Tests of number processing

These tasks investigated the limits of S.F.'s ability to recognize, u n d erstan d and p ro d u ce arabic and verbal num erals. In p a rticu la r these tasks so u g h t to establish the functional locus of S.F. 's deficit in reading aloud arabic num erals.

In trying to und erstan d S.F.'s arabic num eral deficit the m odel of num ber processing p ro p o sed by M cCloskey and his colleagues (see section 1.51a for discussion) w as taken as a starting point. Follow ing this m odel, S.F.'s syntactic errors in reading aloud arabic num erals m ay result from:

(I) som e form of im pairm ent in an early visual processing svstem responsible for identifying the string of characters as an arabic num eral. A deficit at this level w ould com prom ise all further processing stages. A perceptual m isencoding of the arab ic n u m era l w o u ld give rise to an in a p p ro p ria te se m an tic an d phonological representation even if the verbal num eral p roduction m echanism s and the arabic num eral com prehension m echanism s are pro p erly functioning. For exam ple, if the single arabic num eral 5 is m isperceived as 7, th en fu rth er arabic n u m eral com prehension processing w ill p ro d u ce the w ro n g q u a n tity representation { 7 } and the further verbal num eral p ro d u ctio n processing will produce the w rong spoken num ber nam e "seven".

(II) an im pairm ent in the c o m p re h e n sio n of the arabic num erals. This w o u ld com prom ise the generation of a correct abstract internal representation from an arabic num eral stim ulus. The incorrect abstract internal representation w ill then produce an incorrect spoken num ber name. C onsider, for exam ple, the stim ulus 2,501. For this stim u lu s, the arabic n u m b er co m p reh en sio n process sh o u ld generate the abstract internal representation (2) 10EXP3, {5} 10EXP2, {1} lOEXPO. H ow ever, if instead it generates an incorrect abstract internal representation such as m isinterpreting 10EXP2 as lOEXPl, the result w ould be the production of the incorrect sp o k en n u m b er nam e "two hundred and fifty one" since the verbal n u m eral p ro d u ctio n m echanism s are assum ed to o p erate on ly on ab stract sem antic representations.

(HI) a d isruption of the verbal num eral p roduction m echanism s. If the previous two processing stages are intact then, according to the m odel, the error p attern observed w o u ld have to be due to dam age to the verbal n um eral p ro d u ctio n mechanism s. C onsidering the above abstract internal representation of the arabic num eral 2,501: if, for exam ple, the correct sem antic rep resen tatio n 10EXP2 is m istranslated by the verbal num eral syntactic production m echanism as lOEXPl

the resu lt w o u ld be the p roduction of an incorrect spoken num ber nam e (e.g. TENS instead of HUNDREDS).

In o rd er to assess w h eth er S.F.'s erro rs reflected im p aired p ercep tio n a n d /o r com prehension a n d /o r production of arabic num erals a series of num ber recognition, com prehension and production tasks w ere presented to him .

3.32a T ests of n u m b er récognition

In o rd er to control for the effect of the presentation m ode of the stim uli a series of 6 different recognition tasks w as subm itted to S.F. In these tasks the p a tie n t w as ask ed to m atch a n u m ber p re se n te d by the ex am in er to the corresponding target num ber presented together w ith other three alternatives. These 4 num bers w ere placed in front of him on index cards each containing a single num ber. The num bers to be m atched w ere constructed in a sim ilar w ay to those stim uli u sed in the reading aloud task. They differed p rim arily in their o rd er of m ag n itu d e (from length 1 u p to len g th 7) and w ere d iv id e d into different su b g ro u p s labelled a, b, c, and t. An identical set of 183 num bers w ere used in all the recognition tasks. The detailed contents for each stim ulus group are show n in Table 3.11.

(insert table 3.11 about here)

M atching arabic numerals to spoken num ber names. S.F. w as ask ed to m atch 183 spoken num ber names to the corresponding arabic num erals. The 183 num bers w ere spoken aloud in a random o rd er by the exam iner and presented one by one. The corresponding arabic num erals w ere p resented together w ith 3 other arabic num erals on 4 different index cards. The four arabic num erals were: (I) The correct transcoded form.

