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

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Section 5: A computational model of place-value integration in two-digit number comparison Study 7: Two-digit number processing – holistic, decomposed or hybrid? A computational modelling approach Table 1: Predictors included in the final regression model for the holistic data .................... 253 Table 2: Predictors included in the final regression model for the decomposed data ............ 255 Table 3: Predictors included in the final regression model for the hybrid data ..................... 257 Table 4: Predictors included in the final regression model for the holistic data .................... 261 Table 5: Predictors included in the final regression model for the decomposed data ............ 263 XXII
Page 1 and 2: The influence of the place-value st
Page 3: Ich möchte mich an dieser Stelle b
Page 6 and 7: ZUSAMMENFASSUNG Das wissenschaftlic
Page 8 and 9: Study 5: All for one but not one fo
Page 10 and 11: Classification performance ........
Page 12 and 13: The Arabic place-value structure an
Page 14 and 15: Large problem size > small problem
Page 16 and 17: ABSTRACT ..........................
Page 18 and 19: Study 2: On the cognitive instantia
Page 20 and 21: LIST OF FIGURES Section 1: General
Page 22 and 23: Section 4: The neurocognitive under
Page 24 and 25: LIST OF TABLES Section 1: General I
Page 28 and 29: Section 1 General Introduction 2
Page 30 and 31: systems differ between languages an
Page 32 and 33: the number involves power levels. T
Page 34 and 35: Dehaene (1997, p. 101) claims (see
Page 36 and 37: Arabic place-value coding in curren
Page 38 and 39: three representations proposed are
Page 40 and 41: However, at this point it has to be
Page 42 and 43: unit and decade distance must be pr
Page 44 and 45: Johansen-Berg, Behrens, & Rushworth
Page 46 and 47: Taken together, recent empirical ev
Page 48 and 49: whose spatial representation of num
Page 50 and 51: From a developmental point of view
Page 52 and 53: particular theoretical consideratio
Page 54 and 55: Section 2: On task general influenc
Page 56 and 57: of the summands for carry compared
Page 58 and 59: unit digits indicating decomposed p
Page 60 and 61: intergration is specifically releva
Page 62 and 63: OBJECTIVES BEYOND THE SCOPE OF THE
Page 64 and 65: BIBLIOGRAPHY OF THE STUDIES INCORPO
Page 66 and 67: 40n
Page 68 and 69: Study 1 Internal number magnitude r
Page 70 and 71: INTRODUCTION Number magnitude has l
Page 72 and 73: unit 5 (e.g. 65), unit distances ar
Page 74 and 75: preclude any attentional bias towar
Page 76 and 77:
participants for between-decade tri
Page 78 and 79:
DISCUSSION Internal or external dec
Page 80 and 81:
The debate under which conditions h
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All in all, good logarithmic fits w
Page 84:
APPENDIX A Overall distance and pro
Page 87 and 88:
ABSTRACT Recent research indicated
Page 89 and 90:
Sources of difficulty in carry addi
Page 91 and 92:
unit sum has to be carried to the d
Page 93 and 94:
Apparatus: Eye fixation behaviour w
Page 95 and 96:
solution to an addition problem we
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esulted in longer latencies (2772 m
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Total reading time on target 2 : Th
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Comparably, also the number of regr
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DISCUSSION The current study set of
Page 105 and 106:
second summand but not on the first
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associated with actually calculatin
Page 109:
APPENDIX A Stimulus properties of t
Page 112 and 113:
Study 3 Language effects on childre
Page 114 and 115:
INTRODUCTION The understanding and
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analyses Ebersbach and colleagues (
Page 118 and 119:
Language specificities and their in
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- In a second step it was investiga
Page 122 and 123:
Children with an IQ (measured by CF
Page 124 and 125:
53, 64, 75, 82, and 95) we first co
Page 126 and 127:
Estimated value 100 75 Breakpoint l
Page 128 and 129:
epresentation of two-digit numbers
Page 130 and 131:
distance were generally more accura
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estimation was particularly poorer
Page 134 and 135:
Implications for the theoretical un
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especially detrimental in items wit
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epresentation but rather progress i
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linear model as well. In line with
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longer a reliable predictor of esti
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contrasted. In the current study it
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N 60 Distribution of individual bre
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analyses. However, in the following
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124
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ABSTRACT It is assumed that basic n
Page 154 and 155:
have claimed that basic numerical k
Page 156 and 157:
The current study follows up and ex
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argument is corroborated by the imp
Page 160 and 161:
Damian, 2008; Moeller, Fischer, Nue
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place-value structure. For instance
Page 164 and 165:
Following the progression of resear
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As the current manuscript focuses o
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Follow-up assessment: Two years lat
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ackward span tasks was chosen as an
Page 172 and 173:
participating children understood t
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Table 2: Correlation matrix depicti
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Again, a multiple stepwise regressi
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higher score in the CE working memo
