Symbolic development in representational play and early mathematics

Mathematics skills emerge over early childhood and may depend upon the development of domain-general cognitive skills, such as those demonstrated when objects are represented symbolically in play. The purpose of this study was to compare patterns of development in symbolic play and nonverbal mathematics around age 3 when an exact mechanism, or reliably accurate nonverbal calculation of 1 + 1 and 2 - 1, is reported to emerge. The skills of 15 children were assessed at 35- to 37-months and then at 38- to 40-months utilizing a covered-array task to assess mathematics skills and a modeled play scenes procedure to measure play skills. Results showed both the symbolic play and calculation scores increased over the 3-month period. Then, an Exact Mechanism Group was formed with 9 children who calculated both 1 + 1 and 2 - 1 at 38- to 40-months and an Approximate Mechanism Group was formed with 6 children who failed to calculate either or both problems. There were no significant differences between the two groups on the symbolic play or nonverbal mathematics assessments at either session. However, there were suggestions of patterns that could point to differences in the symbolic skills potentially related to the development of mathematics skills. The play style of the Exact Mechanism Group increased in multischeme combinations, while that of the Approximate Mechanism Group increased in original play acts. Additionally, when producing responses during the calculation task, the Exact Mechanism Group demonstrated more behaviors that implied intentional mental planning to solve problems correctly. These results suggested that, by ages 38- to 40-months, the Exact Mechanism Group has begun to learn and to incorporate aspects of operative functioning in play that may assist their understanding of the transformations that occur in nonverbal calculation. The Approximate Mechanism Group may have continued to rely on figurative aspects that suggest new play acts, but when applied to calculation, may not always be reliable. These findings suggest that nonverbal mathematics skills develop gradually over early childhood and provide some support for the hypothesis that the development of simple calculation is influenced by the development of symbolic representation skills.