# The Mathematical Mind of a Child

“Children display a universal love of mathematics, which is
par excellence the science of precision, order, and intelligence.”
E.M. Standing: Maria Montessori: Her Life and Her Work p. 344

Children are aware of numbers and quantities at a very young age. Daily life provides many opportunities to make young children aware of such concepts, for instance, a mother says to her child “two buttons are missing from your jacket, or “our dog had three puppies.” When children enter the Montessori classroom for the first time they can already count a few numerals. They pick up on such information easily and are enthusiastic to grasp more. That is why Maria Montessori thought it was good to introduce mathematics at an earlier age than traditional schools’ did because she felt that children needed to see how easy math is.

The impulse to produce order out of disorder is called the “mathematical mind”. Dr. Montessori borrowed this phrase from the works of Blaise Pascal, a French philosopher and mathematician, who said “man’s mind was mathematical by nature and that knowledge and progress came from accurate observation.” (The Absorbent Mind (1988) page 169). Right now though, let’s distinguish between the words arithmetic and mathematics.

As defined by the Oxford dictionary, arithmetic is “the science of numbers” while mathematics is defined as the “abstract science of space, number and quantity” and mathematical is “rigorously precise”. Therefore, when discussing the “mathematical mind”, one is not necessarily speaking only of numbers and calculations but is also taking into consideration the concepts of order, precision, imagination and abstraction. Montessori mathematical exercises give children the satisfaction of learning by discovery. Basic arithmetic operations are learned as the child separates, combines, shares, counts and compares the mathematical materials. It is impossible to go into a Montessori environment and see the math materials without sensing the genius of Maria Montessori. She had the ability to take complex mathematical concepts and turn them into tangible materials that make mathematical abstractions appear to be nothing but a natural phenomenon. These materials are presented in a manner which show a natural progression taking place. Working with quantities first, because they are concrete and the child is able to use more than one sense in determining the quantity, then moving to the symbol, and eventually a combination of both, the child develops a true understanding of the numbers from 0 – 10 and has an excellent reference for what a number means. This gives the child a sound foundation for later work with the decimal system materials and in mathematical operations like addition, subtraction, multiplication and division. After working with the mathematics materials through touch and manipulative activity, the child discovers the physical nature of numbers and how, when combined, they make new numbers. Work in mathematics is profoundly satisfying to children because mathematical work corresponds with the way their minds naturally work paym8.

A five year old child having just completed the 45 Layout ~ Vertical last week.  This is a part of the concrete foundational work in understanding the decimal system. She loved this work and commented for several days about her joy and pride in herself for completing this challenging, yet awesome experience!

Maria Montessori also states….and I truly love this quote:
“We especially need imagination in science. It is not all mathematics, nor all logic, but it is somewhat beauty and poetry.”

Happiness and joy is what I get to witness when I observe a child making these amazing connections with numbers and quantities! Unbeknownst to them, the mind is laying a strong foundation for understanding the beauty and poetry found within the science of arithmetic!