Your favorite number is special (to you): Evidence for item-level differences in retrieval of information from numerals

Development is in the details: Event-related theta oscillations reveal children and adults verify multiplication facts differently

When verifying the correctness of single-digit multiplication problems, children and adults show a robust ERP correctness effect thought to reflect similar cognitive processes across groups. Recent studies suggest that this effect is instead a modulation of the negative-going N400 component in children, reflecting access to semantic memory, and the positive-going P300 component in adults, reflecting stimulus categorization. However, the relative difference in ERP amplitude is the same for both components, more positive for correct than incorrect solutions, presenting a challenge to ascertaining the appropriate interpretation. Time-frequency analysis (TFA) of the N400/P300 window provides an objective approach to dissociating these effects. TFA measured from solution onset during single-digit multiplication verification revealed significant modulations of event-related as theta power (3-6 Hz) in both groups. Correct trials elicit less power in children (9-12 years) and more power in adults relative to incorrect trials. These findings are consistent with modulations of the N400 and P300, respectively, where opposite effects were predicted for spectral power. The ERP results further support a reinterpretation of the multiplication correctness effect. In contrast, TFA of the N400 effect elicited to a word-picture verification task revealed the same event-related theta effect in both groups, with increased power for mismatched than matched pictures. Together, these findings provide evidence for a developmental shift in cognitive processing specific to the multiplication task. Models of arithmetic should account for this overlooked difference in cognitive processing between children and adults.

Meaning to multiply: Electrophysiological evidence that children and adults treat multiplication facts differently

Multiplication tables are typically memorized verbally, with fluent retrieval leading to better performance in advanced math. Arithmetic development is characterized by strategy shifts from procedural operations to direct fact retrieval, which would not necessitate access to the facts' conceptual meaning. This study tested this hypothesis using a combination of event related brain potentials (ERP) and behavioral measures with 3rd-5th grade children and young adults. Participants verified the solutions to simple multiplication problems (2 × 3 = 6 or = 7) and the semantic fit of word-picture pairs, separately. Children showed an N400 effect to multiplication solutions with larger (more negative) amplitude for incorrect than correct solutions, reflecting meaning-level processing. A similar ERP response was observed in the word-picture verification task, with larger negative amplitude for word-picture pairs that were semantically mismatched compared to matched. In contrast, adults showed a P300 response for correct solutions, suggesting that they treated these solutions as potential targets in over-rehearsed mathematical expressions. This P300 response was specific to math fact processing, as the word-picture verification task elicited a classic N400 in adults. These ERP findings reveal an overlooked developmental transition that occurs after fifth grade, and speak to theories of arithmetic that have been based primarily on adult data.