp one idea at a time, building confidence and mastery before progressing to more complex tasks that combine multiple concepts. An excellent example of both these concepts are the knobbed cylinders. A series of four wooden blogs have a series of holes, each with a matching knobbed cylinder that fits perfectly inside. Each block presents a different introduction to height and diameter. It will be obvious to the child if the cylinder is in the wrong hole: either it will not fit according to its diameter or it will be too tall or too short. As the child masters each block they can then begin to use multiple blocks at once.  Use: engage with the child’s senses and encourage full-body learning  Dr. Montessori was an early advocate for sensorial learning and observed the connection between a child’s cognitive development and movement. Her materials facilitate that link even more. For example, we may not often associate language development with fine and gross motor activity, but Montessori’s sandpaper letters and the large movable alphabet make language learning interactive.  As children learn phonic sounds, they trace a sandpaper letter while saying the sound of the letter. Once the child has mastered all the letters, they will use the large movable alphabet (LMA) to begin to spell.  Appearance: natural, real, beautiful materials that attract and interest children Our classrooms have almost no decoration, instead, the focus is on the beauty of the materials. The materials are usually simple in colour, but made with excellent craftsmanship. Too many designs, flashing lights or glitter ultimately distract from the learning and overwhelm the child. In the right environment, children will be drawn to the stocked shelves where they can learn, problem-solve, and explore.  Dr. Montessori believed that children should experience the real world and learn to carry themselves in it. Everything is made of non-synthetic materials such as wood, metal, ceramic, or even glass. Some of the things are fragile, and so teachers work with children to learn the proper care and gentleness needed.  Montessori Infant materials in our Nido Classroom  The beauty and genius of the materials are not limited to our playgroup and mixed-age classrooms! Dr. Montessori designed materials for even our littlest children, and they can be found in our Nido Classroom. These materials follow the same design principles; they are purposefully designed, beautiful, simple, and engaging.  Some materials are almost exactly the same, just simplified and scaled for smaller hands. All materials have the potential to grow with children as they develop.  All the materials focus on developmental stages appropriate to the ages of the Nido. Children are learning the concepts of object permanence with the object permanence box, and begin to practice fine motor precision and matching with the 3D object fitting tray.  Dr. Montessori believed that children learn best when they are very interested in a subject. She observed in her work with young children that they have a “natural curiosity and zest for learning”. Her materials, lessons, and educational approach are designed to capitalise on the nature of each child. After many years of watching children learning with these materials at House on the Hill, we can confidently corroborate the legitimacy of these findings!