Theoretical perspective

Against the background of the wealth of knowledge that has been generated and is

continuing to be accumulated about typical number representation, numerical processing

and its development, it is important to have a clear theoretical perspective with which to

approach atypical number development, particularly WS.

Numerical cognition in WS could potentially be addressed via a number of different

theoretical and empirical frameworks. One way of examining the basis o f number impairments in WS is to adopt a cognitive neuropsychology perspective. Such an

approach would entail a systematic survey of different numerical abilities in children and adults with WS in search o f a characterization of numerical cognition in terms of

functional dissociations between different numerical competencies. The finding of such dissociations enables researchers to argue that some numerical abilities are intact and

others impaired. In an adult neuropsychological framework, these dissociations would be compared and contrasted with similar dissociations between numerical functions in

previously normal adult patients with acquired brain damage. The adult

neuropsychological framework is indeed frequently applied to the study of developmental

disorders (Temple, 1997).

The promise of using a well-established framework for the structure of the mature adult

mind to understand function and dysfunction in individuals with developmental disorders is certainly appealing at first sight. But is it theoretically valid and empirically well

founded? As discussed above, an adult neuropsychological perspective on

developmental disorders ignores the developmental trajectory underlying these disorders

(Karmiloff-Smith, 1998). Furthermore, even when a syndrome such as WS presents with

relative strengths and weaknesses across cognitive domains, it cannot be taken for

be affected by the disorder, some more subtly than others (Karmiloff-Smith, 1998).

Attractively, an adult neuropsychological perspective enables researchers to map the

architecture of cognitive modules and their purported independence by establishing single

and double dissociations within and between domains. When applied to developmental

disorders, this approach assumes that the modular architecture of the cognitive system remains relatively stable across developmental time, using the adult performance within

or across cognitive domains to predict the performance of young children and infants.

From (Paterson et al., 1999) findings, however, it is clear that infant cognitive profiles in

Williams and Down’s syndrome cannot be predicted from the adult endstate of cognitive

functioning, as would be derived from an adult neuropsychological framework.

One of the crucial differences between brain damaged patients and individuals with a developmental disorder is the degree to which the development o f cognitive systems is

constrained. In adults with acquired damage, the damaged systems had previously

developed normally. Hence it is possible that damage to one fully developed mature system could lead to selective impairments. However, in individuals with developmental disorders, such as WS, the genetic abnormalities constrain the development trajectory of

cognitive abilities from the outset. Often such crucial differences are overlooked because the analysis o f dissociations between functions within or across domains is based

solely on behavioural testing. When similar levels of behavioural functioning are found, it is frequently inferred, or even a priori assumed, that equivalent cognitive processes

drive the behaviour across different groups. However, such potential differences can only be captured by more in-depth analyses of the processes underlying the behavioural

performance, which may differ between populations. In other words, equivalent levels of

behavioural performance do not necessarily equate with the same cognitive processes

(Karmiloff-Smith, 1998).

The theoretical and methodological considerations discussed above have substantial

implications for the way in which numerical cognition should be studied in WS. First, the

adult neuropsychological perspective seems inadequate, theoretically misconceived and

“neuroconstructivist” approach should be sought to understand how number

representations are constructed over developmental time in WS, and how these processes

may go awry. An experimental approach should be adopted that not only focuses on

absolute levels o f behavioural performance and how these may differ in WS in

comparison to the typical case, but also aims to uncover how individuals with WS

process number and whether their underlying number processing competencies differ from the typical case. Another way o f thinking about such issues is to consider one

approach as focusing on the products o f cognitive processes such as calculation and the

other on the processes themselves. Two groups may exhibit similar products (i.e., level

of behavioural performance), but the underlying processes may differ substantially between groups, as is the case for face processing in WS.

Taking a developmental perspective on the processes that constrain performance in numerical tasks necessitates a focus on the low-level processing competencies and on the

representational and developmental foundations of numerical competence (Ansari & Karmiloff-Smith, 2002). A focus on levels o f performance in different high-level, culturally-mediated numerical skills such as addition, subtraction and multiplication

limits the analysis of a deficit in numerical cognition to the products of impairments, but does not provide a research framework for analyzing the representational basis of such

deficits. There is a need to understand whether the basic building blocks of high-level number are impaired and how such impairments constrain and structure number

representations over developmental time. With regard to WS, there is a particular need to understand whether and how the impairment of non-verbal, visuo-spatial processing

competencies might constrain the processes involved in the development of non-verbal

representations o f magnitudes. Impairments to these developmental processes may lead

to difficulties in the construction o f exact number representations despite a relative

proficiency in language among children and adults with WS.

Approaches that focus on the low-level components of cognitive processing have been

successfully applied to gain greater insight into the basis o f reading impairments or

sound processing impairments (Goswami et al., 2002) or visual and sensori-motor

impairments (Stein, 2001). These studies have revealed that low-level auditory

processing and sensori-motor deficits are each predictors of reading impairments. The

study of low-level processing and representational mechanisms allows for the

identification of risk factors in very yoimg children and even among infants (Lyytinen et al., 2001).

Investigations into the nature o f impairments of numerical cognition lag seriously behind

the successful study of dyslexia. The research that has been conducted on deficits in

numeracy in typically developing children and in children with genetic developmental disorders has focused on impairments in higher-level numerical skills and strategy

development (Geary, 1993). As mentioned earlier, the theoretical accounts that have been

put forward to account for number difficulties have usually been explained by recourse to domain-general processing deficits, such as working memory deficits, attention

difficulties, poor use o f strategies and speed o f processing impairments (Geary, Hoard, & Hamson, 1999). While these domain-general impairments may indeed impact on numerical processing, they do not preclude the possibility that impairments of numerical

cognition may in part be due to deviant, low-level, number representations.

Might the area o f numeracy deficits benefit from a theoretical and methodological framework that focuses on the basic processes and competencies of numerical cognition?

Moreover, could such a framework help to elucidate the nature of number difficulties in

children and adults with WS? In order to adopt the theoretical perspective outlined above, it is crucial to have a methodological roadmap. There a number of methodological

issues which need to be carefully considered and discussed in relation to patient-control

group comparisons. These methodological issues will be reviewed and discussed in the

next section.