Math is a struggle for many students and a fear of many parents. Difficulties understanding math can be hard to make up for later in life. An essential part of mathematics fluency is building connections early on, with a firm understanding of basic math concepts.

## How Does Montessori Math Work?

The Montessori math curriculum is highly effective, due to the manipulative materials, providing a physical experience and visual reference, which forms a concrete understanding of basic math concepts. A child’s concrete understanding of math naturally progresses to the ability to think abstractly about math. In Montessori math, most parents are astonished to see their young child’s math capabilities through the use of concrete materials.

Montessori preschool-age children begin exploring math with the ‘number rods’ or ‘spindle box’ materials. These early math materials introduce the concept of quantity, zero, and 1 – 10. Typically, when children recite numbers 1 – 10, or even to 1000, this is a language exercise. However, in Montessori, young children gain a sensorial understanding of the numbers they are reciting – they have a physical and visual idea of the size or quantity of numbers, zero through 9,999!

## Montessori Math Methods

### Golden Bead Work

Another fascinating material is called Golden Beadwork (also known as the bank game). At the primary level, children are introduced to the decimal system around age 4 or 5. The golden bead materials consist of gold-colored beads, bars, squares, and cubes representing the decimal system – unit, ten, hundred, and thousand. Young children engage in static and dynamic math operations with the ‘bank’ material, which lends to a firm understanding of place value, and what happens when we ‘borrow’ (exchange one 100-square for ten 10-bead bars).

In lower elementary, students continue using the Golden Bead materials to multiply and divide numbers. Thus, the materials become an intrinsic characteristic of their math learning process. Elementary students continue using concrete materials, which becomes ingrained in the ‘math mind’ and eventually starts thinking abstractly about math. For example, the ‘Golden Bead’ is later used to introduce ‘parts of a whole.’ In this lesson, beads are arranged in different configurations to demonstrate the decimal system. Each bead is a ‘unit,’ or a one-thousandth. Students absorb ‘parts’ of a number by seeing each as separate pieces and connecting them to a whole structure. This imagery is valuable when presented with fractions and decimal related math problems” (Pebblecreek Montessori).

### The Stamp Game and The Checkerboard

Transitioning from the golden beads to the Stamp Game material leads to a more abstract form of all four operations into the higher hierarchy. ‘Stamp Game’ is another popular piece of material, which consists of a sectioned box with colored tiles. For example, green tiles are units, blue tiles are tens, red tiles are hundreds, and green tiles are thousands.

In lower elementary, children are introduced to operations through golden beads, moving quickly to the stamp game, then to small and large bead frames, and onto the Checkerboard. All of these materials are used simultaneously for students to understand the process. The key here is for children to take time and enjoy the learning.

During this process, students are building their critical thinking skills and soft skills like patience and strengthening their concentration. Recently, one of our students exemplified these skills when working with division using the stamp game. Regardless of the raindrops from the rooftop on her work, she continued to work. My experience observing her was beyond enlightening.

### The Test Tube

While students use the Checkerboard for larger multiplication problems with three to four multipliers, they use the ‘Test Tube’ material for long division. This provides a visual and concrete understanding of division (not to mention they also feel like scientists while using this material). Students continue to practice all these materials until they naturally don’t need to use them and abstractly solve the multiplication and division.

Understanding at an abstract level usually happens around the third year of lower elementary onto the beginning of the upper elementary. However, it depends on the children’s readiness or the ability to achieve it earlier or later. Adults must practice patience and believe in the process of the child at work.

### Other Methods

Besides the operations, fact memorization continues through lower elementary, while students use materials like the ‘strip’ and ‘bead’ boards. Repetition and interaction with the Montessori math materials provide a fun learning experience, far beyond memorizing facts – their experience builds fundamental understanding and lasting knowledge.

## Continued Learning in Math With The Montessori Method

As students understand operations through practice with Montessori materials (Golden Beads, Stamp Game, Checkerboard, Fraction Decimal Boards, and Geometry), connections occur. This lays the foundation for Algebra, which often begins at the 5th and 6th-grade level. Students strengthen their mathematical minds in upper elementary, understanding more complex concepts through binomial and trinomial cubes, multi-base bead frames, and cubing materials.

Montessori Math materials from Early Childhood to Elementary (6-12 years) lay the path for future math success, with a solid foundation of essential math concepts.

Montessori Guide uses specific terms (etymologies), questions, and stories to explore new ideas with students, which helps them build a deeper understanding of the content. More importantly, the Montessori curriculum builds a guided path to reasoning and independent learning.