UC Irvine

Working memory has been broadly implicated in mathematics performance, but some of the underlying mechanisms of how working memory interacts with math learning are not well understood. This dissertation looks across theories of working memory, to evaluate the competing claims regarding its influence on mental arithmetic. I attempt to reconcile differences between correlational and experimental literatures to better understand the specific impacts of working memory on arithmetic by employing meta-analytic and experimental methods following a dual-task paradigm. Dual-task experiment involve the performing a primary task (e.g., solving simple arithmetic problems) while simultaneously performing a secondary working memory task (e.g., recalling a string of letters or numbers). If both tasks use overlapping cognitive resources then primary task performance will get worse as the secondary task becomes more demanding. Some argue that working memory operates within the dual-task paradigm through domain-specific overlap (e.g., visuospatial tasks overlap with subtraction more than multiplication) while others argue it is more domain-general where more demanding tasks consume more cognitive resources from attention. In order to investigate whether working memory is causally linked to mental arithmetic performance, I conducted a meta-analysis on dual-task experiments, summarizing the effects of secondary task load on mental arithmetic performance (Chapter 1). In addition, I tested a number of relevant moderators, including the type of secondary task load, variations in primary arithmetic, difficulty, and a proxy for task combinations using authors’ predictions. While results supported a robust causal effect of working memory, it was unclear if arithmetic performance was affected purely by the cognitive demands of the tasks or if they were also affected by similarly shared resources with the secondary task. Thus, I conducted a registered report in which I probed whether arithmetic operations are differentially impacted by various types of working memory secondary tasks by replicating an influential dual-task experiment and testing other relevant factors that predicted differences in dual-task performance (Chapter 2). I ran a within-subject experiment and tested whether there was differential interference of verbal and visuospatial loads on multiplication and subtraction performance. I investigated whether the differential effect could be observed across a number of subsample analyses (e.g., comparing across sub-populations and difficulty levels). Prior results from the influential experiment were not replicated, so I conducted further analyses including an additional task to test whether different theories of working memory could reliably predict any kind of interaction between working memory and arithmetic tasks (Chapter 3). Then, I tested main effects and interactions between secondary task type, arithmetic operations, and difficulty and explored whether such task features are implicated in arithmetic strategy choice. I found strong evidence for main effects of the aforementioned factors on arithmetic but not interactions between them except in the case of an arithmetic-based secondary task load. Overall, this dissertation found more evidence to support attention-focused, domain-general models of the influence of working memory on arithmetic performance rather than content-based, domain-specific models discussed within many previous dual-task studies. Lastly, I discuss the implications of these results as well as an outlook for future research.