The Meaning of Multiplication: Electrophysiological Evidence of Semantic Memory Access and Organization in Children
How do children access and organize multiplication in memory? Although arithmetic processing has been extensively studied in adults, less attention has been given to the developing brain. This dissertation work takes steps towards informing models of arithmetic that were primarily based on adults. Event-related potentials (ERPs) provided a continuous measure of brain activity to study the cognitive mechanisms engaged during multiplication verification in children. In a series of experiments, ERPs were recorded while children verified single-digit multiplication problems. Experiment 1 directly compared children and adults to clarify the nature of the cognitive processes engaged in the two populations. Results showed that children use meaning-level processes, whereas adults engage target categorization. Experiment 2 investigated problem size in children to determine if small and large problems are treated differently. Results showed that only correct responses were affected, suggesting that access to these facts in memory may depend on practice. Experiment 3 investigated the effect of operand format to determine if children process spoken number words and Arabic digits differently. Children showed no effect of operand format, indicating that they access multiplication comparably across formats. Experiment 4 examined the organization of memory for multiplication by comparing the brain responses of table-related and unrelated solutions. Children were sensitive to solution relatedness, suggesting that multiplication is organized as associated facts. Altogether, these experiments provide compelling evidence that children's memory for arithmetic facts is organized as an associative network with stronger connections for problems that are more frequently encountered in daily life.