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

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Figure 1: fMRI signal for parametric predictors common to bisected and non-bisected triplets. All constrasts were thresholded at p = .001, voxelwise uncorrected, and minimal cluster size set to k = 10. 1A: Bisection range. Regions coloured red depict voxels showing stronger signal for large bisection range. Regions coloured green represent voxels exhibiting stronger signal for small bisection range. 1B: Decade crossing. Regions coloured red represent voxels showing stronger signal for triplets with at least one decade crossing, than for triplets without decade crossing. Regions coloured green depict voxels exhibiting stronger signal for triplets without decade crossing than for triplets with at least one decade crossing. 1C: Problem size. Regions coloured red represent voxels showing stronger signal for large problem size than for small. Regions coloured green indicate voxels showing stronger signal for small problem size than for large. 186
Table 3: Brain areas activated by bisection range (all p < 0.001, voxelwise uncorrected) Large range > small range Region Talairach coordinates x, y, z t-value df=16 Right intraparietal cortex 50, -33, 49 8.26 40 263 Right intraparietal cortex 35, -53, 52 7.79 7 - Left posterior intraparietal cortex -9, -73, 48 8.56 7 276 Left anterior intraparietal cortex -50, -36, 46 4.85 40 10 Right extrastriate cortex 30, -71, 39 9.26 19 29 Right striate cortex 39, -90, 2 4.75 18 26 Left extrastriate cortex -27, -71, 39 7.27 19 76 Left temporo-occipital juction -39, -68, -12 6.31 19/37 50 Left striate cortex -36, -82, -11 5.26 18 16 Right supplementary motor area 6, 20, 43 10.97 8 44 Left supplementary motor area -3, 17, 49 10.33 8 29 Right premotor cortex 30, 14, 44 8.44 6 52 Left premotor cortex -24, 12, 50 7.55 6 104 Right dorsolateral prefrontal cortex 50, 31, 34 5.62 9/46 23 Left dorsolateral prefrontal cortex -45, 4, 27 8.81 9 110 Right homologue of Broca`s area 42, 20, 2 4.74 45 18 Right ventrolateral prefrontal cortex 39, 17, -6 7.22 47 27 Left ventrolateral prefrontal cortex -30, 20, -4 5.14 47 19 Small range > large range Anterior cingulate -3, 46, -10 8.06 32 363 Right dorsolateral prefrontal cortex 18, 32, 51 7.52 9 13 Retrosplenial cortex -3, -45, 33 8.53 7/31 234 BA Cluster size k Small Problem size > large problem size: The left inferior parietal cortex and to a smaller extent the right inferior parietal cortex exhibited increased fMRI signal as a result of small problem size. (Figure 1C, Table 5). In the left hemisphere, a small cluster of activation was present projecting from the inferior to the superior parietal cortex. Small distance to the mean > large distance to the mean: When distance to the mean decreased, stronger fMRI signal was observed in the following regions: Left anterior intraparietal cortex, posterior intraparietal and neighbouring extrastriate cortex bilaterally, 187
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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
Page 161 and 162: Please note that in contrast to Miu
Page 163 and 164: Roid, Prifitera, & Weiss, 1993; see
Page 165 and 166: effect-based approach has never bee
Page 167 and 168: (ii) In the magnitude comparison ta
Page 169 and 170: problem of capitalizing on differen
Page 171 and 172: Error rate in % Error Categories (c
Page 173 and 174: positively correlated with overall
Page 175 and 176: (ii) Effect approach analyses of pr
Page 177 and 178: whether the carry effect for additi
Page 179 and 180: Non-carry problems: For the percent
Page 181 and 182: 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
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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: were found bilaterally in the dorso
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
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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
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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
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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
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digit numbers were engaged. Additio
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single node in an ordered sequence
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modelling to evaluate the plausibil
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A Output Layer 11 99 11 #1 #2 99 In
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expected considering their magnitud
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the output of the right node would
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advantages for these numbers (see a
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Finally, a regression analysis only
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236) = 417.38, p < .001] and incorp
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Regression The stepwise regression
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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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