Two-digit number processing: holistic, decomposed or hybrid? A computational modelling approach

Abstract

Currently, there are three competing theoretical accounts concerning the nature of two-digit number magnitude representation: a holistic, a strictly decomposed, and a hybrid model. Observation of the unit-decade compatibility effect (Nuerk et al. in Cognition 82:B25-B33, 2001) challenged the view of two-digit number magnitude to be represented as one integrated entity. However, at the moment there is no study distinguishing between the decomposed and the hybrid model. The present study addressed this issue using a computational modelling approach. Three network models complying with the constraints of all three theoretical models were programmed and trained on two-digit number comparison. Models were compared as to how well they accounted for empirical effects in the most parsimonious way. Generally, this evaluation indicated that the empirical data were simulated best by the strictly decomposed model. Implications of these results for our understanding of the nature of human number magnitude representation are discussed.

Learning multiplication: An integrated analysis of the multiplication ability of primary school children and the difficulty of single digit and multidigit multiplication problems

“…When two-digit numbers are encoded, units and decades have been shown to be processed separately (Moeller, Huber, Nuerk, & Willmes, 2011). If an analogous process takes place while doing mental calculation, each combination of two digits (one digit from each number) is multiplied and the results are added.…”

Multimodal Semantic Quantity Representations: Further Evidence from Korean Sign Language

“…The exact nature of this interaction is still under debate. Three different scenarios seem possible: first, the internal analog quantity representation, which is often described by the metaphor of a mental number line (Dehaene and Cohen, 1995; Dehaene, 2003), may be influenced by external representations such that it increases its acuity (Verguts and Fias, 2004; Dehaene, 2007) and/or adopts the base-10 structure of the Arabic number system (Nuerk et al, 2001, 2004a; Nuerk and Willmes, 2005; Verguts and De Moor, 2005; Moeller et al, 2011). Second, the inherited analog quantity representation may be replaced by a symbolic quantity representation.…”

Bringing Back the Balance: Domain-General Processes Are Also Important in Numerical Cognition

“…When the within-decade filler trials (i.e., trials in which the unit digit is decisive, e.g., 42_47) are introduced, the unit-decade compatibility effect increases, because participants fixate more on the units even in between-decade trials. Eye-fixation behavior and unit interference has been shown to depend on the proportion of fillers: The more often the unit digit is relevant, the larger the proportions of fixation on the unit in the experiment and the larger the unit-decade compatibility effect (Macizo and Herrera, 2011; Moeller et al, 2011; for children see Mann et al, 2011; Huber et al, 2014). Thus, the effects observed in studies on multi-digit number processing (i.e., proportion of congruent and incongruent trials as well as presence of fillers) correspond to the typical pattern of behavior in tasks assessing cognitive control (including executive attention).…”