How Montessori Teaches Math And Shapes The Mathematical Mind

According to Dr. Maria Montessori, the absorbent mind occurs from birth until approximately the age of six.  

During this time period, a child experiences a period of intense mental activity that allows him or her to “absorb” learning from their environment on an unconscious level with very little effort.  Learning during this absorbent mind period is natural and spontaneous and is the foundation of adult life.  Dr. Montessori believed that this period of learning is what actually shapes a child’s personality.  She believed that children absorb through a process she called “mental chemistry,” which postulates that children build their own identity through what they absorb.

After this six-year period concludes, the child transitions to the reasoning mind that adults possess.  In other words, they begin learning through conscious work and memory.

Dr. Montessori’s observations about the best ways children learn have definitely stood the test of time.  Her learnings have taught us that if we can prepare a rich environment for the young child and they simply live in it, they will absorb from it and learn.  Children will learn through self-chosen, interesting activities and will be able to build a solid foundation through concentration and hands-on techniques.

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Part of the absorbent mind is the mathematical mind – defined in Montessori terms as “the spontaneous, unique tendencies of the human mind to develop and appreciate order, precision, intelligence, abstraction, and even imagination.”  Adults use mathematical knowledge every day in their normal activities without even realizing it. For example…

Morning activity:  

  • Estimating how much time is necessary to get ready and get to work  
  • Adjusting accordingly when listening to the morning traffic report 
  • Measuring coffee into the coffee maker  
  • Driving to work while evaluating speed, stopping distances and how much to turn the steering wheel, etc.

All work in a Montessori classroom is intended to develop the mathematical mind.  In the previous blogs on practical life and sensorial learning, one can see how Maria Montessori so brilliantly developed this aptitude with concrete, hands-on didactic materials.  Both of these areas of the classroom reinforce math concepts such as ordering, sorting, patterns, geometrical shapes, and logical sequencing.  It is not an accident that these materials are based on the quantity of 10.

According to Dr. Montessori, “Education is a natural process carried out by the child and is not acquired by listening to words, but by experience in the environment.” She also demonstrated that if a child has access to concrete mathematical materials, he or she can come to their own understanding of abstraction concerning the concept.  

Usually by the age of four (not the same for every child), a child will be ready to begin work with numeracy, moving from the concrete to abstract.  The child’s curiosity about specific counting and measuring is awakened.  

There is a sequential order in which math materials are introduced to the child.

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Description automatically generatedThe first group of exercises is working with numbers from one to ten.  The child learns these quantities concretely with the number rods.  Once the understanding of quantity is mastered, the number symbols are introduced and the child learns to associate quantity and symbol with the number rods and cards, as well as colored beads.  Children learn to isolate the symbols for the quantities by utilizing sandpaper numbers and tracing the numbers, which prepares the child’s hand for writing numerals.  The spindle boxes introduce the concept of zero, and then the child learns to isolate symbols and quantities from zero to nine.  

Once these skills are mastered, the child progresses to cards and counters. Here, the child learns to lay out the cards and the counters in a precise, orderly way.  This introduces the concept of even and odd numbers.  Playing the memory game, the child then relates what he knows about the numbers from zero to ten, and how they work in his environment.  

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The child will eventually progress to the golden beads, which gives a visual and very concrete experience of the decimal system.  Here, the child learns to understand units, then tens, hundreds and thousands.  He learns quantity first and is then given the symbols.  The child completes the exercise by putting quantity and symbol together.  Once this is mastered, he begins to learn the four operations:  addition, subtraction, multiplication and division.  

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Description automatically generatedThe “Teens and Tens” boardsshort bead chains (squaring chains); long bead chains (cubing chains); and hundreds board introduce and teach linear counting. With these materials, children learn the terminology of individual numbers and how to count and recognize numbers from one to 1000 – and sometimes even beyond, depending upon the child.  These iconic Montessori materials give children many opportunities to find patterns in counting and are foundational for later math concepts such as square roots and prime numbers.

Eventually the child is ready to work with materials in abstract terms.  Lessons are then provided to support his work with addition, subtraction, multiplication and division.  These materials include the stamp game,  charts for each operation, and the bead frame.

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The study of fractions is the last area of math that is introduced in a Montessori preschool.  This begins the child’s transition from the primary classroom to the elementary classroom.  Children will start this study with the “fraction skittles,” which introduce the concepts of halves, thirds, and quarters.  

Hopefully, you now have a better sense for how Montessori methodically and purposefully develops the mathematical mind by providing hands-on materials that allow the child to form concrete impressions of numbers and better comprehend the world of math.  Having this strong base allows children to experience math in a way that supports their natural desire for order as they learn.  Montessori provides children the satisfaction of learning through self-discovery, which fosters a sense of pride and independence – and most of all, cultivates a lifelong love of learning!

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