The influence of the place-value structure of the Arabic number ...

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affected (e.g. Dehaene & Cohen, 1997; Delazer et al., 2006, but see Ashkenazi, Henik, Ifergane, & Shelef, this issue for differing results). However, the left IPS was preserved in our neglect patients as they all had right-hemispheric lesions. Thus, this left IPS area might have compensated for the loss of the right IPS with regard to general magnitude and numerical distance processing. Nuerk et al. (2005) employed a magnitude comparison task in an Eriksen flanker paradigm. They found that the magnitude of the distractors was processed. However, the magnitude of the distractors was not spatially represented on a MNL as no SNARC effect was observed for the distractors’ magnitudes while a robust distance effect was present. Consequently, number magnitude can be processed without automatic activation of its spatial code. This spatial code may only be activated in conditions in which spatial processing is salient and does not require much attention. In the current study, the mental numerical interval may be the most salient spatial reference frame. If the right IPS region were mainly responsible for linking number magnitude and spatial representation, damage to this right IPS region would be particularly impairing for this most salient spatial reference frame. In contrast, magnitude processing which is less spatially salient may be less impaired as the left IPS, which may be less involved in spatial representation of magnitude, can take over. Although this hypothesis of differential involvement of the two IPS in the spatial processing of magnitude offers an account for the result pattern observed in the current study, it should be further investigated in the future. Finally, the fact that we did not observe any group differences with regard to multiplicativity may be due to two reasons: First, multiplication fact knowledge is presumably located in the left gyrus angularis (cf. Dehaene et al., 2003; Delazer et al., 2003) which was not lesioned in our neglect patients (see Table 1 for lesion sites of neglect patients). Second, in contrast to previous studies, we did not even observe a main effect of multiplicativity. The absence of an effect of multiplicativity may be explained by two related factors: first, the low 222
strategic value of retrieving this information, since multiplicative triplets formed only 12.5 % of all triplets instead of 25 % in the original study by Nuerk et al. (2002); and second, by reduced executive resources of both controls and patients. In the original study by Nuerk et al. (2002), 25 % of all triplets were part of a multiplication table. Therefore, activating the representation of multiplicativity was relevant for improving performance, as half of the “Yes” responses could be determined by the recognition of multiplicatively related triplets. In the present study, only 12.5 % of all triplets were part of a multiplication table. This difference in the proportion of multiplicatively related triplets may have an impact on the strategic relevance of multiplicativity. As it is strategically less relevant in the present study, the effect of multiplicativity may have disappeared. Moreover, automatically activating multiplication fact knowledge may have been hampered by general reductions in the capacity of neglect patients and control participants to monitor and integrate information from different sources in parallel due to age. In a recent fMRI study on the NBT, Wood et al. (submitted) showed that the left angular gyrus and in the superior frontal gyrus were sensitive to multiplicativity. While the left angular gyrus may be associated with the retrieval of multiplication facts (cf. Dehaene et al., 2003; Delazer et al., 2003), the superior frontal gyrus was linked to the monitoring of potentially relevant information from different sources (e.g. Brass & von Cramon, 2005). Although there is no reason to doubt that older patients as well as neglect patients can access the representation of multiplicativity, they may not have monitored for the multiplicativity in the present study due to limitations in executive resources and working memory (Doricchi, Guariglia, Gasparini, Tomaiuolo, 2005). CONCLUSIONS Neglect impairs number processing of two-digit numbers in a specific way: neglect patients seem to neglect the left part of a given numerical interval activated on a spatially 223
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The influence of the place-value st
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Ich möchte mich an dieser Stelle b
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ZUSAMMENFASSUNG Das wissenschaftlic
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Study 5: All for one but not one fo
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Classification performance ........
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The Arabic place-value structure an
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Large problem size > small problem
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ABSTRACT ..........................
