An investigation into the structure of numerical cognition
This thesis reports work relating to theoretical frameworks in the area of numerical cognition that have been developed by McCloskey, Caramazza & Basili (1985), Clark & Campbell (1991), Dehaene (1992) and Noel & Seron (1992). The associations between numerical cognition and memory processes in relation to the working memory model of Baddeley (1986) were investigated. The first study used the factor analytic method to elucidate the factor structure of the processes that underlie numerical cognition, and to investigate the various components of the working memory model in relation to arithmetic. A battery of 21 tests was administered to 100 participants. The contribution of the factor analytic study to the structure of numerical cognition is discussed. An examination of the factors (labelled 'access to representations' and 'working memory') identified specific aspects of numerical cognition that were investigated further using experimental methods. The data on magnitude comparisons of numbers and animals that have been found to load onto Factor 1 were reanalysed. Similar patterns were found with the two types of stimuli in some cases. This suggested that Dehaene's notion of a 'number line' might not be specific to numbers. To build on the investigation of magnitude comparisons two experiments were carried out using the dual task paradigm. The results confirmed that magnitude judgements are represented at the level of semantic processing and may not be specific to numbers. The subitizing circles test was also found to load onto Factor 1. This raised a question about the common processes that may be involved both in this test and in other tests loading on that factor. A dual task experiment was used to investigate that possibility. It appeared from the results that the verbally presented tasks in the control and experimental groups produced interference with the s ubitizing task. This result lent support for the view that subitizing is an early pre-lexical perceptual process, possibly based on canonical representations ofthe stimuli. Complex addition and multiplication loaded onto Factor 2, 'working memory' and a further dual task experiment was conducted to investigate the speCUlative view held by Aschraft (1995), that the visuo-spatial sketchpad may playa role in arithmetic problem solving. The results lent support for the view held by Aschraft (1995) of the involvement of the visual-spatial component of working memory in the calculation of multi-digit addition problems. Thus the research reported in this thesis has used a range of investigative techniques and data analysis, with the aim of clarifying the scope and the limitations of major recent models of numerical cognition and the role of working memory in numerical processing. The results of the research programme supported those models which link numerical cognition with other forms of mental processing by identifying specific ways in which diverse numerical processes such as magnitude comparison, subitizing and the calculation of multi-digit problems draw on forms of processing associated with other types of stimuli.