by Dr. Wendy Agnew
I hated math, with an atavistic dread. Its logics were not mine - its figures harsh and meaningless. I cringed, even as an adult, when expected to do the simplest of calculations. Then I became a Montessori teacher and all that changed.
I am writing this article in response to plummeting math scores in our public schools. (See Ontario elementary students lagging in math, test results show, Clare Clancy, Waterloo Record.) What follows, is a personal account of my journey from mathophobe to mathophile. I hope it may offer a different perspective and perhaps a solution to the problem of math.
I started Montessori training in 1979, excited by the prospect of an holistic approach to learning. Contrary to popular thought, Montessori schools cater to children from ages 18 months to 18 years. Classes are designed to accommodate three-year age increments so learning takes place in a community with children often helping children. The Montessori materials are ‘autodidactic’ or self-correcting so children may work independently without over-dependence on one authority figure. As the children mature, concepts that were embedded in the muscular memory through elegant wooden games are complexified to satisfy the growing cognitive needs and abilities of the elementary child. For example, the binomial and trinomial cubes, delightful little wooden, multi-coloured blocks that fit in a charming puzzle, are used to explore the binomial and trinomial theorems. - A child of three, experiences satisfaction and sensorial delight. A child of 11 revisits the blocks and marvels to notice the colours and dimensions are mathematically relevant.
My contention is that it is not only the teachers who need to be developed as mentioned in the above article – it is the method. Children who have grounding in the practical, manipulative logic of patterns, numbers, forms leading to formula, find math a breeze. Not only that, but they see the context and reason for learning about Pythagoras, The binomial and trinomial theorems, numbers to different bases … It’s a game that teaches us more about our world and, as a result, learning math offers a sense of independence, interdependence and cognitive evolution. Students are aware that math is not a human invention, but a language of patterns discovered in nature (botany, zoology, natural history, mapping, dating, personal eurekas!) It reveals relationships between compounds (chemistry), substances (architecture), humans (business). Math emerges as a valuable and relevant tool for Montessori middle and high school students, part of whose mandate is to form a business and balance its books.
The key is first to introduce math at an early age but not through concepts - through beautiful manipulative puzzles that are self-correcting, age-appropriate and graduated from simple to complex challenges. That way, math is embedded in the muscular memory as a pleasurable, sensorial, and social experience.
The language of mathematics is offered in a multiplicity of ways so children with different learning techniques or styles can experiment with a variety of exercises. That way, we remove the forcing of rote learning and inject a sense of fun, challenge and relevance into the process of becoming mathematicians.
Math should not be segregated from other subjects or themes. I have seen students revealing in the role of dramatic persona as they take on the historical characters that gave us the sextant, the theory of relativity, the concept of 0… Math needs to be used by children to construct, to deconstruct, to communicate their interests and passions – graphing baseball scores, endangered species, the distance from earth to the planets…
Math is beautiful. Ratio gives us a sense of peace and proportion and should be taught from the perspective of real measuring and curiosity for what feels good. The Greeks can speak to children about math – try dressing up as Euclid and coming into the class to introduce ‘congruence’ – they will sit up and take notice.
I certainly don’t suggest that Montessori’s is the only way. It is a brilliant way – but the message I have learned from hands on, contextual, interconnected learning is that for knowledge to ‘stick’ it must have relevance. For concepts to be valued, they must prove relative to the students’ psychological, physical, emotional, cognitive realities. To simplify - Montessori math answers the vital needs of children to touch, to literally grasp material handles that connect self and culture.
I return to that first day at U of T in Old Vic College when I held one of the thousand cubes composed of 1,000 glass beads, - when my fellow students and I laid out a chain of five and then folded it to see its transformations, first into the algebraic square of 25 and then the geometric pentagon. ‘That pentagon is the shape of the side plates on the carapace of a turtle,’ said a child working nearby. My father, who tried to help me with math in grade two, always marvelled at the Montessori material. He would say, ‘I would go back, if I could be in this class.’