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$How do Montessori Materials Spark a Love of Mathematics?$

How do Montessori Materials Spark a Love of Mathematics?

“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.

Toddler Lessons in Independence: Meal Prep

If you have a toddler, you know they desire opportunities to be independent and explore something new. In the Montessori classroom, meal preparation lessons are a large part of how the toddler learns to care for themselves and others in their community.

Below, we go over four meal prep lessons – washing strawberries, cutting cheese slices, cutting apple slices, and cutting cucumber slices. Each one uses different kitchen utensils that are age-appropriate for young children.

After watching the lessons, you may wish to present them to your child in a similar way. By having the materials laid out neatly and inviting your child to participate, the lesson can become a fascinating new sensory experience for them. Plus, if you have a picky eater, they are more inclined to eat foods that they have prepared themselves.

Initial Lessons

Before beginning with meal prep, your child will need an introduction to work in the kitchen. This would begin with a lesson on how to wash their hands (and a reminder that we wash our hands before working with food every time), as well as a lesson on how to put on their apron. In the classrooms, these lessons build upon each other, teaching children how to complete a sequence of tasks.

Washing Strawberries

Washing strawberries is an easy activity to start with in the kitchen. Children love the opportunity to turn on the sink and use the water. We recommend having a learning tower or sturdy step stool to make it easier for the child to be independent in this work.

Apple Slicing

Apple slicing is another great meal preparation activity for young children. Using an apple slicer is easy for small hands as they are able to grasp it and put their weight onto the handles. Cutting the apples into smaller slices first makes this task easier for young children.

Cheese Slicing

Cheese offers a harder surface to cut into for the child. By using a chopping tool, the children are able to put their weight onto the top of the utensil. This is a great tool to begin to transition into using knives.

Cutting Cucumber Slices

Using a wavy slicer can create visual interest for the child. This type of slicer can be used for most soft fruits and vegetables, as well as cheeses.

A few items of note:

Before giving these lessons to your child, think about your kitchen space from your child’s perspective. Are there surfaces that are easy for your child to reach? Do you have a way for them to access necessities, such as the sink and the tools they will be using? If you are interested in setting up your kitchen to be accessible, we encourage you to read our blog post A Montessori Kitchen.

If you would like to learn more about kitchen utensils that are safe for your child, we suggest reading the Montessori Toddler Knives and Montessori Knives blog posts from How We Montessori. This blog also shows the progression of knives from one to three years old. These posts provide a good overview of different types of knives that are appropriate for young children and why it is important to expose children early to kitchen safety.

Try it out!

Take some time this week to try one or more of these meal prep activities with your child. If they love a certain fruit or vegetable, you may want to try preparing that in a similar way. Let us know how it goes!

A Montessori Education is More Important Than Ever Before

As the pandemic surges through the summer and into the fall, we are beginning to see the ways in which our world is reshaping. From working remotely and learning from home to businesses being transformed forever by the economic turn, we are just beginning to see that our lives will not return to normalcy. Children are entering into a world that will be vastly different from what we grew up with, and they need to be ready.

Montessori education was founded during another tumultuous time – the early 1900s in Europe. Through two world wars, a global pandemic, and a shattering economic crisis, Dr. Maria Montessori saw to it that her model equipped students with the tools to think critically, adapt, and persevere. Over 100 years later, her tenets are still followed today by a growing number of Montessori schools as well as parents adapting the Montessori method at home.

The truth is: the world needs what Montessori children can do.

Anne Frank in her Montessori classroom in 1936.

Montessori children think creatively and innovate

Unlike traditional learning in which the lesson and assessments are the heart of the school experience, exploration is emphasized in Montessori classrooms. Students are encouraged to follow their interests, decide how to demonstrate their learning, and share their discoveries with their peers. By learning at a young age to manage their time and think creatively, Montessori children are able to be thought leaders in the adult world, especially in science, engineering, technology, and mathematics. Montessori truly builds innovators.

Upper Elementary students dissect a cow brain as part of their chosen science work.

Montessori children develop strong leadership skills

Whether learning remotely or on campus, our Guides are dedicated to setting up an environment that allows the child to work at their own pace, encouraging them to ask questions and push themselves to learn more. This shift allows for students to take ownership of their own learning, having a sense of pride around education and discovery. Multi-age classrooms expand upon this, with our older children taking on the role of leaders in the classroom, teaching their peers as they themselves begin to master a subject. From the start of their Montessori education, our youngest children learn that they can do hard things, setting the stage for the work to come in the Elementary and Adolescent classrooms.

