Introduction

The ability to understand and use symbols is one of the defining characteristics of being human. Symbols allow us to think about information that is not available to direct sensory experience. Symbol systems such as language also allow us to communicate with others and thus provide the foundation for learning. Similarly, numbers allow us to think about and mentally manipulate abstract representations rather than having to rely on the actual physical quantities. It is not surprising that the development of symbolic capacity is an important hallmark in almost all theories of cognitive development.

Much research on symbolic development is motivated by the assumption that young children's thinking is inherently concrete in nature, and that their thinking focuses only on immediately perceptible concepts (Bruner, 1966; Piaget, 1951; Vygotsky & Kozulin, 1986; Werner & Kaplan, 1963). In contrast, older children are more able to think about abstract concepts that are not tied to the concrete, perceptible properties of objects that they can see or feel. Put simply, the general notion that concrete thinking precedes abstract thinking is characteristic of most theories of development.

The general assumption that young children's thinking is inherently concrete in nature has had a tremendous effect on the development of educational curricula and materials. Many researchers and educators believe that the best way to help young children learn to understand the abstract properties of symbolic relations is to first make the symbols less abstract and more concrete (Ball, 1992; Clements & McMillen, 1996; Montessori, 1917). For example, Bruner (1966) suggested that the goal of early education should be to "empty the concept of specific sensory properties [in order to] grasp its abstract properties" (p. 65). This assumption has led to the development of a wide variety of educational materials that are specifically designed to appeal to young children's preference for concrete, tangible objects. Examples include letter blocks, number magnets, and formal manipulative systems, such as Dienes Blocks and Cuisenaire Rods. Many early childhood educators assume that these sorts of materials are the best, or even only, way for young children to learn. The assumption has been that "Concrete is inherently good; abstract is inherently not appropriate—at least at the beginning, at least for young learners" (Ball, 1992, p. 16).

The primary purpose of this chapter is to reexamine the focus on concreteness in cognitive development and early education. We will question both the theoretical background of the assumption as well as its educational implications. We will show that the characterization of development in terms of a shift from concrete to abstract is an oversimplification; there are situations in which very young children seem capable of abstract reasoning, and there are other situations in which older children's thinking is highly concrete. We also question the assumption that concrete objects should necessarily provide the foundation for young children's learning of symbolic relations. In some cases, the use of an attractive concrete object may actually have a negative effect because it may focus children's attention more on the object itself rather than on what the object is intended to represent. These claims are based on a review of both classic and current literature on the development of children's understanding of important symbols, including letters, numbers, mathematical symbols, and scale models. We begin by considering the historical and theoretical origins of the commonly accepted belief that young children's thinking is inherently concrete and that early childhood education therefore should focus on the use of concrete objects. We also review recent theoretical and empirical work that has demonstrated that these assumptions may not always be correct.

TRADITIONAL APPROACHES: THE CONCRETE-TO-ABSTRACT SHIFT

Development often has been characterized as children's struggle to transcend their shallow and shortsighted view of the world (Bruner, Goodnow, & Austin, 1956; Piaget, 1951; Werner & Kaplan, 1963). In classic developmental theories, the acquisition of symbolic competence is seen to proceed through a concrete-to-abstract shift: the progression from thinking that is rooted in concrete reality to thinking that is less constrained by context. Sigel (1993) described this developmental progression as the child's attempt to "separate him- or herself mentally from the ongoing here and now, and project him- or herself to some other temporal plane (past or future or the nonpalpable present), in turn transforming the received communication into some symbol or sign system" (p. 142). Eventually, children's mental representations are no longer directly linked, in an iconic fashion, to the information that they originally experienced. Instead, older children are able to represent information more abstractly, so that the information is now only distantly related to how it was experienced initially.

