Abstract
BackgroundRecent cognitive and computational models (e.g. the Interacting Neighbors Model) state that in simple multiplication decade and unit digits of the candidate answers (including the correct result) are represented separately. Thus, these models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems). Empirical data supporting this view are still scarce.MethodsData of 24 participants who performed a multiplication verification task with Arabic digits (e.g. 8 × 4 = 36 - true or false?) are reported. Behavioral (i.e. RT and errors) and EEG (i.e. ERP) measures were recorded in parallel.ResultsWe provide evidence for neighborhood-consistency effects in the verification of simple multiplication problems (e.g. 8 × 4). Behaviorally, we find that decade-consistent lures, which share their decade digit with the correct result (e.g. 36), are harder to reject than matched inconsistent lures, which differ in both digits from the correct result (e.g. 28). This neighborhood consistency effect in product verification is similar to recent observations in the production of multiplication results. With respect to event-related potentials we find significant differences for consistent compared to inconsistent lures in the N400 (increased negativity) and Late Positive Component (reduced positivity). In this respect consistency effects in our paradigm resemble lexico-semantic effects earlier found in simple arithmetic and in orthographic input processing.ConclusionOur data suggest that neighborhood consistency effects in simple multiplication stem at least partly from central (lexico-semantic') stages of processing. These results are compatible with current models on the representation of simple multiplication facts – in particular with the Interacting Neighbors Model – and with the notion of decomposed representations of two-digit numbers in general.
Highlights
Recent cognitive and computational models state that in simple multiplication decade and unit digits of the candidate answers are represented separately
A 2 × 2 × 2 repeated measurements ANOVA using response times (RTs) as dependent variable including the factors Stimulus Onset Asynchrony (SOA), relatedness, and consistency revealed significant main effects for all three factors: Trials in the long SOA condition were responded to 174 ms faster than trials in the short SOA condition (F (1; 23) =
Consistency interacted with SOA (F (1; 23) = 5.35; MSe = 705.045; p < .05): The consistency effect was larger for the long SOA (30 ms) than for the short SOA (15 ms)
Summary
Recent cognitive and computational models (e.g. the Interacting Neighbors Model) state that in simple multiplication decade and unit digits of the candidate answers (including the correct result) are represented separately These models challenge holistic views of number representation as well as traditional accounts of the classical problem size effect in simple arithmetic (i.e. the finding that large problems are answered slower and less accurate than small problems). Representation, production, and verification of multiplication facts There is broad agreement that most simple multiplication facts are stored in and retrieved from an associative network in declarative memory [1,2,3,4,5]; for an overview see [6]. A similar effect is found in verification tasks: Operand-related incorrect probes (lures'), which are numerically close to the correct result, are harder to reject than neutral' lures [14]
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