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

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Section 3 On the importance of place-value integration in arithmetical development 85
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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
Page 59 and 60: 2. Study 6: Impairments of the ment
Page 61 and 62: eplicate processes of unit-decade i
Page 63 and 64: determinants shall be reviewed. Mor
Page 65 and 66: Study 6: Hoeckner, S., Moeller, K.,
Page 67 and 68: Section 2 Task invariant influences
Page 69 and 70: ABSTRACT Over the last years, evide
Page 71 and 72: The authors used a magnitude compar
Page 73 and 74: Such congruency is important as mos
Page 75 and 76: Procedure: After ten randomly chose
Page 77 and 78: compatibility effect for large unit
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Page 81 and 82: proportions in earlier studies. The
Page 83 and 84: CONCLUSIONS In summary, the conclus
Page 86 and 87: Study 2 On the cognitive instantiat
Page 88 and 89: INTRODUCTION One of the probably mo
Page 90 and 91: eye fixation behaviour for the eval
Page 92 and 93: (see Rayner, 1998 for a review). Tr
Page 94 and 95: Procedure: After being seated with
Page 96 and 97: adjustment of the degrees of freedo
Page 98 and 99: Eye fixation behaviour TRT in ms To
Page 100 and 101: or the decade digits was found (393
Page 102 and 103: egressions were directed to the sec
Page 104 and 105: the requirement of a carry is deter
Page 106 and 107: In line with this prediction, total
Page 108 and 109: Instead, it seems to involve differ
Page 112 and 113: Study 3 Language effects on childre
Page 114 and 115: INTRODUCTION The understanding and
Page 116 and 117: analyses Ebersbach and colleagues (
Page 118 and 119: Language specificities and their in
Page 120 and 121: - 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
Page 132 and 133: estimation was particularly poorer
Page 134 and 135: Implications for the theoretical un
Page 136 and 137: especially detrimental in items wit
Page 138 and 139: epresentation but rather progress i
Page 140 and 141: linear model as well. In line with
Page 142 and 143: longer a reliable predictor of esti
Page 144 and 145: contrasted. In the current study it
Page 146 and 147: N 60 Distribution of individual bre
Page 148 and 149: analyses. However, in the following
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Page 152 and 153: 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
Page 158 and 159: argument is corroborated by the imp
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Damian, 2008; Moeller, Fischer, Nue
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place-value structure. For instance
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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
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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
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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
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developmental trajectories of basic
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multi-digit numbers which in turn p
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esearch. The present data rather su
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172
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Study 5 All for one but not one for
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INTRODUCTION Dealing with and the p
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ehavioural performance in the NBT:
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impossible to bisect by an integer
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HRF function (Büchel, Holmes, Rees
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Table 2: Regresion analysis for bis
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Figure 1: fMRI signal for parametri
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Broca’s area, SMA/pre-SMA, fronta
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Non-multiplicative > multiplicative
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Table 7: Brain areas activated by m
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(applicable only for non-bisected t
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Other areas associated with the fro
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von Cramon, 2004) and inhibition of
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the rules applied, participants nee
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inhibiting irrelevant information a
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ABSTRACT Humans represent numbers a
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systematically neglected the left p
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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
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4 blocks of 40 trials each, which t
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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
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affected (e.g. Dehaene & Cohen, 199
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oriented MNL. Moreover, our data al
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APPENDIX B Factorial analyses (ANOV
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for triplets crossing a decade boun
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Section 5 A computational model of
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ABSTRACT Currently, there are three
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Two-digit number processing Basical
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3. The hybrid model The hybrid mode
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model allow for quantitatively pred
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ventral “what” and the “dorsa
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egression model evaluating the data
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The detailed description of the thr
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The output function of the hidden l
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In the holistic model, two input ar
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Modelling two-digit number comparis
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Comparisons to a variable standard
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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
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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
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learning pattern mirrored the one f
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Appendix C On the interrelation of
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286
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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
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SYNOPSIS At the end of the general
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However, unlike in previous studies
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distance. And indeed, such a distin
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hypothetical number line. Compared
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Ansari, 2009; Halberda, Mazzocco, &
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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
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Further evidence for place-value in
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executing the carry by updating the
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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.
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place-value knowledge in numerical
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strong influence on numerical devel
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330
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Delazer, M., Karner, E., Zamarian,
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Moeller, K. (2006). Factors affecti
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Zorzi, M., Priftis, K., & Umiltà,
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Erklärung Hiermit erkläre ich, da
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