Mathematics Curricula in Early Childhood. (Early Childhood Corner)
Clements, Douglas H., Sarama, Julie, Teaching Children Mathematics
When we talk about our prekindergarten curriculum development project, we sometimes hear statements such as the following:
"I think it's a shame that we have turned our backs on the long tradition of early childhood education and have to teach mathematics."
"It's great that someone is finally introducing mathematics to this age child."
It would seem natural to hope that the audience agrees more with the second person than the first. However, both statements make the common but incorrect assumption that engaging young children in mathematics is a new development. Before we decide whether early childhood mathematics is "shameful" or "greats" we should look at its history.
Mathematics in Early Childhood through the Years
Frederick Froebel (1782--1852), the inventor of kindergarten, was a crystallographer. Almost every aspect of his kindergarten incorporated his interest in the "universal, perfect, alternative language of geometric form" (Brosterman 1997, p. 12). Its ultimate aim was to instill in children an understanding of what an earlier generation would have called "the music of the spheres"--the mathematically generated logic underlying the ebb and flow of creation. Froebel used "gifts" to teach children the geometric language of the universe. Cylinders, spheres, cubes, and other materials were arranged and moved to show geometric relationships. Structured activities followed that included exercises in basic arithmetic, geometry, and beginning reading skills. For example, the cubes that children used to form chairs and stoves would be rearranged to make a geometric design on the grid etched into every kindergarten table (see fig. 1). Later, the cubes were laid into two rows of four each and expressed as "4 + 4." Connecti ons were important to the students' understanding: the "chair" became an aesthetic geometric design, which became a number sentence.
Triangles, well known to children as parts of faces or other pictures (see fig. 2), were used to teach concepts in plane geometry (see fig. 3). Children covered the faces of cubes with square tiles and peeled them away to show parts, properties, and congruence. Many blocks and tiles composed carefully planned shapes that fit in the grids in different ways. "All the blocks and sticks and rings and slats were used in plain view on the ever-present grid of the kindergarten table, arranged and rearranged into shifting, kaleidoscopic patterns or decorative, geometric borders" (Brosterman 1997, p. 38). Using these materials, Froebel helped his students to develop skills that had been--and still are--reserved for students in higher grades. Many of the children in Froebel's schools ranged in age from 3 to 7; so he can be said to have invented kindergarten and preschool as well.
It has been claimed that the experiences of R. Buckminster Fuller, Frank Lloyd Wright, and Paul Klee in Froebelian kindergartens are the foundation of all their creative work (Brosterman 1997). This supports the contention that mathematics in the early years is not a recent invention.
To explore this position, consider another example, the traditional material of kindergarten building blocks. Children create forms and structures that are based on mathematical relationships. For example, children may struggle with length relationships in finding a roof for a building. They must understand length and equivalence to substitute two shorter blocks for one long block. Children also must consider height, area, and volume when working with building blocks. The inventor of modern unit blocks, Caroline Pratt, tells of children making enough room for a toy horse to fit inside a stable (Pratt 1948). In Pratt's example, the teacher told preschooler Diana that she could have the horse when she had made a stable for it. Diana made a large stable with a low roof. After several unsuccessful attempts to fit the horse in the stable, she removed the roof, added blocks to the walls to make the roof higher, and replaced the roof. …