Almost all classic theories of cognitive development have appealed to the idea that young children's thinking is inherently concrete. For example, Piaget (Inhelder & Piaget, 1958; Piaget, 1951) suggested that the development of the ability to reason in terms of abstract, hypothetical propositions, without reference to more concrete information, was the end point or goal of cognitive development. Piaget found that concrete operational children had trouble reasoning about false propositions that involved relations that could not exist in the real world. For example, if concrete operational children are given the statements, "If mice are bigger than dogs and dogs are bigger than elephants," they typically cannot deduce "then mice are bigger than elephants." These sorts of problems require that children reason abstractly about the relations as given, rather than about the actual relations in the world (Werner & Kaplan, 1963). Concrete operational children fail because there is no concrete basis from which to reason about and solve the problem.

Other prominent theorists have also characterized development in terms of a shift from concrete to abstract. For example, in studies of early categorization, Bruner et al. (1956) described conceptual development as a perceptual-to-conceptual shift; children first think of objects only in terms of the properties directly available to their senses but eventually begin to consider abstract properties of objects. For example, children may think that birds and bats are in the same category because they look similar and because they both fly. With development, children become able to categorize objects and living things more on the basis of abstract and nonobservable information. Consequently, they now realize that bats and birds should be in separate categories, and that a creature that does not fly, such as a penguin, may nevertheless belong in the bird category. The developmental transition is thus from a reliance on concrete and perceptible properties to more abstract and less observable ones.

Some of Vygotsky's writings are reminiscent of the concrete-to-abstract shift. Specifically, Vygotsky (Vygotsky & Kozulin, 1986) conducted two lines of work that were motivated by this general assumption. First, he suggested that young children's classification is inherently thematic in nature. Thematic categories (e.g., rabbit and carrot) are based on highly concrete, salient properties that bind objects or living things together in a common setting, rather than on the underlying and abstract relations; they are developmentally primitive. The more developmentally advanced form of categorization (e.g., carrot and potato) is based on taxonomic properties. To think about objects in this way, children must learn to look beyond the concrete and perceptually similar characteristics in favor of deeper but less obvious similarities. Second, Vygotsky also pointed out the important role of concreteness in symbolic play. Young children's pretend play often involves the substitution of concrete objects for something else in the real world (e.g., a stick for a horse). He suggested that the use of concrete objects in this way was an early form of symbolization. In the context of the game, children are less bound to the properties of the objects and feel comfortable substituting the objects for something else. Pretend play thus serves the important function of helping children to see that the physical object can be thought of in a different way, as a representation of something else.

Werner and Kaplan (1963) provided what is perhaps the most specific articulation of the relation between concreteness and symbolic development. They argued that development involved a shift from holistic to analytic thinking. Young children initially focus on "physicochemical stimuli" from the environment. By this Werner and Kaplan meant that young children interpret stimuli in terms of their concrete, physical properties. Eventually, children transform stimuli and interpret them as "stimulus-signs or signals" (p. 9). For example, a young child might interpret the letter "A" as two diagonal lines and a crossbar. An older child instead interprets the letter as being related to language, even if he or she does not precisely know how this relation works (see Bialystok et al., 2000).

ALTERNATE PERSPECTIVES: DOES DEVELOPMENT ALWAYS PROCEED FROM CONCRETE TO ABSTRACT?

The notion that young children's thinking is inherently concrete in nature is not universally accepted. For example, researchers have recently presented evidence that even infants are capable of thinking about abstract concepts. Other researchers have challenged the notion that development proceeds from concrete to abstract, suggesting that in some cases the opposite could be true. In this section we briefly summarize these findings and theoretical perspectives.

