Abstract
A four experiment investigation was carried out into two types of inhibitory control and whether or not they were involved in mental arithmetic division. Previous research had either focussed on the central executive component of working memory as a single entity or split this component into response selection, memory updating, input monitoring and inhibition and has examined how these components relate to addition, subtraction and multiplication. The first two experiments reported here represent an attempt to split inhibition into two separate abilities, namely prepotent response inhibition and resistance to distracter interference and investigate how they might relate to complex division. The Two experiments were loosely based on the Stop-Signal Task and the Eriksen Flanker Task, respectively. Experiment One followed a 3x3x3 factorial design whereas Experiment Two was a 3x2 design. All factors were varied entirely within-subjects. The results suggested a major rôle in mental division for both types of inhibition and some results were unexpected. The results of Experiment Two suggested a speed-accuracy trade-off as an effect of the flanker digits.
Experiment Three was designed to extract the short division procedure from the division process. Experiment Four was created to extract the carrying procedure. The results suggested a rôle for both prepotent response inhibition and resistance to distracter interference in monitoring the procedural aspects of complex division. Only resistance to distracter interference had a rôle in monitoring magnitudes of short-division and carry-values. The speed-accuracy trade-off apparent in Experiment Two may, at least in part, be as a result of the involvement of resistance to distracter interference in preventing interference with regard to carry procedures and the value of the carry. The results were discussed, amongst other aspects, in terms of their relationship to conflict monitoring theory and dual mechanism of control theory (Braver et al, 2007, 2009; Botvinick et al, 2001) and a two-channel system of inhibition was proposed, resistance to distracter interference being a proactive subcomponent and prepotent response inhibition being reactive.