Geometric Construction & Montessori

Children love to build, and the book Block Play by Sharon MacDonald and Katheryn Davis explains both why they do, and what such a love of construction means for their holistic development. By using building blocks, students learn how to: 

• use oral language in a variety of situations
• explore cause and effect
• represent a thought or idea
• develop problem-solving techniques
• enhance creative and critical thinking skills
• match objects in one-to-one correspondence
• express quantities
• demonstrate an understanding of part and whole
• use vocabulary to compare same and different objects
• form groups by sorting and matching objects according to attributes
• acquire non-locomotor movement skills
• create, repeat, and extend patterns
• develop hand-eye coordination
• order items using specific criteria
• understand mapping skills
• use physical representations of addition and subtraction
• develop classification skills
• differentiate between sizes and shapes
• understand gravity, stability, weight, and balance
• think creatively to make and implement plans
• discover names and functions of buildings. (p. 12)

The use of concrete work is core to the Montessori philosophy. This seemingly simple "work" feels to a child like "play" and was one of Maria Montessori's gifts in preparing her classrooms over a century ago. By using their hands with meaningful materials as many times as needed or desired, children reinforce by themselves understanding of the curriculum and the world outside the classroom.

In geometry, students use the geometric solids to comprehend two- and three-dimensional shapes. The geometric cabinet contains wooden insets and frames of circles (small to large), quadrilaterals, and polygons. In lessons on the Seven Triangles of Reality, students measure with rulers and protractors three-sided polygons with varying side lengths and angles to find the one triangle which fits into both categories. Another hands-on material is the stick box, a container filled with color-coded wooden rods which aid in lessons involving lines. The 6-9 Montessori child can free his/her love of construction by using colored geometric blocks and natural wood building blocks.

In my classroom, students use these blocks as a "break" activity after they complete their daily responsibilities in language, math, and cultural studies. Boys and girls enjoy working with partners or individually to construct, discuss and/or describe, draw their creations on paper with colored pencils, and take photographs before triumphantly destroying their architecture. Children have a preternatural gift for creating their imaginative worlds in three-dimensional form. All these photos were taken by children, whose perspective takes in many viewpoints, gets down low or inside work, or zooms in for optimal effect.  In the coming months, our class will be studying architecture and construction in more depth -- through books, projects, and special visitors with experience in the adult world of building.

Curriculum: Geometry

Students explore practical math work like geometry (as well as fractions, measurement, story problems, time, money, and decimals) through hands-on materials first, then gradually build toward abstraction. Maria Montessori devised such brilliant and attractive materials as the geometric solids (which show spheres, cubes, rectangular prisms, cylinders, cones, etc.) to demonstrate three dimensions of shape. Geometry means measuring the earth, and student explore the classroom and natural environment by assessing their shape and measuring them. 

A fun activity for students is using a camera to capture themselves in the environment with those shapes, even in their sometimes favorite setting -- the playground. This combination of going out, use of technology, review of nomenclature, and identification of geometric form helps solidify the concepts introduced through lessons in a way that keeps their eyes moving and their minds engaged.

Recently, students have been exploring the emergence of botany and zoology through their evolutionary development. The impact of this approach in the elementary 6-9 year old Montessori curriculum is that children notice throughout the course of the school year how slowly animals and plants developed from one form to another. They also notice common aspects of each organism, just as scientists have noticed in the classification and understanding of life on our planet.

Before Leeuwenhoek improved the microscope and founded the study of microbiology, many scientists relied upon living creatures and fossil records in order to group plants and animals. For example, reptiles were originally classified by their facial features, then by their form of reproduction, then eventually by the shape of their skulls. One can see from this example how the grouping began more superficially and gradually attained depth. No area of study exists in isolation. Language is fully integrated with cultural studies in three-part cards, research, and writing.

Math also informs the study of plants and animals, not merely as arithmetic but as a way of exploring the practical applications of mathematics such as fractions, measurement, geometry, and time. Students really enjoy using their hands: to touch animals and plants, to manipulate a microscope and specimen slides, and to create models from common materials. During a recent cultural group, students worked together to make a model of the smallest adult Giant Squid, which is 24 feet in length. Some students drew the mantle, which was six feet long and cylindrical. Other students used the planesphere (geography) stencil to trace foot-long eyeballs for the head, while ten students each measured seventeen-foot-long tentacles. Students have also created a larger than life starfish for our echinoderm study, cutting and gluing or taping parts of the animal onto its pink paper body.

Students are able to document their own imaginative designs of arthropods, mollusks, and echinoderms using pattern blocks. On rugs or tables, students worked independently or with partners to make these animal forms out of colored, geometric, two-dimensional blocks. Their creativity speaks for itself in the photographs they took using a digital camera; yet something much deeper can be gleaned here. Children learn through tactile contact, as Maria Montessori herself knew when she began her observational work over a century ago. Children internalize shapes and functions of animals, because they too are animals and see the world through geometry. Children still have their eyes open to the amazing details of life. We adults can learn so much from them.