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Table 4: Regression model predictin
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Thereby, the present data allowed f
Page 184 and 185:
it is conclusive that the number of
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numbers up to 20 and their arithmet
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easily solve. As no backup strategi
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problems, respectively. This was su
Page 192 and 193:
developmental trajectories of basic
Page 194 and 195:
multi-digit numbers which in turn p
Page 196 and 197:
esearch. The present data rather su
Page 198 and 199:
172
Page 200 and 201:
Study 5 All for one but not one for
Page 202 and 203:
INTRODUCTION Dealing with and the p
Page 204 and 205:
ehavioural performance in the NBT:
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impossible to bisect by an integer
Page 208 and 209:
HRF function (Büchel, Holmes, Rees
Page 210 and 211:
Table 2: Regresion analysis for bis
Page 212 and 213:
Figure 1: fMRI signal for parametri
Page 214 and 215:
Broca’s area, SMA/pre-SMA, fronta
Page 216 and 217:
Non-multiplicative > multiplicative
Page 218 and 219:
Table 7: Brain areas activated by m
Page 220 and 221:
(applicable only for non-bisected t
Page 222 and 223:
Other areas associated with the fro
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von Cramon, 2004) and inhibition of
Page 226 and 227:
the rules applied, participants nee
Page 228 and 229:
inhibiting irrelevant information a
Page 230 and 231:
ABSTRACT Humans represent numbers a
Page 232 and 233:
systematically neglected the left p
Page 234 and 235:
et al., 2006). However, we hypothes
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None of the participants showed cli
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Table 2: Scores of each participant
Page 240 and 241:
4 blocks of 40 trials each, which t
Page 242 and 243:
neglect patients for triplets invol
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meaning that larger problem size wa
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al. 2006). Neglect not only impairs
Page 248 and 249:
affected (e.g. Dehaene & Cohen, 199
Page 250 and 251:
oriented MNL. Moreover, our data al
Page 252 and 253:
APPENDIX B Factorial analyses (ANOV
Page 254 and 255:
for triplets crossing a decade boun
Page 256 and 257:
Section 5 A computational model of
Page 258 and 259:
ABSTRACT Currently, there are three
Page 260 and 261:
Two-digit number processing Basical
Page 262 and 263:
3. The hybrid model The hybrid mode
Page 264 and 265:
model allow for quantitatively pred
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ventral “what” and the “dorsa
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egression model evaluating the data
Page 270 and 271:
The detailed description of the thr
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The output function of the hidden l
Page 274 and 275:
In the holistic model, two input ar
Page 276 and 277:
Modelling two-digit number comparis
Page 278 and 279:
Comparisons to a variable standard
Page 280 and 281:
found that only the influence of lo
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.09]. Taken together, analyzing the
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data again indicated that decompose
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epresented separately also in the i
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strictly decomposed model revealed
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eliable main effect of compatibilit
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them. As could already been inferre
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Nevertheless, the results pattern w
Page 296 and 297:
Different origins of the compatibil
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As already mentioned in the introdu
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magnitude representation is notatio
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versions the strictly decomposed as
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APPENDIX A N 10000 Frequency of occ
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Decomposed model The connection wei
Page 308 and 309:
learning pattern mirrored the one f
Page 310 and 311:
Appendix C On the interrelation of
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286
Page 314 and 315:
SUMMARY Before evaluating the impli
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fixations on the result’s decade
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early place-value understanding for
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variable standard the strictly deco
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Section 7 General Discussion 296
Page 324 and 325:
SYNOPSIS At the end of the general
Page 326 and 327:
However, unlike in previous studies
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distance. And indeed, such a distin
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hypothetical number line. Compared
Page 332 and 333:
Ansari, 2009; Halberda, Mazzocco, &
Page 334 and 335:
system would not be too problematic
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limited set of symbols (cf. Verguts
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is reflected in the human number ma
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one even before having seen the sec
Page 342 and 343:
Further evidence for place-value in
Page 344 and 345:
executing the carry by updating the
Page 346 and 347:
prominent role of the unit digits o
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corroborated by a variety of observ
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epresentation of number magnitude.
Page 352 and 353:
place-value knowledge in numerical
Page 354 and 355:
strong influence on numerical devel
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330
Page 358 and 359:
Delazer, M., Karner, E., Zamarian,
Page 360 and 361:
Moeller, K. (2006). Factors affecti
Page 362 and 363:
Zorzi, M., Priftis, K., & Umiltà,
Page 364:
Erklärung Hiermit erkläre ich, da
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