Curriculum Area Highlight - Math

The following information relates to the Montessori math curriculum. Included are excerpts from “Math Works: Montessori Math and the Developing Brain” Second Edition by Michael Duffy. This book is a highly recommended read for deeper understanding of the Montessori math curriculum. 

Maria Montessori created an educational approach designed to maximize the growth and development of each stage of development of a child’s life. This approach is a foundational pillar of Montessori education. She focused on the development of the whole child; intellectual, emotional, social, and spiritual.

Many educators and education theorists see an elementary math curriculum “to be a purely intellectual development. Children are taught to find answers to problems as quickly and efficiently as possible.” Maria Montessori saw it differently!

Montessori believed the focus is not on the answer. She believed that the focus is on how the child gets the answer. Montessori believed that the math curriculum was designed to develop the child’s “mathematical mind”, and the materials she developed for learning arithmetic, in her words, are a “gym for mental gymnastics” to assist children in learning to think and reason logically and clearly.

One of the basic principles of Montessori mathematics is that students always learn new concepts with concrete materials. These materials are designed to lead the child step by step from the most concrete representation to pure abstraction.

Static Stamp Game Addition

Dynamic Stamp Game Addition"

The first step is learning how to count. This is followed by learning the four basic operations of addition, subtraction, multiplication, and division, first with a whole number and later with fractions and decimals. Memorization of facts is typically the last step. This is opposite of how many adults learned math. Rote memorization of facts was the first step. Montessori math emphasizes the process with concrete materials for a deeper understanding of why, not just how.

Materials used in the Montessori elementary classroom for process include number rods (learning to count) golden beads (learning to count and all four functions), stamp games (all four operations), bead frame (all four operations), checkerboard (multiplication with multi digit multipliers and multiplicands), and test tube division, also referred to as “racks and tubes” (division with multiple divisors and dividends). Upper level math materials include decimal checkerboard, factor board, powers of numbers, squaring, square root and cubing and cube root materials and concrete materials for geometry concepts.

Simultaneously, as children move from the concrete to the abstract in process, they are moving from the concrete to the abstract in memorization of facts. Again, this is done with concrete materials.

Finally, Michael Duffy cites the following benefits of Montessori Math Materials:

1. Montessori Materials are three-dimensional and multi-sensory;
2. Montessori Materials are “manipulatives” meaning they are hands-on;
3. Montessori Materials promote active, discovery learning;
4. Montessori Materials encourage collaborative learning;
5. Montessori Materials are self correcting;
6. Montessori Materials are Geometric representations of abstract concepts.

Bead Frames

Checkerboard

(for multiplication with large numbers)