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Study 2: On the cognitive instantia
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LIST OF FIGURES Section 1: General
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Section 4: The neurocognitive under
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LIST OF TABLES Section 1: General I
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Section 5: A computational model of
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Number, the simplest and most unive
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limited set of symbols. To achieve
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interexponential structuring princi
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(i) separating power and base dimen
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Abstract Code Model Verbal number C
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of the Arabic number system within
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previous studies on two-digit numbe
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eview), questions concerning repres
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esponses are easier (i) for problem
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2009c). Based on the framework of t
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scarce (but see Domahs et al., 2006
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y Studies 5 and 6 of the current th
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OVERVIEW OVER THE STUDIES INCORPORA
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a view was corroborated by a variet
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would indicate influences of verbal
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2. Study 6: Impairments of the ment
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eplicate processes of unit-decade i
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determinants shall be reviewed. Mor
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Study 6: Hoeckner, S., Moeller, K.,
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Section 2 Task invariant influences
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ABSTRACT Over the last years, evide
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The authors used a magnitude compar
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Such congruency is important as mos
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Procedure: After ten randomly chose
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compatibility effect for large unit
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2004). So, increasing the maximum u
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proportions in earlier studies. The
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CONCLUSIONS In summary, the conclus
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Study 2 On the cognitive instantiat
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INTRODUCTION One of the probably mo
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eye fixation behaviour for the eval
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(see Rayner, 1998 for a review). Tr
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Procedure: After being seated with
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adjustment of the degrees of freedo
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Eye fixation behaviour TRT in ms To
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or the decade digits was found (393
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egressions were directed to the sec
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the requirement of a carry is deter
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In line with this prediction, total
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Instead, it seems to involve differ
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Section 3 On the importance of plac
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ABSTRACT The mental number line of
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preschoolers aged 4). However, the
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still represented even when only th
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specificity. Yet, in adults it has
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METHOD The reported experiment was
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child separately to obtain estimati
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indicated that Italian children’s
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striking similarity between the ori
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Inversion influences on estimation
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% overall Estimation Error 25 20 15
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seem to be the origin of the perfor
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this system. In this case no langua
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two-linear model with one linear re
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and 40 is 10 times as large as the
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APPENDIX A A remark on how to evalu
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Splitting the overall interval in t
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much closer to the proposed breakpo
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the individual approach may be more
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Contrarily, data produced by a two-
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Study 4 Early place-value understan
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INTRODUCTION Dealing with (multi-di
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has been shown that other represent
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number system as formalized by its
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124 10024, see Deloche & Seron, 19
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Please note that in contrast to Miu
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Roid, Prifitera, & Weiss, 1993; see
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effect-based approach has never bee
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(ii) In the magnitude comparison ta
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problem of capitalizing on differen
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Error rate in % Error Categories (c
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positively correlated with overall
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(ii) Effect approach analyses of pr
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whether the carry effect for additi
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Non-carry problems: For the percent
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from basic numerical concepts to ar
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transcoding and/or who showed relat
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A word on the validity of the curre
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e adapted for the results of the pr
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Non-monotonous Model of the Relatio
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of the probes unit and/or decade di
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the place-value structure of the Ar
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Therefore, we believe that this stu
Page 197 and 198: APPENDIX A: Correlation tables of s
Page 199 and 200: Section 4 The neurocognitive underp
Page 201 and 202: ABSTRACT Mental arithmetic and calc
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Page 207 and 208: correctly bisected by the second nu
Page 209 and 210: Table 1: Behavioural performance in
Page 211 and 212: were found bilaterally in the dorso
Page 213 and 214: Table 3: Brain areas activated by b
Page 215 and 216: portion of the superior frontal gyr
Page 217 and 218: Figure 3: fMRI signal for parametri
Page 219 and 220: The fronto-parietal network and the
Page 221 and 222: Finally, increased activation in th
Page 223 and 224: Inferior parietal cortex, the angul
Page 225 and 226: primarily necessary for solving the
Page 227 and 228: Tippet (1996) have shown that patie
Page 229 and 230: Study 6 Impairments of the mental n
Page 231 and 232: INTRODUCTION Patients suffering fro
Page 233 and 234: 2005), triplets in which the interv
Page 235 and 236: Visual field assessment showed no s
Page 237 and 238: Table 1: Demographic and clinical d
Page 239 and 240: For 80 bisected triplets the factor
Page 241 and 242: Factorial Analyses (ANOVA and t-tes
Page 243 and 244: Errors: The ANOVA revealed a main e
Page 245 and 246: DISCUSSION The effects of neglect o
Page 247: decade digits but they even process
Page 251 and 252: APPENDIX A Test results of patients
Page 253 and 254: the middle the beneficial effect of
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Page 257 and 258: Study 7 Two-digit number processing
Page 259 and 260: INTRODUCTION The internal represent
Page 261 and 262: all numbers the overlap for larger
Page 263 and 264: digit numbers were engaged. Additio
Page 265 and 266: single node in an ordered sequence
Page 267 and 268: modelling to evaluate the plausibil
Page 269 and 270: A Output Layer 11 99 11 #1 #2 99 In
Page 271 and 272: expected considering their magnitud
Page 273 and 274: the output of the right node would
Page 275 and 276: advantages for these numbers (see a
Page 277 and 278: Finally, a regression analysis only
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Page 281 and 282: Regression The stepwise regression
Page 283 and 284: compared numbers, unit distance, lo
Page 285 and 286: RT in ms 780 770 Compatible Number
Page 287 and 288: esponse latencies increased as dist
Page 289 and 290: Table 5: Predictors included in the
Page 291 and 292: Taken together, these results revea
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The nature of the representation of
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Thereby, possible interactions and
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decomposed model did not include an
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APPERNDIX B Development of connecti
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Figure C: Development of connection
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Figure E: Development of connection
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Interestingly, one might infer from
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Section 6 Summary 287
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may be determined by the presentati
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tens and units: German-speaking chi
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Study 6 examined the influence of t
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295
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GENERAL DISCUSSION In the last sect
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to-be-evaluated triplet crossed a d
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specific processing of place-value
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explanation of the decade consisten
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verbal recoding of tens and units d
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system and the ordinality of the me
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epresentation itself as well as its
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Furthermore, converging evidence is
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methodological problems. In most of
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jittering the positions of the sequ
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numbers within the triplets, proces
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Pollatsek, 1989) states that an obj
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computational models were programme
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The developmental influence of plac
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correspond to the order of tens and
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Asian languages (e.g., Japanese, Ko
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indicating that decomposed processi
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REFERENCES Banks, W. P. (1977). Enc
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Karmiloff-Smith, Annette (1996). Be
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Pixner, S. (2009). How do children
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