By Brenda Nelson
What is the Mathematical Mind? According to AMI’s (Association Montessori International) website, the glossary of Montessori terms describes the Mathematical Mind as, “All babies are born with mathematical minds, that is, they have a propensity to learn things which enhance their ability to be exact and orderly, to observe, compare, and classify. Humans naturally tend to calculate, measure, reason, abstract, imagine and create. But this vital part of intelligence must be given help and direction for it to develop and function. If mathematics is not part of the young child’s experience, his subconscious mind will not be accepting of it at a later date.”
In the prepared environment of a Montessori classroom, there is a flow, an order, to how the materials are placed on the shelves and how they are introduced to the children. We begin with the simple moving to more complex ideas; concrete materials to the abstract. Why is this important? Maria Montessori stated, “What the hand does the mind remembers.” When children are working with materials that are designed to be used concretely they are able to hold them, touch them and manipulate them. It is only after a child has had the opportunity to work with these materials with their hands, can they begin to understand the concepts abstractly.
What stands out for learning math in a Montessori classroom are the materials. Before we can address the math materials, it must be said that the materials in the Practical Life and Sensorial areas are just as important to building the mathematical mind. The hands-on opportunities in these curriculum areas allow children to work with concepts such as size, measurement, and counting, while they also aid in the development of order and exactness. The pink tower, from the Sensorial area, is an excellent example of this. When a child works with this material, stacking them from largest to smallest, it requires visual discrimination, coordination, and precision (direct aims). An indirect aim of this work is preparation for math, working with cubing. These opportunities, in Practical Life and Sensorial lay a foundation for the work that will be done later on in Math.
As with the other curriculum areas of a Montessori classroom, there is an array of materials that children are able to work with after they have been given a presentation. The first materials a child will be introduced to in math are the ones that are associated with numerals 1-10. With the number rods, the spindle box, or the short bead stairs, a child can feel and see the difference between the numbers 1 and 10, and any number between. The teen and ten boards are introductions to greater numbers, still allowing the children to touch and manipulate the beads associated with these materials. My favorite is the golden beads, the introduction to the decimal system. To be able to feel the difference between one unit bead, a ten bar, a hundred square, and the thousand cube, sets the foundation to be able to understand what these numbers can represent. I enjoy observing the children making connections as they are setting up the 45 Layout, displaying the quantities of 1 to 9000. Through concentration and repetition of working with these concrete materials, the child will be able to move towards abstract work in the classroom. A wonderful opportunity for children to move from concrete, using the golden beads, to abstract is the stamp game. The first presentation allows the children to see golden beads represented by tiles with the numbers 1, 10, 100 and 1000. The stamp game allows the children to continue with their work of mathematical operations without the time and space that working with the golden beads can take. There are many more Montessori materials and opportunities, throughout the classroom, that support the children’s’ transition work from concrete to abstract.
In order to allow a child to fully experience and support the growth of the mathematical mind, we must support their work in Practical Life and Sensorial, just as much as we do when they work with the materials in Math. We have to allow them the opportunities and time to work with the materials that are designed for hands-on exploration before introducing them to the concept of abstraction.
As a child, I remember math being a favorite subject in school. Like others, over time I lost the enjoyment for the subject. That changed when I was enrolled in my Montessori training; I rediscovered a love for math. During a group discussion, a common thought among us was, “I wish I had learned math this way. (the Montessori way).”