The nature of most every concept in a Montessori curriculum is one of connection and integration. It is rare that we find a lesson or idea that isn’t predicated on a previous experience in our classrooms. In this way, a Montessori environment is a more accurate reflection of the world around the child than in a traditional pedagogy, where geography is a separate study from zoology, a separate study from botany, a separate study from history, when clearly all four curricula form a tight weave of intersecting causes and effects. We see this in mathematics as well, where often a textbook will include geometry as a chapter unto itself, robbing the child of the benefit of seeing the many areas (pun intended) of overlap.
Both of these concepts, connection to prior experience and connection to other subjects are present in the Constructive Triangles. Squaring and factoring informs our study of area and cubing supports the study of volume to mention just one. Geometry as a whole also presents materials that a child will use over a large span of their school “career”, each time returning and moving, as always, from the concrete and the tactile, to the abstract and logical. The Constructive Triangles and the Geometric Solids are part of a Primary, Lower Elementary, and Upper Elementary classroom offering the strength of prior experience with the challenge of a new way to see and manipulate them.
As teachers, we notice the same strengths and challenges inherent. We proceed with all of our students hoping they have worked through their sensitive periods in any area of the room, to set the stage for what we present to them. In the case of geometry, in the case of area, we go back quite far to the child’s first years in school. Those children acquire prerequisites if you will, that will greatly enhance their work in the study of area, especially the creation of formulas. One is the concept of equivalence, learned in Primary sensorially; I can make this figure with these other figures. The other is the nomenclature describing the various parts of polygons; this is an “angle”, show me “height”, what is this?
In upper elementary, the Study of Area, then, must commence with the Study of Equivalence, the relationship between figures. A station of arrival that gathers what the child has done previously; a station of departure for what comes next.
Follow the Child 