Building the Foundation For Math

Practical Life and Sensorial Activities in a Montessori 3-6 Classroom Are Foundational for Math.

Math is an abstract concept. The ability to count, compute and use numerical relationships are hugely significant human achievements. The number system is an abstract invention that has been created over thousands of years. In primitive societies, the counting went “one, two, many.” It is exciting to witness the young child’s readiness to understand this same concept.

Children are naturally attracted to the science of number. They are trying to understand their world and make sense of their environment. They have an inborn ability to see differences and similarities, patterns and sequences. The child learns to notice and adapt to changes in the environment and as the child’s knowledge of the environment grows, he/she is able to make a mental map and feel comfortable in his/her space. The Montessori materials that are designed for categorizing and sorting help build this internal order.

The mathematical concepts covered in the primary Montessori classroom are numeration, the decimal system, computation, the arithmetic tables, whole numbers, fractions and positive numbers. Arithmetic is the process of addition, subtraction, multiplication, and division. Geometry and algebra are introduced in the sensorial area of the classroom.

The sensorial and practical life areas of the classroom prepare the child for math and language. The foundation for geometry is developed through the sensorial materials. For instance, some of the materials are graded by size. Children experience spatial relations by manipulating these materials (the pink tower, the brown stair, red rods, constructive triangles, two main types of graded cylinders, plane shapes and geometric solids.) The plane shapes and geometric solids are the basis for computing volume and surface area. The monomial, binomial and trinomial cubes are all geometric representations of algebraic equations, used in higher math. Squares and cubes pave the way for the golden beads where the child experiences the concept of one hundred beads joined to make a square and a thousand beads joined to make a cube. Sensorial activities also indirectly prepare for base ten counting. The pink tower has ten graded cubes, increasing in size by 1 cm.; the brown stair has ten graded square prisms, each 1 cm. larger than the last; the ten red rods are graded from 10 cm. to 100 cm. in length.

The numerical rods in the math area are similar rods but are divided into ten consecutive red and blue sections of 10cm. The child can set the rods out from numbers one to ten so it shows that the longer the rod, the higher the number. Simple math calculations can be performed with the red and blue rods. It is easy to see how the “two” rod and the “three” rod combine to make the “five” rod. In mathematics, objects are classified and have a definite order. All parts of the sensorial curriculum have classification activities. Practical life activities are done in a definite order, which is internalized. Pre-reading activities include matching, sorting and sequencing activities.

The practical life activities are the foundation of the entire Montessori curriculum. Its direct aims are coordination, confidence, independence, concentration and order. These five attributes are internalized and benefit the child throughout life. Manipulation of the materials requires coordination. Finally, the child must have the confidence to work independently.

The Montessori math program addresses three separate concepts: number, quantity, and the relationship of the two together. The child uses concrete materials that isolate each concept. Then the child is shown how to label a quantity with the appropriate numerical symbol. The child then advances to a progression of sequential materials that combine number and quantity. In the same way that a child can learn the “Alphabet Song” without having any idea of the sounds of the letters, similarly a child can learn to count without actually understanding what it all means, but the concrete Montessori materials make sense of it all.

After children have become familiar with the numbers one through ten, they progress to the teens, and then focus on numbers to one hundred. After that, he child is ready for the golden beads which are used for large number recognition over one hundred. Golden beads are also used for the basic arithmetic functions of addition, subtraction, multiplication, and division. Children enjoy working with large numbers and compute easily with hundreds and thousands using golden beads and numeral cards.

Golden beads are all the same size. A single bead comprises one unit; ten beads strung on a wire make a ten bar; one hundred is a square made up of ten ten-bars side by side and one thousand is ten one hundred squares stacked on top of each other to form a cube.

Additional work is introduced with the number chains–which are separate chains of beads one through ten–that demonstrate squares and cubes of numbers. Children love to skip count using these chains, which forms the concrete basis of the multiplication tables.

There are many more math materials to challenge students since the Montessori math curriculum in a 3-6 classroom actually extends to 3rd grade. They are varied and enticing and children are never bored and can work at their own level with joy and confidence. It is amazing how far these students can progress with the foundation of confidence, curiosity, and order they learned in the practical life and sensorial areas of the classroom.

About the Article’s Author: Joan Starling, Founder, Sammamish Montessori School serving preschool, kindergarten and elementary students in Redmond WA.  
Joan established The Sammamish Montessori School in 1977.  She began her long career in Montessori education nearly 4 decades ago training under two Montessori trainers who were themselves trained directly by Dr. Maria Montessori. One of them, a wise and practical woman, Margaret Homfray, when young in the late 1930s, accompanied Dr. Montessori on trips to translate her lectures on her speaking tours.  Joan has been a pioneer of Montessori education in the greater Seattle area, establishing one of the oldest Montessori schools on Seattle’s Eastside and now one of the largest Montessori schools in the state.  Joan’s two daughters share the running of the school (Janet Villella is now the school’s director) and are supported by a wonderful group of exceptionally talented, well-educated and experienced teachers, assistants and supporting staff from all over the world. 


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