(II) Two w rong alternatives representing a possible syntactic error of the higher and low er m agnitude.

(HI) A w rong alternative representing a lexical error.

For ex am p le, for the spoken n u m b er n am e " H u n d re d a n d th ir ty " , t h e alternatives w ere 130, 13, 140, 1300. For g roup 1, th at covered the num bers 0-9, the tw o w ro n g syntactic alternatives w ere both of higher m agnitude. S.F. w as able to correctly point to 174 out of 183 arabic num erals (95% correct answers).

M atching spoken number names to w ritten number names. S.F. w as asked to p o in t to the w ritten num ber nam e corresponding to the spoken n u m b er nam e given by the examiner. The sam e stim uli em ployed in the p revious task w ere used. This tim e the stim uli w ere w ritten as num ber nam es. So for exam ple, for the spoken num ber nam e " F o u rte e n " the alternatives w ere H undred and Forty, Fourteen, Fifteen, Four. A s in the previous task, S.F.'s perform ance w as nearly flawless. H e w as able to correctly po in t to 179 o u t of the 183 w ritten num ber nam es (98% correct answers).

M atching arabic numerals to the corresponding arabic numerals. S.F. was asked to point to the arabic num eral corresponding to the arabic num eral given by the examiner. So, for example, for the arabic num eral 1, the alternatives were 2, 7, 0 ,1 . S.F. w as able to m atch correctly 177 o u t of 183 arabic num erals (97% correct answers).

M a tching arabic numerals to the corresponding w ritten num ber names. S.F. w as asked to point to the w ritten num ber nam e corresponding to the arabic num eral given by the exam iner. So, for exam ple, for the arabic num eral 1, the a lte r n a tiv e s p resen ted w ere two, seven, zero, one. S.F. w as able to m atch correctly 179 out of the 183 num erals (98% correct answers).

M atch in g w ritten num ber names to w ritten num ber names. S.F. was asked to point to the w ritten num ber nam e corresponding to the arabic num eral given by the exam iner. So, for exam ple, for the w ritten n u m b er o n e , the alternatives w ere one, two seven, zero. S.F.'s perform ance w as very good. H e was correct on 175 of the 183 trials (96%)

M atching w ritten number names to the corresponding arabic numerals. S.F. w as required to m atch a w ritten num ber nam e w ith the corresponding arabic n u m eral presented am ong three other arabic num erals. So for exam ple, for the w ritte n n u m b er nam e o n e , the alternatives w ere 2, 7 , 0 , 1 . As in the previous tasks S.F.'s perform ance was largely preserved: he gave 172 o u t of the 183 correct answ ers (94% correct answers).

S u m m ary . Taken together, the results of these six tasks suggest th at S.F.'s ability to encode num bers is largely intact and therefore his deficit in reading a lo u d arabic num erals cannot be d u e to any m isp ercep tio n of the n u m ber stim u li.

Table 3.11

The contents of the num ber recognition battery

Subgroups Stim ulus type Exam ples N o .

single num ber 1 ,2 ,3 ,4 ,5 10

2t 2a 2b

2 num bers from 10 to 19 2 num bers from 20 to 90 other tw o num bers

11,12,13,14 10 2 0,30,40,50 8 46,27,83,91 10

3a 3 num bers ending in zeros

3b 3 num bers w ithout internal zeros 3c 3 num bers w ith internal zeros

100,200,300 9 364,670,940 10 107,502,806 10 4a 4b 4c

4 num bers ending in zeros 1000,2000 9 4 num bers w ithout internal zeros 1850,8734 10 4 num bers w ith internal zeros 5019,2007 10

5a 5b 5c

5 num bers ending in zeros

5 num bers w ithout internal zeros 5 num bers w ith internal zeros

30000,40000 9 56780,14900 10 89705,10500 10 6a 6b 6c

6 num bers ending in zeros

6 num bers w ithout internal zeros 6 num bers w ith internal zeros

500000,600000 9 142380,795800 10 180924,670340 10

7a 7 num bers ending in zeros 7000000 9

7b 7 num bers w ithout internal zeros 4500000 10 7c 7 num bers w ith internal zeros 2870940 10