Learning From Symbolic Objects

Perhaps the most important challenge of early-childhood education is helping children to master a variety of symbol systems. Within a few short years, children must learn to understand and use letters, numbers, mathematical symbols, maps, and other symbol systems. Parents, educators, and researchers naturally want to find the most effective educational techniques and tools to help them learn.

A variety of objects have been designed to help young children learn letters and numbers. For example, letter and number magnets and blocks are found in the homes of many American preschoolers. In the classroom, teachers sometimes use more formal manipulative systems composed of concrete symbolic objects, such as Cuisenaire Rods or Digi-Blocks, that have been explicitly designed to help young children learn mathematics.

The design and use of these concrete symbolic objects is motivated by the assumption that young children’s thinking is concrete (rather than abstract) by nature. Based on the writings of scholars such as Piaget, Bruner, and Montessori, educators have suggested that young children learn best through the use of highly concrete objects. However, our prior research on a variety of symbol systems (e.g., scale models, pictures, and maps) leads us to think twice about the value of having young children play with objects that are intended to be used as symbols.

All symbolic objects have a dual nature: They are both objects in their own right and representations of something else. Therefore, to use a symbol as a representation of something else, one must focus more on what it represents and less on the symbol as an object. We suggest that using letter and number toys as representations may have just the opposite effect than what is intended: making children focus more on them as objects and less on what they stand for.

This theoretical perspective has motivated a line of IES funded research on the effects of using concrete objects. In one set of studies (Uttal, Bostwick, Amaya, & DeLoache, in preparation), we examined the consequences of having children play with objects such as letter or number blocks and magnets. We observed that in everyday situations, young children often treat these objects as toys. Therefore, we asked whether experience playing with symbolic objects as toys would affect using those objects as symbols. We randomly assigned 3- and 4-year-olds to play games either with plastic letters or numbers or with more traditional (non-symbolic) materials. For example, one group of children blew bubbles using the letters “O” or “P” as wands, while the control group simply blew bubbles with standard bubble wands.

The children who played with the symbolic objects showed no advantage with respect to their letter and number knowledge. If anything, playing with the symbolic objects actually hurt; the control group, who did not play with the letters, knew significantly more letters at the end of the study than did the children who had played games with letters or numbers.

There was, however, one way in which using concrete letters or numbers in a symbolic manner facilitated children’s understandings of letters’ and numbers’ symbolic properties. We asked the children to construct representations to help them remember the contents of objects hidden in a box. For example, we hid a toy bear in a box, and the children were asked to use either a crayon and paper or letter magnets to indicate (and hence to remember) what was in the box. Although most of the children could not write letters, they nevertheless could use the magnetic letters to represent the contents. For example, many placed a “B” magnet on the box to indicate that a bear was hidden inside it. Moreover, children who were initially given the opportunity to represent objects symbolically with magnets were more likely to construct symbolic representations when asked to do the crayon version of this task. We believe that using the concrete objects in a symbolic fashion — as representations of the contents of the boxes — helped children gain insight into the idea of using letters as representations.

In another series of studies (Amaya, Uttal, & DeLoache, under review) we investigated the effectiveness of concrete symbolic objects, known as manipulatives, in helping young elementary-school children learn the procedures associated with two-digit subtraction. We taught children using either using the traditional written method or a commercially available manipulatives set, per the manufactures instructions. This set was composed of small individual blocks that could be assembled into larger units of ten to represent both the tens and ones units of a quantity. Children could physically remove blocks from this quantity to concretely carry out the process of double-digit subtraction.

We found that children initially performed equally well in both training conditions. However, those children who learned with the manipulatives had trouble transferring knowledge to written versions of the math problems; they did not use what they had learned using the manipulatives to solve written versions of the same or similar problems. Moreover, learning with the manipulatives took almost three times as long as learning with the written method. This result does not mean that manipulatives are never useful, but it does challenge the typical assumption that they are more effective than other teaching tools in all contexts.

Our work shows that the theories and methods of developmental psychology are highly relevant to issues of concern in education. Evidence-based research both challenges traditional assumptions regarding the education of young children and points to exciting and promising new directions.

References

• Amaya, M. M., Uttal, D. H., & DeLoache, J. S. Procedural knowledge in two-digit subtraction: Comparing concrete and abstract. Manuscript submitted for publication.
• Uttal, D. H., Bostwick, M., Amaya, M. M., & DeLoache, J. S. Concreteness and symbolic development: The effect of manipulatives on children’s early literacy skills. Manuscript in preparation.