Geometry has been defined as an awareness of the relationship between man and the objects in his environment. Montessori saw the study of geometry as practical, based on the physical reality of our world. Exploration of fundamental shapes, and their names and structure, provide the ground work for later studies ranging outside the confines of the classroom. As in most areas of study, the etymologies for geometry nomenclature both interest and add to the students’ knowledge of concepts.
Reviewing Montessori sensorial geometry materials is the starting point for the curriculum at the Lower Elementary level. Children go on to study all aspects of lines: their types, parts and their relationships. This leads to the study of the different kinds of angles and their parts, and the introduction of congruency, similarity, and equivalence. A continuing study of triangles teaches their classification by kinds of sides and angles. Other plane figures are next, with classification of polygons, from 3-sided to dodecagons (12-sided figures) in both regular and irregular forms. Measurement of plane figures is then introduced.
Continuing into the Upper Elementary, students learn construction of angles, relationships between lines and between angles, including introduction of complementary and supplementary pairs. More complex polygons are explored followed by a thorough study of the circle and its parts.
Similarity, congruency, and equivalence are explored in greater depth using materials showing subdivisions of squares and triangles in order to illustrate these concepts.
Formulas for calculating the Area of plane figures are discovered through brilliant manipulative metal inset materials that illustrate concrete proofs of formulas; for example: Area of Triangle equals ½ height times the base (A = ½ h x b).
Other materials lead to calculating Volume. Students work with three-dimensional square and triangular pyramids, hexagonal prisms, cylinders, and other forms- concrete representations leading to the formulas for finding volume.
Here too, the work in Geometry begins with the concrete and experiential. Children then come to abstract understanding of concepts and formulas, benefitting from the synthesis of concrete/experiential and symbolic representation to ensure the strongest possible comprehension. |
