Montessori's Mathematical Mind

Over the next four weeks, our Montessori Messages will focus on the study of mathematics. We hope you will enjoy this journey across the levels and begin with an introduction to Montessori’s concept of the mathematical mind.

The foundation of mathematical thinking lies in our human tendencies for order and exactness, tendencies with which we are all born. The infant begins it’s life with the first essential ordering of his world as he forms an attachment to his parents. Within days, he knows his parents and will cry when separated. This is one of the first manifestations of our human drive to classify and order our world; the infant has meaningfully placed these people in a different category from all others and intuitively wishes to stay close to those on whom he depends for survival and who love him best.

Fast forward a year to the child’s first words or even earlier to the gestures and signs of an infant whose verbal utterances are not yet words. We see this drive to order the world and build connections between what he has learned and what he longs to know and understand. There is a desire to abstract an idea from the concrete experience. The toddler may incorrectly abstract the concept of a bird, calling all birds ‘ducks’ until offered new language for goose, canary, and so forth. With new language, the child develops further classifications and begins to absorb the differences in quality associated with each different type of bird.

During this sensitive time for order, the young child may become frustrated or attempt to correct any perception of disorder. If dad kicks off his shoes under the table, for example, the child may retrieve them and move them to the family’s shoe rack, or if mom uses a different cup for the breakfast juice, the child may demand the usual cup. This is actually a good thing as the child is showing their ability to symbolically hold the ‘right’ cup in their mind from one day to the next. Montessori describes Order as forming the basis of the human mind. She states that “… the form of man’s mind, the warp into which can be worked all the riches of perception and imagination, is fundamentally a matter of order.” Our Montessori classroom environments honor this need for order and it is one of the reasons our Guides consider the preparation of these environments among their primary responsibilities. When the child gets support for Order (patterns, categories, relationships) to be made clear, it is a great support to the child’s developing brain which is actively working to categorize and contextualize information.

Movement and manipulation is essential to this development. The child must walk, see the birds, point, clap, speak, and so forth to have the experience on which to base his impressions. The child needs, and truly all humans need, what neuropsychologists now term ‘experimental interactions with the environment’ to self-construct. No one can see the bird for us, we must do it for ourselves. The battle cry of the two-year old to do it ‘by myself’ and my four-year-old’s insistence that she ‘help’ with every cooking, cleaning, building project in our home are but two examples of this drive for experience, knowledge and independence that fuel the ordering of the world for the young child. Setting the table, stacking the blocks, getting dressed; all these big ‘works’ of early childhood are exercises in order, sequence, and exactness which build the capacity for more symbolic work with quantity, numbers, and operations. The active work we offer the children in our Montessori and home environments offers appropriate possibilities for the child to access the potential of their developing mathematical mind.

These experiences then naturally lead to the concept of numbers and quantity. The child knows that one shoe will not work, he needs two for both his feet. He knows the members of his family and learns to count. Often he is asked his age. Increasingly he meets or creates situations that need the exactness numbers offer such as “How many cookies can I have?” They become ready for new lessons and concepts to manipulate and abstract and the more formal exploration of mathematics takes shape. Fundamentally, math is simply seeing order, patterns, relationships and expressing it with numbers. In the coming weeks, we will share more specifically about the math lessons, work and materials the children work with in the classrooms across the levels.

Dawn Cowan, Assistant Program Director
Childpeace Montessori School