Research

Neighborhood consistency in mental arithmetic: Behavioral and ERP evidence

Frank Domahs^1,2 , Ulrike Domahs³ , Matthias Schlesewsky³ , Elie Ratinckx⁴ , Tom Verguts⁴ , Klaus Willmes^1,2 and Hans-Christoph Nuerk⁵

¹  Interdisziplinäres Zentrum für Klinische Forschung BIOMAT., Universitätsklinikum der RWTH Aachen, Germany

²  Lehr- und Forschungsgebiet Neuropsychologie, Universitätsklinikum der RWTH Aachen, Germany

³  Institut für Germanistische Sprachwissenschaft, Philipps-Universität Marburg, Germany

⁴  Department of Experimental Psychology, Ghent University, Belgium

⁵  Fachbereich Psychologie, Paris Lodron Universität Salzburg, Austria

author email corresponding author email

Behavioral and Brain Functions 2007, 3:66doi:10.1186/1744-9081-3-66

Published:	28 December 2007

Abstract

Background

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. 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.

Methods

Data 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.

Results

We 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.

Conclusion

Our 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.