Upper Elementary students attending the Montessori Model United Nations Conference in New York to represent the country of Gayana.

A Greenspring student presents his biography research to parents and peers.

Montessori children engage in thoughtful dialogue about our past histories

Children are given the “big picture” – especially through the Cosmic Curriculum at the Elementary level. Academic subjects are not taught separately but woven together to show the interconnectedness of the disciplines. In our Elementary classrooms, children begin to wonder about how the world works, and we are consistently surprised and inspired by the ways in which these young people are ready to change the world for the better. In the Adolescent Community, students are eager to engage in respectful dialogue with their peers, discussing everything from moral philosophy to civil rights and beyond.

An Adolescent student reads a speech she wrote in support of Leia’s Law for gun control on the steps of the Baltimore County Courthouse.

Montessori children have an unwavering commitment to supporting those most vulnerable in our communities

In the Toddler and Children’s House classrooms, much of the child’s work involves the need and desire to serve the community in a way that challenges them. From serving tea and feeding classroom pets to organizing food and clothing drives and sharing art with people in a local retirement community, the children begin to generate their own service initiatives when they see there is a need in the world. Throughout their time at Greenspring, children and adolescents are taught that they have a voice and that they matter in the world. These early lessons help to define who they are and push them to continue making a difference, as we’ve seen with countless Greenspring alumni dedicated to service, the environment, and their communities.

Adolescents plant seedlings with Real Food Farm in Baltimore to support people with limited access to healthy food.

As we look toward the coming year and beyond, we are inspired to think about the direction our children will take us. This is truly a pivot point in history and we as Montessori educators are here to help shape that world with our students. We are not just looking for ways for our children to catch up on academics. We are looking ahead in order to understand what our children need in this new world.

To learn more about Montessori and learning options for your child, plan your visit today.

Montessori Discipline for the Home

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This webinar provides parents with strategies for implementing Montessori discipline and connection in the home. Led by Tamara Sheesley Balis, Head of School at Greenspring Montessori School, this webinar draws on strategies from the book No-Drama Discipline by Daniel J. Siegel and Tina Payne Bryson, psychologist Ross Greene, and Hand in Hand Parenting.

If you have questions or would like to suggest topics for future events, please contact us at learn@greenspringmontessori.org. To learn more about the Montessori Method, please visit our Research and Resources page.

Raising Toddlers with Montessori Discipline

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Greenspring Montessori School Toddler Guides, Danuta Wilson and Kim McCaslin, discuss strategies to encourage your child to self-regulate their behaviors and emotions at home. They provide simple strategies that can be implemented at home today, all based off of their Montessori training, 15+ years combined classroom experience, and their own experiences as parents.

If you have questions or would like to suggest topics for future events, please contact us at learn@greenspringmontessori.org.

Supporting Your Toddler’s Independence

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If you are interested in learning more about how to support your toddler’s growing independence at home, take a moment to watch this webinar with Greenspring Montessori School Toddler Guides, Allie Alexander and Michelle Donohue. Allie and Michelle have over twenty years combined teaching experience and they both have Montessori toddlers at home. They offer practical advice that is easy to impliment, as well as suggested products to aid in your child’s independence.

For a full list of products for your child, please take a look below:

Drinkware

We recommend that you wean children off of bottles and pacifiers once they are twelve months old. Current research suggests that bottles and sippy cups can be damaging to your child’s oral development, so we recommend starting with an open mouth cup, or if you are on the go, a straw cup with a lid or a child’s water bottle.

Cups with Straws

Munchkin Weighted Straw Cup

Contigo Cup

OXO Tot Cup

Children’s Water Bottles

Contigo Kids’ Water Bottle

Summit Water Bottle

Most water bottles found in the children’s section (not the baby section) will work well.

Ikea is also a great place to find inexpensive child-sized open cups, silverware, plates, etc. for when you are eating at the table. We recommend that parents avoid plates and bowls that suction to the table after 18 months.

Footwear

Soft-soled shoes are best for children learning to walk. Once your child’s dexterity begins to improve, we recommend shoes and boots that are also easy to pull on and off.

Stride Rite Early Walkers or Soft Motion

Target, Carter’s, and Kohl’s have soft-soled booties as well.

Baby Bogs Waterproof Insulated Boots

Kids’ Bogs Waterproof Boots

Many of these items can be purchased used on sites like Facebook Marketplace or at your local consignment shop if you are looking for some less expensive options.

We also recommend searching the For Small Hands website if you are looking for something specific for your child. They have a variety of child-sized materials for every area of the home.

Take a look at our Montessori in the Home series for more tips for toddlers and infants:

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