Modelo de Adsorción de Freundlich

Dehaene and Cohen (1991), on the basis of the residual num erical skills of p a tie n t N.A.U., suggested th at M cCloskey et al.'s m odel w as in ad eq u ate to account for the processing of num bers and calculation (see section 1.44 for a d e scrip tio n of p a tie n t N .A .U .). They p ro p o se d th a t a d d itio n a l processing m echanism s are needed. In particular, they suggested the existence of specific n u m b er processing m echanism s und erly in g the cognitive ability to perform "approxim ate com putations". These num ber processing m echanism s have been h y p o th esiz ed as a d d itio n a l an d fun ctio n ally in d e p e n d e n t of the n u m b er p ro cessin g m echanism s assu m ed by M cC loskey et al. to u n d e rlie "exact calculation". The additional m echanism s proposed by D ehaene an d Cohen are assum ed to be specialized in "the representations of approxim ate m agnitudes in analog form". These analog representations are assum ed to be generally used in tasks req u irin g estim ation of quantities. Tasks req u irin g know ledge of exact quantities are assum ed to use "digital representations" of the type described by M cCloskey et al. The calculation perform ance of the p a tien t N.A.U. has been interpreted as supporting the notion of specific num ber processing m echanism s un d erly in g approxim ate com putations. His spared ability to carry o u t num ber

and arithm etical estim ation tasks is assum ed to reflect a selective sparing of the ap p ro x im ate com p u tatio n m echanism s w hen the exact d ig ital com putations m echanism s are im paired.

It is im portant to bear in m ind that D ehaene an d C ohen's proposal is not as em pirically strong as it m ight be (see section 1.44 for a discussion of their em pirical evidence). Also, som e im portant aspects of their theoretical proposal are n o t clearly articulated. First, the authors d id n o t specify the n atu re of the processes involved in "approxim ate calculation" a n d secondly they d id not explain w h y they should be considered different from those involved in "exact" calculation.

W eddell and D avidoff (1991) on the basis of the perform ance of patient J.C., described in section 1.44, m odified McCloskey et al.'s m odel such that the in p u t an d o u tp u t m echanism s w ere interlinked in a m ore sim ilar w ay to the M orton and Patterson' m odel (1980; Patterson and M orton, 1985) (see figure 1.8 below).

(insert figure 1.8 about here)

The authors stated th at although they interlinked the in p u t and o u tp u t num ber processing m echanism s in their m odel in a sim ilar w ay to M orton and Patterso n 's m odel is interlinked lexical m echanism s, th is d id n o t im ply th at num ber processes are perform ed w ithin general language m odules. In the model the au th o rs d id not rep resen t syntactic modules. They assu m ed th a t syntactic m o d u le s receiv ed in fo rm a tio n s from the in p u t lex ico n s to g e n erate , in M cCloskey et al.'s term inology, syntactic fram es w hich are then translated into sem an tic re p re se n ta tio n s by the num ber/operation encoder. In contrast to M cCloskey et al.'s p roposal the syntactic fram es th a t the n u m b er/o p era tio n encoder receives as input in clu d e slots for the n u m b ers as w ell as for the operations. Sim ilar syntactic modules are assum ed to convert num ber/operation encoder rep resen tatio n s into the a p p ro p ria te form for th e phonological and orthographic o u tp u t lexicons. The authors suggested th at the calculation system is m ad e u p of three in terlin k ed com ponents: the procedure store, the fact store and the num ber/operation encoder. The first tw o com p o n en ts are sim ilar to those described by McCloskey et al. The number/operation encoder th at convert syntactic fram es into sem antic forms is assum ed to hold, at least in patient J.C, re p re se n ta tio n s b a sed o n v isu al codes. A cco rd in g to th e a u th o rs these

representations are then m atched w ith the set of possible arithm etical problem s stored in the tw o calculation stores w hen perform ing a calculation task. W hen a m atch is found the associated calculation program is activated. They suggested that J.C. w ho had particular difficulties w ith the num bers 7 an d 9 in calculation tasks, should have suffered a degradation of the visual representations for the n u m b er 7 and 9 at the level of the num ber/operation encoder. The a u th o rs concluded by acknow ledging that am ong different individuals there m ight be a considerable in d iv id u al v ariatio n in the arch itectu re of n u m b e r processing m odules and their interconnections. Therefore, for exam ple, it is possible th at for m ost individuals the rep resen tatio n s w ithin the number/operation encoder a re am odal rather than visual. If this is true their calculation m odel has a lim ited pow er of description of the processing m echanism s involved in calculation.

C am pbell and C lark (1988) have also p ro p o sed a th eo ry of num erical processing different from th a t of M cCloskey et al. This th eo ry n am ed the encoding-complex theory suggests a non m o d u lar arch itectu re for num erical processing. Cam pbell and C lark challenge McCloskey et al.'s assum ption that num erical processing involves an abstract num erical coding system . In contrast, they p ro p o se th at calculation an d other num erical o p eratio n s are based on several m odality specific number codes th at can be directly in terlin k ed in an associative netw ork. The n u m b er codes are verbal a n d n on verbal. V erbal num ber codes include articu lato ry , au d ito ry , o rth o g rap h ic, m o to r codes and codes for special p o p u latio n s (e.g. sign language). N on verbal number codes include visual and m otor codes for digits, imaginai and other analogue codes for m ag n itu d e an d com bined visu al-m o to r rep resen tatio n s for v ario u s n u m ber rela te d activities (e.g. finger counting). M ultiple codes are assu m ed to be im plicated at any point in num erical processing d ep en d in g on excitatory and inhibitory mechanism s. The specific p attern of codes activated on a given task m ay also d ep en d on "an in d iv id u al's idiosyncratic learn in g history, culture- specific strategies, and other factors, including brain dam age" (p. 209). Clark and C am pbell (1991) present an interesting review of the em pirical evidence based on data collected on norm al as well as on brain dam aged patients in favour of the encoding-complex theory. Their proposal of code d ep en d en t fo rm at underlying n u m b er processing and calculation is u n d oubtedly interesting. H ow ever, their m odel is still in need of further investigation and developm ent before it can be considered a well articulated m odel of the cognitive arch itectu re u nderlying num erical skills (see chapter 5 for further discussion).

Figure 1.8

A schem atic d escrip tio n of W eddell and D avidoff's m o d el of calculation processes Acoustic Analysis Visual Analysis Auditory Input Lexicon Orthographic input Lexicon Number/Operation Encoder Procedure Store Fact Store Phonological Output Lexicon Orthographic Output Lexicon 7 3