Abstract Concepts in Infants

Recent research on cognitive development in infancy provides an important challenge to the idea that development proceeds from concrete to abstract. Several lines of research have revealed that infants can interpret movements or actions in terms of abstract concepts. For example, Quinn and colleagues (Quinn, 2003; Quinn, Adams, Kennedy, Shettler, & Wasnik, 2003) have found that infants interpret the position of objects in terms of abstract spatial concepts, such as above, below, and between. By 10 months of age, infants will notice if an object is moved from between two lines to above or below one of the lines, even if the object itself changes. Their judgments of spatial position therefore are not tied to the concrete properties of the objects themselves but are instead based on more abstract concepts such as "between." Likewise, young children are capable of interpreting another person's actions in terms of the goals or intentions that motivate those actions. For example, infants will interpret the hand motion of another person as related to the goal of opening a box to obtain a toy (Gergely, Nadasdy, Csibra, & Biro, 1995; Woodward, 2003; Woodward & Sommerville, 2000). After observing a person opening a box to obtain a toy, they are more surprised when the hand moves to a different box than when the hand moves in a different pattern to the same box. Moving to a different box indicates that the person has a different goal in mind. The infants appear to understand the association between where the hand moves and what the person's intent is. This sort of abstract knowledge allows infants to interpret an action, for example, "as getting a drink of milk rather than grasping a milk carton" (Woodward & Sommerville, 2000, p. 76).

Other research has demonstrated that preschoolers use abstracts concepts as a basis for reasoning, inference generation, and problem solving. For example, Gelman and colleagues (Gelman, 2000, 2003; Gelman & Wellman, 1991) have suggested that children understand that certain objects have an internal "essence" that is distinct from the outward appearance of the objects. Gelman has suggested that this understanding can exist in the absence of detailed scientific understanding of the essence. Gelman and Wellman (1991) tested children's understanding of this "inside-outside" distinction using a category induction task. Children 3 and 4 years of age were shown a target object and two choice objects. They were asked (1) to choose which of the two choice objects "looks most like" the target, and (2) to choose which of the two "has the same kinds of insides" as the target. For example, children were presented with triads of objects from which they could either choose the pair sharing the same outside (e.g., an orange and an orange balloon) or the pair sharing the same inside (e.g., an orange and a lemon). Counter to the idea that object concreteness exerts the primary influence on children's object categorization, they found that children as young as 3 years of age could correctly report both that oranges and orange balloons "look alike" and that oranges and lemons "share the same insides."

Thus, young children's understanding of objects is not inevitably bound to external appearances. Rather, children's understanding of the inside-outside distinction demonstrates that nonobvious and abstract object properties also are available to children (Gelman, 2003). These findings highlight the need to question the unqualified characterization of young children's thinking as being concrete. Children's performance on these sorts of tasks forms part of the basis for Gelman's (2003) claim that young children are essentialists. Even young children reason about animals and other entities in terms of abstract-like principles that define their essential characteristics. What matters most to young children, for example, is what is inside an animal, rather than its superficial appearance.

Simons and Keil (1995) presented the most radical reformulation to date of the developmental relation between abstract and concrete thinking. They suggest that the development of children's thinking may, in fact, proceed from abstract to concrete. They argued that very young children may first reason at an abstract level because they lack specific knowledge about objects and events. For example, a child explaining the function of a camera might initially discuss a camera's ability to capture a single point in time, such as its ability to record the moment when she blew out the candles on her birthday cake. Simons and Keil argued that this functional understanding of the camera can precede a more concrete and mechanistic understanding of how light enters the lens and how the various parts of the camera interact. In Simon and Keil's (1995) words, "Although ignorance of the physical components of a system may preclude a concrete explanation for the system's behavior, it is quite possible to generate a principled, abstract explanation without any knowledge of the physical components" (p. 131).

In summary, the notion that young children's thinking is inherently concrete in nature has been challenged in many ways. There is evidence that young children (perhaps even infants) can think in terms of abstract concepts, and there is also evidence that development may sometimes proceed in the opposite direction—from abstract to concrete. In the next section, we consider the relevance of these findings for research on symbolic development. The difficulties children have in using certain kinds of symbols shed light on the question of whether concrete objects do, in fact, facilitate children's learning of symbolic relations.

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