Working memory and multi-digit arithmetic: the effects of dual-tasks, carries, format and strategy

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Cross, S.R., 2004. Working memory and multi-digit arithmetic: the effects of dual-tasks, carries, format and strategy. PhD, Nottingham Trent University.

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Abstract

Following a review of working memory (WM), cognitive arithmetic and associated cognitive models, this study identified and investigated the lack of consensus on WM involvement in cognitive arithmetic. Two series of dual-task experiments extended previous studies through the inclusion of multi-digit problems from all four arithmetic operations, and through various manipulations of number of carries, visual format of presentation and solution difficulty. The effect of strategy was also explored, as was the effectiveness of different secondary tasks. The following conclusions are offered:

The involvement of the WM components described in the Baddeley and Hitch WM model (1974, 2000) is supported, but this involvement is heavily dependent not only on task and problem factors but also on the type of arithmetic operation. The phonological loop was implicated in multiplication, and the central executive in addition, while subtraction and division provided no evidence implicating either of these components.

The studies of Heathcote (1994) and Trbovitch and LeFevre (2003) are supported, in that there is evidence that linear (horizontal) format of presentation does appear to support phonological reading processes, while columnar (vertical) format does appear to engage visuo-spatial processing, with the latter providing greater support for the carry operation.

These results provide partial support for the existence of a separate cognitive module for number processing, (Butterworth, 2000), but also suggest that the triple-code model, (Dehaene and Cohen, 1995), needs to accommodate the possibility that the phonological loop is only involved when rote-learned 'verbal word frame' multiplication facts are retrieved, and that additions are solved by the use of the central executive to calculate or count addition totals.

The existence of task x problem interactions supports the encoding complex - interactive model of Campbell and Clarke (1998), but brings into question the abstract modular model of McCloskey, Caramazza and Basili (1985).

Secondary tasks cannot be assumed to load WM simply in virtue of their phonological, visuo-spatial and executive associations, and different secondary random generation tasks are not equivalent in terms of their ability to load the executive components of WM.

Response times and error rates demonstrated different patterns of main effects and interactions. This suggests that they measure different aspects of cognitive load. Response times possibly being more indicative of encoding processes, and error rates more indicative of calculation processes. Error scores should therefore be the preferred measure in future studies that investigate WM involvement in arithmetic processes.

Analysis of strategy use supports and extends the findings of Hecht (2002), in that relatively few participants change their solution strategy when faced with problems at different experimental levels, but different strategies can demonstrate significantly different response times. Consequently, strategy use, if not controlled and analysed, has the ability to undermine the logic of dual-task studies.