Young Children's Developing Understanding of Geometric Shapes
Hannibal, Mary Anne, Teaching Children Mathematics
How can we improve geometry instruction at the preschool and primary levels? To answer that question, I conducted research to analyze young children's understanding of the geometric concepts of triangle and rectangle and to determine patterns in the development of this understanding from ages 3 through 6. The research suggests that early childhood educators need to rethink the way that basic shapes are introduced to young children. Since a basic understanding of shapes is essential to a future study of geometry, teachers need to focus on how best to help children develop that initial understanding of shape categories. After a brief explanation of the research, specific ways to present developmentally appropriate activities designed to enhance children's understanding of basic shapes are discussed.
Research focusing on children's concepts of space and geometric shapes began in the 1950s with psychologists' initial observations of developmental levels of geometric understanding (Piaget and Inhelder 1956, 1967). Since then, several studies have either verified (Laurendau and Pinard 1970; Liben 1978) or contradicted (Darke 1982; Dodwell 1963; Fisher 1965; Geeslin and Shar 1979; Stevens 1988) some or all of the original hypotheses. Peel's research (1959) both supported and contradicted some of Piaget's findings.
Another body of research has focused on children's reasoning about the geometric concepts that they have formed. Five sequential levels of geometric reasoning have been hypothesized by Pierre van Hiele and Dina van Hiele-Geldof (1959/1985). At the first level, the "visual level," the van Hieles propose that the child looks at a shape as a whole and not as a sum of its parts. They theorize that at this stage, the child does not attend to the properties of the shape but rather to whether it "looks like" a prototype. Therefore, at this level, an elongated triangle may not be recognized as a triangle because it is "too pointy" when compared with the child's mental prototype. Clements and Battista (1992) suggest that young children differentiate shapes by using a combination of a visual prototype and an unsophisticated understanding of property. They proposed that the van Hieles' visual level be redefined as a "syncretic level" of geometric understanding.
To date, the research on geometry has yet to establish a consistent pattern of development on which to base instructional programs. "Research is needed to identify the specific, original intuitions and ideas that develop and the order in which they develop" (Clements and Battista 1992).
Summary of the Study
A child's introduction to geometric shapes begins in infancy with mobiles, books, blocks, puzzles, sorting toys, and segments on various television programs. Without direct instruction, young children form an understanding of what defines a circle, triangle, and rectangle by observing and manipulating these basic shapes and identifying them by name. When children enter preschool or kindergarten, what understanding do they have of these geometric concepts, and how does this understanding develop as they mature and receive additional instruction?
The study of shapes is included in the curriculum in nearly every early childhood program. Teachers need to uncover and use the initial knowledge of shapes that children have when they enter the classroom. Only with an understanding of the young child's concept and perception of shapes can we develop a meaningful and age-appropriate geometry program.
Data were gathered by observing and interviewing twenty-four children from ages 3 through 6 as they manipulated and categorized forms as being members or nonmembers of shape categories. In two pilot studies, children as young as 3 had no difficulty identifying a circle and could even distinguish a circle from an oval. However, young children notice the nonintegral attributes of size, orientation, aspect ratio (i. …