How To Teach Math With Montessori Materials

In the Montessori classroom, materials are presented in a thoughtful sequence and follow a specific progression to help learners begin their mathematical journeys. There is an emphasis on learning from the concrete to the abstract, and this concept especially holds true in the Math area of our prepared environment. As Dr. Maria Montessori explains, “Small children count by reciting from memory the natural order of the numbers, but they are confused when confronted with quantities corresponding to these numbers.” She observed that often, children recite the names of numbers, but many times, they do not understand that those numbers represent an actual quantity. The materials Dr. Montessori designed for teaching numeracy are meant to help young learners understand concrete concepts before moving on to more abstract mathematical ideas. That is why the order in which the teachers present these materials is so crucial.

Classroom D first introduced the Montessori mathematical lesson sequence by beginning with a material not found in the Math area - the Red Rods from the Sensorial Shelf. These linear Montessori designed rods are mathematically related, meaning the second rod is twice as long as the first, the third rod is three times longer than the first, and so on, up to ten. The purpose of the Red Rods is to teach children about lengths by organizing the rods from shortest to longest, which is a perfect introduction to mathematical concepts. 

Once the children can conceptualize how the Red Rods work, the teachers introduce the Number Rods. These rods are identical to the Red Rods, except they are divided into equally sized red and blue sections; each one corresponding to a number. The Number Rods are one of the earliest Montessori mathematical presentations because they build on what the children have learned with the Red Rods and introduce the concept of 1-10. 

As the year progresses, the teachers have begun to introduce the Sandpaper Numbers, which are boards with the numbers 1-10 written in sandpaper that the children can trace with their fingertips. This multi-sensory tracing experience allows young learners to understand how to write and learn the number names. Eventually, they will show the next presentation where the sandpaper numbers are used with the Number Rod by placing the sandpaper number next to the rod that corresponds to that number. With the children, they will practice saying, “This is one (ie. the rod), this says one (i.e. the sandpaper numeral),” and this reinforces that numbers have a name and a quantity attached to them. With this mathematical foundation established, they can move on to more complicated teen numbers and the decimal system, laying the foundation for their understanding of the mathematical concepts that children will encounter throughout their learning journey, long after they leave The Washington Market School.