The Mathematical Mind

The study of the human mind has consumed psychologists and educators since the late 1800's. In today's world, we can add neuroscientists to this listing. Now we know much more about the apparatus and workings of the human mind than ever before. Often Montessorians are asked to justify the continued study of Dr. Maria Montessori's understandings of human nature. There is a tacit assumption that any theory 100 years old must be limited in scope and possibly invalidated by more recent discoveries and understandings…In actuality, these theories are being validated and our understanding enriched by current neuroscientific studies.

One aspect of Dr. Montessori's theory of child development, that of the mathematical mind, is as important today as ever before. Dr. Montessori found this term ‘the mathematical mind’ in the writings of Blaise Pascal. For her this term gave focus to the phenomena she witnessed in the developing lives of children throughout the world.

Teachers come away from their Montessori training with a strong understanding of the nature and beauty of the mathematical materials. They are in awe of the wonderful knowledge that children can glean from their interactions with these materials. They take from this experience the thinking that it is these materials that cultivate the mathematical mind. This is the first and foremost myth about the nature of the mathematical mind.

…Dr. Montessori gives great insight through her view of the child as a reflection of the essence of human nature… Familiar to many Montessori teachers are the stories regarding the explosion into writing and the explosion into reading. Teachers know them well and may also have experienced these phenomena for themselves through their work with children. The phenomenon that is not heard about or recognised as easily is the explosion into mathematics.

Dr. Montessori discerned that the manifestation of every phenomenon followed a similar progression. It was this pattern that she built upon in offering activities to the child. The progression involves:
1) indirect preparation
2) formation of subconscious knowledge - gathering of experience and impressions
3) awakening of the consciousness with the accompanying powers of application

By definition, the mathematical mind is a power to organise, classify and quantify within the context of our life experiences. This is spontaneous activity of the mind, it is uniquely human and it is a capacity found in all human beings. Adults use mathematical knowledge informally throughout every day of their lives:

Driving to school in the morning...
- assessing speed
- stopping distances
- anticipating turning ratios.

Making breakfast...
- measuring coffee into the filter
- stopping the flow of the coffee directly out of the machine into the cup
- estimating the amount of sugar or milk to be added.

The young child, through the developmental powers of the Absorbent Mind, the Sensitive Periods and the Human Tendencies, also gleans informal mathematical knowledge. The child sees other human beings acting within this mathematical context, and takes in the patterns and relationships. The child utilises the Human Tendencies for orientation and exploration to broaden the perspective from which the world is viewed.

There are three characteristics that reflect the workings of the mathematical mind:
1) the drive toward accurate observation
2) the motivation to create order out of chaos
3) the ability to perceive patterns of relationships leading to the creation of abstractions and the use of the imagination.

Ms Helfrich further explores these characteristics in a lively and clear article.