This is followed by the symbolic representation or written symbol. After the material, its appropriate verbal language, and its symbolic representation are each studied in turn, they are then associated with one another. In Montessori mathematics, this sequence is referred to as quantity, symbol, and association. Geometry began as a concrete experience with abstractions following at a later time. Each child follows the same sequence.
Geometry is experienced sensorially through manipulation of both plane and solid geometric figures.
These materials induce a creative activity that involves two and three dimensional construction of various forms, artistic drawings, and ornamentation. As much geometric nomenclature is supplied as the child is able to assimilate, so that the child will have as much information as possible at his or her command when entering the stage of exploring why, how and when sensorial experience in geometry is made available immediately upon entrance into the Elementary Classroom. The foundation of the study of geometry is familiarity through sensorial experience. Therefore, there are no clear distinctions or lines of demarcation among any of the various areas which are included in this section when they are studied in the classroom. Areas of study include anthropology, astronomy, botany, chemistry, economics, geology, government, philosophy, physics, political behavior, sociology and zoology.