Modelling complex span performance: activation, attentional capacity, and interference

Complex span tasks, combining storage and processing requirements, are widely used working memory measures. They are related to executive attention and predict fluid intelligence and performance on cognitively demanding tasks. The two most prominent models of complex span performance are the Time-Based Resource Sharing and the Serial Order in a Box model. The former posits a refreshing process that re-activates decaying memory representations, whereas the latter is based on interference among representations and suppression of distractors. Both of these models have merits and can account for several findings, but none provides a complete explanation. We propose an alternative model that includes both capacity-limited activation and interference, framed within the Theory of Constructive Operators. Our model assumes: (a) an attentional resource activates a limited number (M capacity, increasing during development) of task-relevant information units; (b) during stimuli presentation this resource is used to activate representations of memoranda as well as encoding and order-keeping operations; (c) also the concurrent processing task uses a share of M capacity; (d) activation of the memoranda representations that exceed M capacity decreases over subsequent operations, and (e) continues decreasing during list recall; (f) interference among representations is a power function of the number of them whose activation is decreasing; (g) fully activated representations are recalled correctly, and partly activated representations are retrieved with a specified probability. The model includes one free parameter (rate of activation decrease, mainly due to interference) and one parameter (M capacity) that can be independently estimated from other tasks. Two experiments (one with adults and one with 10- to 13-year-olds) supported this model, and M capacity accounted for approximately half of the developmental variance.