Maria Montessori's Philosophy of Geometry

In the chaos and hustle of everyday life, it is not often that an individual will stop to take a deeper look at the world that surrounds her. But if she was to pause for only a moment, open her eyes, and truly take in the world that she is living in, she would recognize the beauty of the patterns that surround her. Every single day, without even realizing it, individuals are interacting with patterns and relationships that are at the very core of geometry. Maria Montessori was exceptionally aware of the world of geometry that she was surrounded by and was capable of designing geometry materials within her curriculum that support the understanding of patterns, relationships, and functions to represent and explain real-world phenomena in a variety of ways. These simplistic materials allow students to explore the world of geometry from a very young age. They also use real-world examples that allow the eyes of the child to be opened to the prevalence of geometry around her. And lastly, these materials allow the child to construct and create works of art which leads to further expansion in her understanding and view of geometry.

Dr. Montessori’s curriculum does not hesitate to immerse the child into the world of geometry. The exploration of geometry begins in the 3 to 6 early childhood education classroom. At this age the child is equipped with an “absorbent mind” as Montessori refers to it. She capitalizes on the young child’s ability to absorb information from their environment “through the active exploration of her surroundings and the materials placed within them” (The Kavanaugh Report). Even at such a young age, the child is being provided the opportunity to dive into and discover geometric concepts in a sensorial way. Materials such as the geometric solids and the geometry cabinet are available to the child to explore using her hands—tracing the edges with her finger or a pencil and feeling the weight of the solids that she holds. Through her investigation and experience with the materials she is capable of putting names to the shapes and solids that she is working with. The work with these materials does not stop in the early childhood setting.

As the child enters into the 6-9, lower elementary classroom she is provided more opportunities to work with these same materials. A new material, the box of sticks, is introduced to the child in this grade level. The concepts that she had the opportunity to absorb sensorially in early childhood are now being taken one step further. She is being invited to understand these figures in more detail. The child in 6-9 works with the geometry materials to explore the concepts of lines, angles, triangles, quadrilaterals, and more. The use of nomenclature cards becomes important during this step of geometric discovery. Soon, the child will begin to understand these simple definitions and she will be able to express these newfound concepts in her own words. The exposure to the geometry materials at such a young age sets a path for the child’s discovery of geometric patterns, relationships, and functions in her environment that explain and represent real-world phenomena. As the child progresses through her Montessori education, these early foundations in geometry will allow her to recognize patterns in real world phenomena are important for the mathematical formulas that she will learn in 9-12.

Another way in which the Montessori geometric materials support the understanding of patterns, relationships, and functions to represent and explain real-world phenomena is that they are paired with lessons that incorporate the exploration of the world around the child. Maria Montessori viewed the child’s learning environment as both the classroom as well as the “extensions beyond the classroom into nature and the arts” (Cohen). She briefly explains this in her book Education for a New World, when states that “Education is a natural process carried out by the human individual, and is acquired not by listening to words, but by experiences in the environment” (Montessori, 1946, p. 3). It is evident that this belief of hers was taken into careful consideration as she was going through the process of designed her geometry curriculum.

The simplistic materials used for the instruction of geometry are paired with connections to the child’s real world—to experiences that the child is familiar with and to discoveries that the child will soon make. One example of how the curriculum allows the child to explore concepts in the world surrounding her is evident in the Study of Lines. In the lesson Positions of a Straight Line the child is invited to look outside to find where the earth seems to meet the sky to learn about horizontal lines. Furthermore, at the conclusion of this same lesson, the child is given a task to explore her classroom and the environment around her to discover examples of the different positions of lines that she just learned about. Because the child is being given this opportunity, no longer sees the legs of a table as just that. She now sees that the legs look like vertical lines. There are several lessons that provide the child with this opportunity to explore the world around her and make connections between geometric concepts and her daily life. This opportunity allows the eyes of the child to be opened to the astounding prevalence of patterns, relationships, and functions that she is surrounded by.

Lastly, one of the most critical ways that Maria Montessori’s geometric materials support the understanding of patterns, relationships, and functions to represent and explain real-world phenomena is through their innate ability to allow the child to construct figures and create works of art. The child is provided with a geometry journal which, in a sense, will become the child’s artistic portfolio. Using the box of sticks, the child constructs the different shapes, figures, and concepts that she has been learning about. She then transfers these creations into the journal with precision. In the same way, the teacher may instruct the child to compose a work of art based off of a concept that the child has just learned about. These creations are filled in with colored pencils or watercolor paints. Through a discussion about the iron inset material in her book Advanced Montessori Methods II, Maria Montessori explains the importance of having the child combine geometry with art. She states that:

The exercises with this material not only are exercises of composition with the pieces of an inset or of the substitution of them into their relative metal plates; they are also exercises in drawing which, because of the labor they require, allow the child to take cognizance of every detail and to meditate upon it. (Montessori, 2007, p.263) Not only is the child working with the figures that she has created, but the close attention to detail that the inclusion of art is providing allows for the student to truly take in the details of the figures and concepts. Furthermore, by incorporating art into the geometry curriculum the child begins to see it as more than just another mathematical concept. Integrating art into geometry gives it more meaning and opens the child’s eyes even more to the creations around them—just as the incorporation of real-world experiences into the lessons does. Just as the child begins to see geometry in the world, she begins to see geometry in pieces of artwork. In turn, she sees art in the world around her. For example, if the child was asked to explore the world around her and draw a picture of geometric concepts in her environment, she may choose to draw a brick wall. This wall that she draws is now so much more complex to her than it had initially appeared to be. She recognizes patterns in the shades of red of the rectangular bricks. She sees the similarity and congruency of the rectangles, the lines now have names, she realizes that these lines make angles, and so much more. Because the Montessori geometric materials give the student the ability to construct and create works of art, they are capable of supporting the child’s understanding of patterns, relationships, and functions to represent and explain real-world phenomena.

Maria Montessori’s hyperawareness of the prevalence of geometry in the world around her lead to her design of geometric materials within her curriculum that support the understanding of patterns, relationships, and functions to represent and explain real-world phenomena. By introducing these materials at the very beginning of a child’s education, pairing real-world examples with the materials, and incorporating concepts of art and construction into the materials the child is capable of grasping onto the patterns, relationships, and functions that represent and explain real-world phenomena.