From the Concrete to the Abstract, Part One

An overarching theme of movement from the concrete to the abstract in a Montessori pedagogy can be discovered at each level. At the Primary level (3- to 6-year-olds), this can be seen reflected in the environment itself. Primary rooms contain three distinct areas: the sensorial, practical life, and academic areas, the latter of which is itself composed of arithmetic, geometry, language, and cultural areas. While these learning opportunities are available to all the children, they tend to have a particular developmental appeal and are selected by the students accordingly. For instance, a 3-year-old, who is likely a more concrete thinker, will be drawn more intently towards the sensorial materials. The Pink Tower, the Red Rods, the Broad Stair, and the Sound Cylinders are just a few of the many materials and activities that allow children to learn for themselves the distinctions between dimension and form, i.e., size and shape. Likewise, the practical life area, with its pouring works, polishing activities, and buttoning and zippering frames, also calls to a developmentally younger student. As the child matures, his or her attention is drawn to more challenging, more abstract, and more conceptual learning. In the Primary environment, this translates to the areas of language, arithmetic, geometry, and the cultural subjects (biology, geography, and history). 

  The advantages of a multiage classroom are manifold. An environment that encompasses learning materials ranging from the concrete to the abstract, and available to children over a 3-year age span, allows them to be successful where they are developmentally, regardless of their chronological age. This is not to say that a 5-year-old never uses the Lacing Frame, but one can speculate that for a 3-year-old it is a work of great concentration, while the 5-year-old uses it to take a mental break. And while the different areas of a Primary classroom are separated spatially, it is important that they are well integrated with each other. For example, the sensorial area serves as an indirect preparation for math, while the practical life area guides the child’s fine motor skills towards the development of writing skills.

At the Lower Elementary level, this development can be understood most clearly if we discuss the scope and sequence of the arithmetic curriculum. The Lower Elementary arithmetic curriculum includes, among many other concepts, computation in whole numbers, using all four operations. As they enter the environment, children are, by and large, in the nascent stages of “formal” computation. By the end of this 3-year cycle, many, though certainly not all, will gain a facility with math facts and will be able to add, subtract, multiply, and divide abstractly, to some extent, using just pencil and paper and no materials. This example represents a remarkable academic, psychological, and spiritual journey taken within each student. 

Through the use of manipulative materials, the child constructs an understanding of concept and a memorization of computation that eventually lead to abstraction. When we explore the materials and activities, it becomes obvious how they lead the child from stage to stage. Let’s look only at addition and allow this specific study to serve as a microcosm of the whole. The Golden Bead material consists of individual golden beads, beads strung into ten-bars, bars wired into hundred-squares, and squares wired into thousand-cubes. Thus, a child adding two four-digit numbers is adding actual quantities of beads. As the child gains understanding, he or she will be presented the Stamp Game, which represents a large step towards abstraction. In this material, individual tiles are stamped with various place values (1, 10, 100, and 1,000) in the hierarchical colors for units, tens, and hundreds. The child, however, still lays out each quantity, making exchanges if a column’s total exceeds nine. Next in the sequence of materials is the Bead Frame, an abacus that uses the same hierarchical colors as those in the Stamp Game and that represents another step towards abstraction. A bead on the Bead Frame gains its value by its placement on the wire, and there are only nine of each type; thus, this work is a triumph of representational thought!

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