Primary to Elementary, Concrete to Abstract
Inspired by Aristotle and John Locke, Dr. Montessori believed that nothing could exist in the intellect that did not first exist in the senses. One of the hallmarks of Montessori education is the elegant materials, designed to lead children from concrete to abstract representations of a variety of ideas.The Primary materials, which are self-correcting and introduce the child to basic concepts like numeration, phonetics, and geometric shapes, also facilitate the transition from Primary to Elementary, both in terms of curriculum flow and in helping the child situate herself in a new environment.
On the child’s first day of Elementary, she will walk into the classroom and see many of what Dr. Montessori referred to as “old friends.” Having used many of the materials already, the child experiences an immediate sense of familiarity with her new environment. She will encounter and use many of the materials she used in Primary, but at a higher level. The pink tower, for example, is in the sensorial area of the Primary classroom, but on the geometry shelf in the mathematics area in Elementary, where it will be used to study the concept of volume. In this way, the Primary child’s work with the pink tower is indirect preparation for her later work with operations on volume. All of the materials, in fact, that the child works with in Primary are direct or indirect preparation for her work during the Elementary years; the materials can be viewed as a bridge linking the different levels of the curriculum.
The geometry materials offer a useful illustration of how a child works with the same materials, yet on entirely different cognitive levels, in both Primary and Elementary. A sensorial material at the Primary level, the geometric plane and solid figures are explored in a variety of ways. Circles, squares, triangles, and other polygons are manipulated in order to feel the difference between straight and curved edges, obtuse and acute angles. In metal inset form, the polygons are carefully traced, promoting coordination and fine motor control as preparation for writing. The constructive triangles material encourages the child to form new shapes by placing two or more triangles together. Two triangles, depending on which kind, will make any number of different quadrilaterals; six equilateral triangles will form a hexagon. Concurrent with manipulation and other sensorial exploration, the Primary child learns the names of the polygons and solids.
Fast forward to the Elementary years, where the child will encounter the same materials, but on the geometry shelf in the math area. Although the child will continue to manipulate the planes and solids, he will begin to study them from a mathematical perspective as well, identifying and measuring, for example, types of angles, bases, altitudes, and diagonals. He will learn how to measure perimeter and area of polygons and volume and surface area of solids. The child is able to explore these properties on an abstract level thanks to his emerging power of reason—one of the “sensitivities,” or distinguishing characteristics of the Elementary-aged child (this transition congruent with the observations of Jean Piaget).
Dr. Montessori wrote much about the “sensitive periods,” or natural dispositions that children have toward certain activities during specific times in their development. While the Primary child can distinguish, sensorially, between a square and a rectangle, the Elementary child, in the sensitive period for reason and abstract thought, can conceptualize and articulate, for example, why all squares are rectangles, but not all rectangles are squares. And while the Primary child knows that two triangles placed together form a rectangle or other quadrilateral, the Elementary child, because he has learned to measure angles, can also extrapolate that since the sum of any triangle is 180 degrees, the sum of the angles of any quadrilateral, formed by two triangles, must be 360 degrees, or 180 X 2. It is a short leap from here to begin the formal study of geometry theorems, part of the upper elementary geometry curriculum.
The materials lead the child from sensorial exploration to abstract reasoning in a carefully designed and stepwise sequence that spans the Primary and Elementary years. And while the Primary child who moves on to a non-Montessori setting for the Elementary years will still have gained some knowledge from her sensorial work, the Montessori child who has worked with the full spectrum of the materials, from Primary through Elementary, will have gained not only more knowledge, but a more thorough understanding of complex ideas in mathematics, language, science, and more.
By Cindy Conesa