N400 Effects Reflect Activation Spread During Retrieval of Arithmetic Facts

Abstract

Arithmetic facts are stored in densely interconnected memory networks, and retrieval errors may occur because activation spreads to associated results. We studied the extension of activation spread by means of the so-called N400 effect of the event-related brain potential (ERP). With semantic stimuli, N400 amplitude has proved to be inversely proportional to the amount of activation that originates from a priming context. ERPs were recorded from 61 scalp positions while 16 subjects verified 600 multiplication problems (a × b = c). The solution to each problem could be correct or incorrect. Incorrect solutions were either table related to one of the operands (e.g., 5 × 8 = 32, 24, or 16) or unrelated (e.g., 5 × 8 = 34, 26, or 18), and were either a small, medium, or large numerical distance from the correct product. Our findings suggest that activation spread in an arithmetic memory network is restricted to numbers that are table related to one of the operands and that are numerically plausible.Results of simple multiplication problems are retrieved from declarative memory as well-established facts. Retrieval models (Campbell & Graham, 1985;Stazyk, Ashcraft, & Hamann, 1982) assume that each operand and the problem as a whole trigger an automatic spread of activation within a densely interconnected memory network. The total activation creates a candidate set of answers, and the most strongly activated answer node triggers the response. This basic idea can explain several findings obtained with tasks involving retrieval of arithmetic facts. For example, in a verification task, participants have to decide on the correctness of a multiplication problem. A basic finding is that decision time is shorter and error rate smaller for unrelated errors (3 × 8 = 34) than for related errors (3 × 8 = 32; i.e., errors that are multiples of either the first or the second operand). This can be attributed to the fact that solutions associated with one operand have a higher competitive activation level than nonassociated solutions.Another significant factor that affects decision time in arithmetic verification tasks is the numerical distance between a correct and an incorrect solution (3 × 8 = 32 vs. 3 × 8 = 48). Reaction time (RT) to incorrect equations becomes smaller with increasing numerical distance from the correct solution (Ashcraft & Stazyk, 1981). Up to now, it has not been clear if this effect of numerical distance has the same functional basis as the relatedness effect. It could be that the relatedness effect is due to activation spread and the distance effect is due to a process that estimates the plausibility of the size of a solution (see, e.g., Zbrodoff & Logan, 1986). It is difficult to tease such factors apart by means of RT alone, because RT represents the accumulation of the effects of all delaying factors on a task.Studies with semantic materials have revealed that the strength of activation in memory networks can be measured by using eventrelated brain potentials (ERPs; Kutas & Hillyard, 1980;Kutas & Van Petten,...

Interacting neighbors: A connectionist model of retrieval in single-digit multiplication

“…Recall that Galfano et al (2003) found that presentation of a problem activates not only the answer, but also the neighbors of this problem, which provides direct evidence for this assumption. Niedeggen and Rösler (1999) have provided event-related potential (ERP) evidence for this same assumption, which we will discuss below in more detail. The second assumption is that not all problems are represented; rather, for each commutative pair of problems (e.g., 7 ϫ 5 and 5 ϫ 7), there is only one representational unit.…”

Event-related potentials of single-digit addition, subtraction, and multiplication

“…First, in verbal-production tasks, the tongue movement and muscle activities might add artifacts to the EEG recording. For this reason alone, many other similar studies have used delayed verification tasks (e.g., Galfano, Mazza, Angrilli, & Umiltà, 2004;Niedeggen & Rosler, 1999;Szucs & Csepe, 2005). Second, multiplication problems generally involve larger numbers as their answers (ranging from 6 to 72) than do other operations such as addition (5-17) and subtraction (1-7).…”

Dopamine modulates attentional control of auditory perception: DARPP-32 (PPP1R1B) genotype effects on behavior and cortical evoked potentials

“…2006;Sanders & Astheimer, 2008). The effects of attentional control incurred, for instance, by stimulus competition, stimulus-response conflict or error detection, are more commonly observed in an ERP modulation effect around 400-550 ms after stimulus onset (Frühholz et al, 2009;Larson et al, 2009;Liotti et al, 2000;Niedeggen & Rösler, 1999;West & Alain, 1999). Our findings suggest that the DARPP-32 gene is associated with the amplitude of these components.…”

“…Furthermore, we were interested in analyzing DARPP-32 genotype effects on the late N450 modulation effect, which has been previously shown to reflect the deployment of attentional resources when cognitive conflict (e.g., Larson et al, 2009;West & Alain, 1999), error monitoring (Niedeggen & Rösler, 1999) or attention orienting (Kanske et al, 2011) was involved. Previous studies showed a more posterior distribution of the N450 component when not using the classical Stroop but other conflict paradigms (e.g., Frühholz et al, 2009;Schirmer & Kotz, 2003).…”