When 2 × 4 is meaningful: the N400 and P300 reveal operand format effects in multiplication verification

Abstract

Arithmetic problems share many surface-level features with typical sentences. They assert information about the world, and readers can evaluate this information for sensibility by consulting their memories as the statement unfolds. When people encounter the solution to the problem 3 × 4, the brain elicits a robust ERP effect as a function of answer expectancy (12 being the expected completion; 15 being unexpected). Initially, this was labeled an N400 effect, implying that semantic memory had been accessed. Subsequent work suggested instead that the effect was driven by a target P300 to the correct solutions. The current study manipulates operand format to differentially promote access to language-based semantic representations of arithmetic. Operands were presented either as spoken number words or as sequential Arabic numerals. The critical solution was always an Arabic numeral. In Experiment 1, the correctness of solutions preceded by spoken operands modulated N400 amplitude, whereas solutions preceded by Arabic numerals elicited a P300 for correct problems. In Experiment 2, using only spoken operands, the delay between the second operand and the Arabic numeral solution was manipulated to determine if additional processing time would result in a P300. With a longer delay, an earlier N400 and no distinct P300 were observed. In brief, highly familiar digit operands promoted target detection, whereas spoken numbers promoted semantic level processing-even when solution format itself was held constant. This provides evidence that the brain can process arithmetic fact information at different levels of representational meaningfulness as a function of symbolic format.

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

“…5 ) revealed the typical sensory components (P1-N1-P2) in both tasks after the onset of either the solution or the drawing. In the digit task, a subsequent P300 response is visible for correct solutions consistent with Dickson et al (2018) ; Dickson and Federmeier (2017) ; Dickson and Wicha (2019) , and Jasinski and Coch (2012) . In contrast, in the word-picture task an N400 is visible for both match and mismatch trials peaking around 400 ms after picture onset.…”

“…Initial research therefore implied that both children and adults construct meaning-level representations for simple multiplication problems. However, as alluded to above, more recent studies from multiple labs have reexamined the nature of this arithmetic correctness effect in adults and came to the same independent conclusion that the adult brain response was functionally and morphologically different than the N400 ( Dickson et al, 2018 ; Dickson and Federmeier, 2017 ; Dickson and Wicha, 2019 ; Jasinski and Coch, 2012 ; Wicha et al, 2018 ). Essentially, what was originally interpreted as an N400 modulation, with larger amplitude for incorrect solutions, was more in-line with a modulation of the P300, with larger amplitude for correct solutions (see Dickson and Wicha, 2019 for a more in-depth discussion of this reexamination of the adult correctness effect).…”

“…However, some behavioral researchers have argued that the developmental transition between calculation and retrieval may happen more gradually ( LeFevre et al, 1996 ; Siegler, 1996 ). Moreover, recent neuroimaging studies with adults have reinterpreted the ERP response observed to mathematical fact expressions, implying that children might not process arithmetic like adults do ( Dickson et al, 2018 ; Dickson and Federmeier, 2017 ; Jasinski and Coch, 2012 ). The current study adds critical new evidence to the limited literature on the neurocognitive basis of arithmetic in elementary school children and tests whether a slower developmental trajectory toward adult-like processing has indeed been overlooked.…”

“…Research using ERPs to study how arithmetic is processed has revealed robust brain responses to proposed solutions in both children and adults. This research has been dominated by studies that include adult populations ( Dickson et al, 2018 ; Dickson and Federmeier, 2017 ; Jasinski and Coch, 2012 ; Jost et al, 2003 ; Martinez-Lincoln et al, 2015 ; Niedeggen et al, 1999 ; Núñez-Peña et al, 2006 ; Salillas and Wicha, 2012 ), with a smaller group of studies that have compared child and adult brain responses ( Moore et al, 2014 ; Prieto-Corona et al, 2010 ; Xuan et al, 2007 ; Zhou et al, 2011 ). The methods used in these studies have varied, with some using verification tasks and others production, or different operations (addition vs multiplication, etc.).…”

“…A P300 is typically observed during stimulus categorization and is larger for task-relevant targets than non-target items ( Polich, 1987 , 2007 , 2012 ; Sutton et al, 1965 , 1982 ). Studies that measured the pattern of ERPs in adults across multiple methodological manipulations have confirmed that the brain response to arithmetic facts is more consistent with the P300 than the N400 ( Dickson and Wicha, 2019 ; Dickson et al, 2018 ). Thus, to the extent that the reports of the arithmetic N400 effect in children are true, this reinterpretation of the adult ERPs implies that children and adults may actually engage qualitatively different neurocognitive processes when verifying arithmetic facts, with only children reliably building meaning-level expectations for the solutions.…”