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

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et al., 2006). However, we hypothesize that the effect of decade crossing might be altered by neglect. Neglect patients may have particular difficulties with triplets in which a decade boundary is crossed: in such decade-crossing triplets, not only perception and representation of the units is required, but in addition the decade digits, which are perceptually and perhaps mentally on the neglected left side within a two-digit number, need to be processed. This can be accounted for by a deeper magnitude and base-ten processing required to correctly classify these triplets (Nuerk et al., 2002; Wood, Nuerk, & Willmes, 2006). More specifically, the impact of decade crossing should be more pronounced for those triplets that involve a decade crossing between the first and the central number as deeper magnitude evaluation on the left of a given numerical interval is needed. In summary, neglect patients should be particularly affected (i) in triplets involving central numbers smaller than the arithmetical middle of the interval (which are presumably located on the left of the mental numerical interval) and (ii) in triplets crossing a decade boundary; they should not be affected by (iii) general distance properties or (iv) multiplicativity. MATERIALS AND METHODS Participants: Eighteen German-speaking participants took part in this study. Participants were pooled into three groups of 6 persons matched for age, gender, education and time post-lesion (4 males/2 females each, see Table 1): a patient group including 6 patients with right-sided lesions who suffered from left-sided neglect; a patient control group involving 6 patients with right-sided lesions but no clinical signs of neglect; and a healthy control group of 6 participants with no history of neurological or psychological illness. In all cases of stroke, (patient group and patient control group) lesions were confirmed by either MRI or CT. However, one patient (patient control group) was tested four years post-lesion and could not be matched for the parameter time post-lesion. 208
Visual field assessment showed no sign of hemianopia in any one of the participants. All participants had normal or corrected-to-normal vision, and were right-handed. Participation in this study was voluntary. To diagnose neglect (patient group) and to rule out neglect (patient control group), a standardised neuropsychological neglect test-battery was carried out: Neglect Test (NET; Fels & Geissner, 1997 adapted German version of the Behavioural Inattention Test - BIT; Wilson, Cockburn, & Halligan, 1987). This test-battery includes 17 different tasks that can be allocated into the categories conventional sub-tests (e.g. line bisection, line and star crossing, figure and shape copying, representational drawing) and behavioural subtests (e.g. picture scanning, menu reading, article reading, telling the time from analogue and digital clock faces, set the time). Moreover, to rule out degenerative cognitive processing, the SIDAM (Structured Interview for the Diagnosis of dementia of the Alzheimer type, Multi-infarct dementia and dementias of other aetiology; Zaudig et al., 1996) was carried out. The SIDAM is a questionnaire for diagnosing dementia according to international diagnostic guidelines (ICD 10, DSM IV). This instrument includes simple questions and problems covering areas such as orientation, instantaneous recall, memory (short-, long-term), intellectual/cognitive abilities, verbal and numerical abilities, visual-spatial abilities, Aphasia and Apraxia. Additionally, the SIDAM also includes the Mini-Mental State Examination (MMSE; Folstein, Folstein, & McHugh, 2000), a dementia screening. The participants’ numerical and mathematical abilities were further evaluated using the EC 301 R (Claros Salinas, 1994). The EC 301 R is a test battery for assessing calculation and number processing in brain-damaged patients. It comprises the subtests: dot counting, free backward counting, number transcoding, mental arithmetic, array on a physical number line, number comparison (auditory as well as symbolically), multi-digit arithmetic (i.e. addition, subtraction and multiplication), as well as perceptive and contextual estimations. 209
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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
Page 183 and 184: transcoding and/or who showed relat
Page 185 and 186: A word on the validity of the curre
Page 187 and 188: e adapted for the results of the pr
Page 189 and 190: Non-monotonous Model of the Relatio
Page 191 and 192: of the probes unit and/or decade di
Page 193 and 194: the place-value structure of the Ar
Page 195 and 196: 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
Page 203 and 204: manipulations cannot be distinguish
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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: 2005), triplets in which the interv
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 and 248: decade digits but they even process
Page 249 and 250: strategic value of retrieving this
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
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RT in ms 780 770 Compatible Number
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esponse latencies increased as dist
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Table 5: Predictors included in the
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Taken together, these results revea
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of overall distance necessarily req
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most important predictor in a multi
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activation of the output layer is a
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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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