Montessori Tools For Introducing Mathematics

Dr. Maria Montessori believed that the human mind is naturally mathematical, which means that it is a latent but inherent ability in our children. She also believed children crave order and precision – which is something you’ll immediately notice in the Montessori environment and materials preparation in any Montessori classroom environment.

Given the proper foundation and the freedom to explore, the understanding of basic mathematics emerges from the child’s experimentation as part of a completely natural growth & learning process. Her materials were designed with Montessori math in mind and help to contribute to the development of mathematical thinking, based on a self-directed approach to education.

Dr. Montessori believed that when children are given both freedom and the right materials to learn with, they will lead their own learning. Hence, her methods for teaching counting follow her principles of minimal guidance. Children are naturally drawn to mathematical activities as part of their work to understand the world, so it is important to foster their learning in a self-directed manner.

The Montessori Method favors hands-on approaches to learning, along with a progression from concrete to abstract concepts. In the classroom, the Montessori mathematics materials are presented to support this learning framework by first introducing basic concepts such as understanding the numbers themselves, and later progressing to addition, subtraction, and the even beginning concepts in algebra.

Montessori Mathematics Materials

Here is a collection of commonly used mathematics materials in the Montessori classroom, along with descriptions of how they introduce and reinforce mathematics learning in preschool aged children. This is not a complete list, and creative teachers find many novel ways to introduce math concepts to children using materials from other learning avenues and the surrounding environment. Mathematics should be fun and exciting, and the tools below are some of the more useful ways to engage preschool children in this learning avenue.

  1. Number Cards & Counters: Children prepare for counting skills by learning to identify the one through 10, which are the foundation of mathematics. They need to learn the names, symbols and quantities that these numbers represent, and number cards can help them explore the shapes of the numbers when written down. Children should practice putting numbers in sequence, and can then place counters under each card to represent each number’s quantity.
  2. Number Rods: Montessori number rods help reinforce the growing quantities associated with numbers one through 10. There are 10 wooden rods of varying lengths, colored in an alternating red and blue pattern. Children are encouraged to lay out the rods in a stair-like pattern, one on top of the other, shortest to longest, which helps them to count both the number of rods as well as the colored sections within them.
  3. Spindle Boxes: Maria Montessori believed that children need to use concrete materials to graphically see what happens during a mathematical process. She felt it was much more important than rote memorization, which doesn’t encourage deep understanding. The Montessori spindle box activity involves a long wooden box with 10 slots, numbered zero to nine, and helps children see rising quantity as numbers increase and teaches the concept of zero.
  4. Number Memory: For children who can already count through the number ten, give each child a folded piece of paper with a hidden number written on it. Set up collections of materials like crayons, cotton balls, paper clips and paper squares around the room, and give child a turn to open his secret number. Have them collect the number of objects stated on their paper, which encourages the child to remember a given number and its associated quantity.
  5. Sandpaper Numbers: The Montessori sandpaper numerals in the math avenue correspond to the sandpaper letters used in the language avenue. The numbers 0-9 are mounted to smooth wooden sandpaper boards. This mathematics material helps children to recognize and become comfortable with numbers and engages their visual and tactile senses in the process. Children are able to feel the different shapes of the letters with their fingers, associate the shapes with the names of the numbers, and later on will learn to organize them in ascending order.
  6. Pink Tower: The Pink Tower teaches children to stack a series of progressively larger blocks that are arranged visually in descending order, from smallest to largest. The cubes that compose the power are mathematically sized, with the largest cube in the pink tower being 10 centimeters cubed, the next 9 cm cubed, then 8 cm cubed, etc. This material is a concrete example of the decimal numbering system and also an exercise in using incremental measurement of different volumes. The Pink Tower helps children internalize the tactile and visual differences in size and weight of the blocks that compose it.
  7. Bead Cabinet: This mathematics material is a wooden frame that hands long strands of colored beads, ordered from longest to shortest. The bead cabinet is visually attractive and invites the child to engage with it. In addition to the hanging beads, a series of shelves in the cabinet match the order of the hanging beads with an array of multi-colored beads arranged in lines of squares, as well as one shelf containing bead cubes. The beads are used by children for counting exercises, and naturally show the beginning of multiplication progressions as children see that 4 bars of 4 beads adds up to 16 beads. Again, this is a tactile and visual tool that engages children to count and arrange numbers, and gently introduces them even more advanced mathematics concepts in the process.
  8. Binomial Cube: The Montessori binomial cube is essentially a wooden framework containing eight wooden blocks that fit together into a cube. Each of the blocks is uniquely colored, and can be arranged to match a display painted on the wooden lid of the binomial cube. The blocks include one red cube, three red and black matching prisms, one blue cube and three blue and black matching prisms. Using the display as a guide, preschool children can stack and arrange the wooden blocks to assemble the cube within the box framework, which helps them develop hand-eye coordination, while also introducing them to mathematical concepts similar to the bead cabinet. The binomial cube is presented to children as a puzzle to solve, but in doing so they also develop coordination and an awareness of the role of square and cube numbers, which helps prepare them for more advanced mathematics in the future.

All of the mathematics materials we’ve presented are multi-sensory in nature, and incorporate visual appeal with tactile engagement to help preschool children learn mathematics in a holistic manner. Maria Montessori realized that learning was more effective when reinforced by multiple senses, and she also understood that hands-on learning helped to cement new knowledge in the child’s mind.

Not only are Montessori tools for mathematics a highly-effective approach to engaging children in self-directed learning activities, but the Montessori approach to mathematics also blends seamlessly with the recently implemented Common Core Standards in the USA, making it a great way to get your preschool age child a solid foundation for future STEM proficiency.