In the math area of the classroom, children develop a  “mathematical mind,” meaning the human nature to place things in order and understand their world.  Through third grade, students learn math by manipulating materials, moving from concrete materials to abstract operations.  When students learn math by memorization or rote, they often do not understand how to apply the mathematical process to every day situations.  Dr. Montessori explained, “I present the idea in a material or concrete form; and always combined with an activity.  As the child works for a long time with this material, gradually there comes from the material, the very essence of the operation. This sinks quietly into his mind and becomes a part of him.” (From Maria Montessori: Her Life and Work by E.M. Standing)  When students manipulate the materials and can see the mathematical operations, their understanding and comprehension of math is completely different than rote memorization.  Even for the youngest children, Montessori math includes the fundamentals of algebra, plane and solid geometry, fractions and statistics; these operations are never separated from arithmetic, but woven into the problems and exercises. All of the materials are hands-on meaning the child actually sees the process of how to solve an equation and can also feel the weight difference between a unit and a ten for example.


Initial materials in the math area:

  • Number rods
  • Sandpaper numbers
  • Quantity & symbol combined in Number Rods & Number Cards
  • Spindle Box
  • Number cards & counters
  • Memory game
  • Hundred board

As students master the concept of numbers and counting, teachers will introduce the decimal system:

  • Golden beads & colored bead bars
  • Presentation with cards
  • Formation of numbers with beads & cards
  • Collective exercises & stamp game for addition, multiplication, subtraction & division
  • Bank game with complex numbers (all operations)
  • Teens & tens boards & beads
  • Linear counting using bead chains to count beads, squares & cubes
  • Skip counting with beads

Teachers then introduce materials for memorization of math facts and processes:

  • Snake game
  • Strip board
  • Addition practice charts
  • Geometric multiplication with bead bars
  • Multiplication board
  • Division board
  • Bead frame


Through the Montessori method of problem solving, activity and engaging materials, students absorb math concepts in a joyful and relaxed environment.  Dr. Montessori said in her book, The Absorbent Mind, “The results we obtain with our little ones contrast oddly with the fact that mathematics is so often held to be a scourge rather than a pleasure in school programs.”