Modeling the SiCE: When numerical magnitudes affect physical-size comparisons

Background: This work presents a connectionist model for the emergence of automaticity in the processing of numerical magnitudes. In line with the proposal of Tzelgov & Ganor-Stern (2005), the model predicts the size congruity effect (SiCE): Training participants to decide which of two symbols represents a larger magnitude results in a Stroop-like effect when they need to decide which symbol is physically larger. Method: The model assumes that in the context of the task, after training participants to perform numerical and physical-size comparisons, these comparisons are performed in parallel while being modulated by attention given specifically to the physical dimension due to task requirements. It further assumes that the results of the two comparisons activate a shared response process based on evidence accumulators, thereby affecting latency. The proposed model includes a module that can learn the order of magnitudes represented by a set of symbolic stimuli, based on the symbolic comparison model developed by Leth-Steensen & Marley (2000), which is superimposed on a model of automatic processing of two dimensions, adapted from a model for the Stroop effect developed by Cohen, Dunbar & McClelland (1990). Training consisted of teaching the model to perform numerical and physical-size comparisons separately using adjacent pairs of ordered stimuli. Results & Conclusions: After training the model simulated the SiCE, modulated by intra-pair distance, as exhibited by participants who were trained in a similar manner. Accordingly, the model shows how learning order relations of adjacent pairs could lead to the automatization of an internal representation of numerical magnitudes on a “mental number line”.