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.