Young Children's Ideas about Geometric Shapes
Clements, Douglas H., Sarama, Julie, Teaching Children Mathematics
A toddler, after some experimentation, puts a square peg into a square hole. What does she know about shapes? What more will she learn in preschool and elementary school. What might she learn?
Educators have learned a great deal about young children's knowledge of shapes. Much of it is quite surprising. In this article, we describe research on young children's thinking about geometric shapes and draw implications for teaching and learning.
What Do Children Know about Shapes?
Children's levels of understanding
As children develop, they think of shapes differently. At the prerecognition level, children perceive shapes but are unable to identify and distinguish among many shapes. They often draw the same irregular curve when copying circles, squares, or triangles (Clements and Battista 1992b). At the next, visual, level, children identify shapes according to their appearance (Clements and Battista 1992b; van Hiele 1959/1985). For example, they might say that a shape "is a rectangle because it looks like a door." At the descriptive level, children recognize and can characterize shapes by their properties. For instance, a student might think of a rectangle as being a figure that has two pairs of equal sides and all right angles. Because progress in children's levels of thinking depends of their education, children may achieve this level in the intermediate grades [ldots] or not until college!
Children at different levels think about shapes in different ways, and they construe such words as square with different meanings. To the prerecognition thinker, square may mean only a prototypical, horizontal square. To the visual thinker, squares might mean a variety of shapes that "look like a perfect box" no matter which way they are rotated. To a descriptive thinker, a square should be a closed figure with four equal sides and four right angles. But even to this child, the square has no relationship to the class of rectangles, as it does for thinkers at higher levels. These levels can help us understand how children think about shapes. We might remind ourselves to ask what children see when they view a shape. When we say "square," they might seem to agree with us for many prototypical cases but still mean something very different. The levels can also guide teachers in providing appropriate learning opportunities for children.
Children's ideas about common shapes
Young children have many ideas about common shapes. Levels alone, however, do not give teachers sufficient detail. For this reason, we conducted several studies of young children's ideas about shapes to help complete the picture (Clements et al. 1999; Hannibal 1999). In all, we interviewed 128 children, ages 3 to 6, for a total of an hour over several sessions. Children identified shapes in collections of shapes on paper and manipulable shapes cut from wood. The shapes were presented in different settings. For example, sometimes we had the children handle the shapes, and other times we asked them to identify the shapes placed in various orientations in either a fixed rectangular frame or a round hoop. Our conclusions from these interviews regarding the basic shapes are described here.
Circles. Children accurately identify circles, although children younger than six years old more often choose ellipses as circles. Apart from these infrequent exceptions (only 4 percent incorrect on our paper task), early childhood teachers can assume that most children know something about circles.
Squares. Young children are almost as accurate in identifying squares (87 percent correct on our paper task) as in identifying circles, although preschoolers are more likely to call nonsquare rhombus squares." However, they were just as accurate as older children in naming "tilted" squares.
Triangles. Young children are less accurate in identifying triangles (60 percent correct). They are likely to accept triangular forms with curved sides and reject triangles that are too "long," "bent over," or "point not at the top. …