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

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APPENDIX A Overall distance and problem size of the respective stimulus groups Standard 53 57 Compatibility compatible incompatible compatible incompatible Unit Distance small large small large small large small large Before adjustment Overall distance 16.8 20.0 13.2 10.0 16.8 20.0 13.2 10.0 Log overall distance 1.23 1.30 1.12 1.00 1.23 1.30 1.12 1.00 Problem size 54.8 63.0 51.8 48.0 55.2 47.0 58.2 62.0 After adjustment Overall distance 14.6 15.0 15.4 15.0 14.6 15.0 15.4 15.0 Log overall distance 1.16 1.18 1.19 1.18 1.16 1.18 1.19 1.18 Problem size 50.8 60.5 53.0 45.5 59.1 49.5 57.0 64.5 Adjustment comprised exclusion of selective trials to match overall distance between all stimulus groups. Such an adjustment is important because otherwise compatibility effects and distance effects are confounded and holistic processing cannot be distinguished from decomposed processing. Due to this adjustment the incompatible probes 44, 45, 46, 47, 48, 49 as well as the compatible probes 74, 75, 76, 77, 78, 79 were excluded in the standard 53 condition. Probes 31, 32, 33, 34, 35, 36 (compatible) and 61, 62, 63, 64, 65, 66 (incompatible) were omitted from the analysis for standard 57. Please note that the role of problems size was addressed in the ANCOVA and in the regression analysis. 58
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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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Page 35 and 36: (i) separating power and base dimen
Page 37 and 38: Abstract Code Model Verbal number C
Page 39 and 40: of the Arabic number system within
Page 41 and 42: previous studies on two-digit numbe
Page 43 and 44: eview), questions concerning repres
Page 45 and 46: esponses are easier (i) for problem
Page 47 and 48: 2009c). Based on the framework of t
Page 49 and 50: scarce (but see Domahs et al., 2006
Page 51 and 52: y Studies 5 and 6 of the current th
Page 53 and 54: OVERVIEW OVER THE STUDIES INCORPORA
Page 55 and 56: a view was corroborated by a variet
Page 57 and 58: 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
Page 79 and 80: 2004). So, increasing the maximum u
Page 81 and 82: proportions in earlier studies. The
Page 83: CONCLUSIONS In summary, the conclus
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
Page 97 and 98: esulted in longer latencies (2772 m
Page 99 and 100: Total reading time on target 2 : Th
Page 101 and 102: Comparably, also the number of regr
Page 103 and 104: DISCUSSION The current study set of
Page 105 and 106: second summand but not on the first
Page 107 and 108: 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
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
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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
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have claimed that basic numerical k
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The current study follows up and ex
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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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