![]() Montessori geometric materials support the understanding of patterns, relationships, and functions to represent and explain real-world phenomena by integrating all subjects together to point outward to answer inward questions children ask. Independence in answering those questions through experiment, experience, and personal expertise scaffold the child towards deeper knowledge of math, the world around them, and themselves. The sequential preparation both of the three-year cycle and further planes of development capitalizes on current stages and sensitivities in preparation for the future. Early childhood sensorial materials such as the geometric solids prepare the child sensorially through impressionistic lessons to build vocabulary and synthesis in lower elementary grades. Abstraction, rooted in memory of sensorial experience with their environment, takes flight from a solid foundation. Furthermore, some materials don’t showcase a resurgence until the upper elementary environment, such as the binomial cube, which can now be represented using algebraic functions. Geometry, like all Montessori subjects, requires a careful dance between peaking curiosity in children and overstepping their Zone of Proximal Development. Much like the transition from pre-modernity to post-Cartesian principles, “we may say that the adult works to perfect his environment, whereas the child works to perfect himself using the environment as the means” (Standing, p. 143, 1998). The child, like Aquinas, uses the material world, taken in through sensation, to take on its perfection to fill the previous void and take on the form and perfection of the environment. Descartes, inventor of algebraic geometry and a singular method for math, would later argue for a new world wherein man is master and possessor of nature. If we want children to thrive in a post-modern world, we must first teach them the laws of the universe Descartes pursued through mathematical physics, and then use the standard of certainty found in this singular mathematical method of algebraic geometry as arbiter for certainty in all else. Handing the child the method inspires independence to reason and use the world around them to construct not only their consciousness, but tools and machines as they deem useful and necessary. This mature specimen, raised up according to the perfected environment for education, is set forth into freedom with reason and nature at their disposal. Montessori argued that “his hands under the guidance of his intellect transform his environment and thus enable him to fulfill his mission in the world,” and thus our pedagogy, aimed at the preparation of this, prepares the child for this faculty (Montessori, p. 81, 1936). Our prepared environment molds the consciousness of young children, but is therefore limited to our classroom. However, “to consider the school as the place where instruction is given is one point of view. But to consider the school as a preparation for life is another. In the latter case the school must satisfy all the needs of life” (Montessori, p. 5, 1973). When we emphasize the “real-world” of geometry, we re-center our instruction around children rather than standards, administration, or fleeting fads. Teaching children to gaze out the window during class, Montessori is dedicated to expanding the walls of a child’s classroom as broad as their little feet can carry them. The real world is unshakingly relevant across decades of instruction and future growth of children after they leave our care. The natural world sends a message all around: that math is ubiquitous, useful, and unrelenting in application. Trusting children to take in from the environment real experiences which they are independently capable of developing definitions and drawing conclusions from can feel overwhelming and threatening to both educator and student. Suddenly, struggling students appear as a liability, intelligent students in danger of moving to much further than their peers for you to assist in, and the diversity of experience a threat to standardized anything. Through preparation of the environment and preparation of the inner teacher, however, leaning into the natural perfection of geometry and its availability to the intellect can allow for greater educational acquisition than ever imagined. Through the normalization and extension of geometry into the natural world, educators and families can collaborate to create a community culture of recognizing geometry in all. “Creating an environment in which math is part of everyday life won't transform kids into overnight math sensations,” Ernst argues, “but perhaps it can help kids realize math is a subject for curiosity, discussion and growth” (Ernst, 2018). Other pedagogical masters agree, including Van Hiele’s Levels of Geometric Reasoning. Van Hiele’s levels, which must occur subsequently and over up to a decade of instruction require special activities for facilitating children through each stage through informal geometry activities, which ought to be focused on exploration and investigation, constructing and taking apart, hands-on drawings, and aimed at making “observations about shapes in the world around them” (Van de Walle). Stories and conversations about math ignite curiosity and capitalize on the emotional portions of the brain more likely to enter long-term memory. In addition to serving as an entry point into math, according to Ernst, children tend to “solidify their fear of math” from first to third grade, and they learn it from us; their educators, parents, and role models (Ernst, 2018). It is time we began a new narrative: one where geometry serves the child as a tool to master their environment, leads to creativity, and extends to deeper learning across all subjects. Squealing, “acute! A cute cute cute angle! It is so small and so cute!” may sound alarming to a neighboring classroom, but students will always remember the name of the littlest angle. They remember, not because they necessarily gained something more useful than the other names of angles, but because of how you made them feel, how you made them laugh, how you connected with something within themselves. Geometry connects with a variety of students for a plethora of different motivating factors, but with nature as your leverage, the buy-in power is often greater than other mathematical concepts. Math is the language of reason, but geometry is the language of creation. Patterns found in the universe and natural world remind us that those same patterns make up not only our experiences, but who we are. If the heart is a machine and a sickled cell is a cell which has lost its geometric perfection, suddenly geometry is a matter of life or death. Elliptical eyeballs impede eyesight, mis-calculated angles on bridges crash to the ground, and unevenly sliced pizzas lead to familial brawls. Visual imagery and personal buy-in lend themselves easily to mathematics focused on quality rather than pure quantity. For example, the function of a spider web is to catch and hold the weight of a bug horizontally and vertically to prevent it from falling. In the real-world, the function is to feed the fly to maintain the food chain, however, mathematically, the function of the structure is to provide the necessary strength, through the types of triangles, the distance of the threads between each other, the thickness or thinness of the material. The spider does not have a PhD in engineering, but rather, nature, just like an engineer, works smarter not harder. The real-world patterns that repeat do so intentionally, not necessarily by divine intention, but by the usefulness of the thing. Like Descartes, what is useful is what we will to be, given our present circumstance, with nature as our vessel towards satiating those needs and desires. A new creation narrative centers the child, in awe of the creation of patterns of the universe, creating from nature a new world and a new self: an independent problem solver. The personal interest of children for independence, community, and creation can be satiated by geometry, if taught correctly. Suddenly, children are allowed to self-regulate throughout the day by taking breaks to draw a still life of a geometric solid, take ownership of their research assignments by decorating a border using straight line designs, or finding a piece of themselves in the stories we tell about divergent lines who move to new schools. When we allow students to see that we have made room for all of who they are in every facet of our classroom, we give children our trust in exchange for the most meaningful, engaged work an educator could hope to receive from students. Comprehension skyrockets, quality of work increases, and most importantly, our community practices engage with who children are rather than what they can recite. The implications of Montessori’s geometry method stem beyond mathematics; they create a pattern in our classroom of building relationships of trust that children will function according to their own intellectual perfection, if only given the perfect environment and a teacher willing to sit on her hands. Works Cited Ernst, S. (2018, December 18). “How to make sure your math anxiety doesn't make your kids hate math.” Retrieved from https://www.kqed.org/mindshift/52749/how-to-make-sure-your-math-anxiety-doesnt-make-your-kids-hate-math. Montessori, M., & Carter, B. (1936). The Secret of Childhood. London: Longmans, Green and Co. Montessori, M. (1973). From Childhood to Adolescence. New York: Schocken Books. Standing, E. M. (1998). Maria Montessori, Her Life and Work. New York: Plume. Van de Walle, Elementary and middle school mathematics, pp. 311-349. Van Hiele, P. (1999). "Developing geometric thinking through activities that begin with play," Teaching Children Mathematics 5, no. 6. pp. 310-16.
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AuthorHi! My name is Brittany Wells, and I am a Montessori 6-9 major. I was born and raised in Cincinnati and attended Xavier University Montessori Lab School, Mercy Montessori, McAuley High School, and now Xavier University! Archives
May 2020
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