The Magic of Montessori Math
Many children enjoy counting. Yet, as they grow, they develop a complex relationship to math. What was once enjoyable, no longer is. They might think, “I’m bad at math,” or experience math anxiety. Math anxiety is a phenomenon in which children and adults have a poor concept of their ability to do math and fear doing math.
Yet, in Montessori classrooms, many children continue to enjoy math and love advancing their knowledge. That’s because math isn’t something “hard” or undesirable in Montessori classrooms. Through engaging materials that help bring concepts to life, children can master math at their own pace.
Making Sense of Math: From Concrete to Abstract
Math involves working with quantities. Yet, most of the time we think of math as numbers. Why not represent the numbers with real objects? This is what Montessori math does.
Montessori created beautiful materials that demonstrate math concepts in real life. By counting out real objects such as counters, beads, squares, etc., children can truly experience math.
Montessori math materials slowly take the child from a concrete expression of math to an abstract understanding. In other words, they start counting real objects and are later able to perform operations on paper or in their heads.
Working in a logical order, the Montessori math materials help children understand more and more advanced concepts. For the youngest children, Montessori math materials start with simple concepts like zero, counting from 1 to 10, the decimal or base ten system, and the four basic math operations (addition, subtraction, multiplication, and division).
How do Montessori math materials work? Let’s take a look at some basic math materials you’ll find in early childhood Montessori classrooms.
Montessori Math Materials: Discovering Math
Children discover the world of math through hands-on activities that clearly demonstrate concepts. Here’s how it works.
Sensorial: Concepts of Math
The sensorial area helps children understand many math concepts like sizes, quantities, lengths, geometric shapes, patterns, and more. For example, children learn to build the pink tower and brown stair. Each of these materials demonstrates incremental changes in size. Both the pink tower and brown stair feature ten blocks each. The pink tower’s smallest block is 1 cm cubed, while the largest is 10 cm cubed. By exploring the sensorial materials, children prepare for more complex math concepts.
Sandpaper Numbers
When you think of numbers, you likely think of numerals. Numerals are the symbols that represent numbers. For example, 1, 2, 3. Children need to learn each numeral and the quantity it represents.
The sandpaper letters help children learn each number and its name. Children can both see and touch the shape of the number, as it’s made of sandpaper. By tracing the number, children learn its shape. Additionally, they learn the number’s name.
Typically, children start out learning just a few numbers at a time. As they learn to recognize numbers, they can practice with more of them. During Montessori teacher training, soon-to-be-teachers learn various activities to do with the sandpaper numbers. Through these activities, children build their knowledge.
Counters and Number Cards
Children learn the quantities associated with each number by counting objects. First, children lay out the number cards in order from 1 to 10. Then, they place the correct number of counters below each card.
Young children may start with fewer numbers, such as 1 to 3 or 1 to 5. Older children may count out numbers for larger numbers including the teens.
The Number Rods
The number rods also provide a visual representation of numbers and quantity. There are ten rods in total. The rods are blue and red and represent each number from 1 to 10. Children can count the alternating sections of blue and red color to put them in order. Also, each rod gets progressively larger, also demonstrating that higher numbers are bigger and represent a greater quantity than smaller numbers.
In addition to putting the rods in order, children can also use them in combination with the sandpaper letters, labeling each rod with the correct number.
The Bead Stair
The bead stair offers another way for children to practice counting. The bead stair features 9 bead bars from 1 to 9. Each bead bar features a set of beads, all the same color, wired together.Children learn to put them in order. When in order, the beads create a stair shape or a triangle.
The Seguin Boards
This material helps children learn the numbers from 10 to 20, as well as to count by tens (10, 20, 30, 40, and so).
Children represent the numbers with numerals and beads. They use a bar with ten beads on it to represent each ten and the bead stair. So, to represent eleven, children use one ten-bar and one bead. To represent twelve, children use a ten-bar and the two-bar. To represent 60, children use six ten-bars.
The Golden Beads
The golden beads represent the decimal system or the base ten system. Using beads, children can see one unit, ten, one hundred, and one thousand. Then, children can create large, four digit numbers using the beads. For example, children use number cards to show a number such as 3,423. To represent this number, children use 3 thousand cubes, four hundred squares, two ten-bars, and three units.
Later, children can add, subtract, multiply, and divide using the golden beads. Using the golden beads helps children understand regrouping. For example, when adding units and the answer is greater than ten, they exchange the units for a ten-bar.
Operations Boards
Children learn the concept of addition with the addition strip board. This board shows children that addition involves combining two quantities.
Similarly, the multiplication board uses a grid to show children that multiplication is repeated addition. While using the division board, children divide beads among skittles or wooden player pieces.
Finally, children can practice all operations using the stamp game. The stamp game is slightly more abstract than working with the golden beads. However, it still allows children to work with four-digit numbers.
These are just a few of the Montessori math materials you may find in an early childhood classroom. There are many others including charts, the bead cabinet, tables, and more.
Beyond Montessori Materials: Cultivating the Mathematical Mind
Montessori noticed that, “Children display a universal love of mathematics, which is par excellence the science of precision, order, and intelligence.”
In Montessori teacher training, future teachers learn to help children discover this part of themselves. The materials use enticing sensory features. Shiny beads, smooth wooden boards and pieces, and attractive colors invite children to count and perform operations. Yet, the teacher’s invitations to lessons are also important.
Teachers also lead lessons that help children understand and experience the concept of “0” and invite children to create a number roll, in which they write numbers as high as they can. This work, when presented correctly, helps children discover their love for math.
Most importantly, children are at the center. Montessori teachers learn to follow the needs of the child and let them set the pace. By not forcing children to complete lessons, teachers help children build intrinsic motivation. Then, when they decide to try math activities, children are motivated and interested.
Math in Montessori Teacher Training
During Montessori teacher training, whether online or in-person, many teachers fall in love math in a way they had never experienced before. Perhaps where they had learned rote arithmetic in childhood, teachers experience math and its operations in new ways when working with the materials. This newfound understanding leads teachers to share their excitement with the children they later teach.
Are you ready to discover the magic of Montessori math? MPTC offers various online Montessori teacher training courses that can introduce you to the world of Montessori math. Try our Montessori Early Childhood Assistant Course or our Montessori Early Childhood Advanced Course. Have questions about our courses? Contact us!
