Imagine a time when our ancestors’ senses were so finely tuned as to keep them constantly alert and watchful and curious; a time when our fossil human relatives had not the distractions or conveniences of today’s world, but lived in and for the moment.
I asked this group of well-educated professionals what they remembered from their own education about pi. Someone responded, “3.14159.” “You’re right,” I said, “that is the value of pi, but does anyone remember what pi means?” At once they seemed to adopt the sheepish demeanor of students in a traditional math class, each of whom is saying to him or herself: “I should know this but am afraid to answer because I might get it wrong. I hope the teacher doesn’t call on me!” To relieve their discomfort, I supplied the answer: “It is the ratio of the circumference of a circle to its diameter.”
The Montessori primary program is designed as a three-year cycle. Much of the material and exercises in the first year or two not only help the child achieve a direct, immediate goal (such as dressing and cleaning after themselves, or learning the sounds of each letter of the alphabet), but also serve an indirect purpose of laying the foundation for future work and learning.
As a student, I started doing math on paper with a pencil; in Montessori the abstract process of math is the final step of a long series of exercises. To me, and most traditional school students, numbers on the page are just that – symbols we are taught how to manipulate. To Montessori students, those symbols represent very concrete ideas that they have physically manipulated; they fully understand what they mean, how they work, and why.