The role of multi-digit number processing in the development of numerical cognition [Elektronische Ressource] / vorgelegt von Helga Krinzinger

Krinzinger

Informations

• Publié par: rheinisch-westfalischen_technischen_hochschule_-rwth-_aachen
• Publié le: 01 janvier 2010
• Nombre de lectures: 130
• Langue: English

Extrait

The role of multi-digit number processing in the
development of numerical cognition

Von der Philosophischen Fakultät der Rheinisch-Westfälischen
Technischen Hochschule Aachen zur Erlangung des akademischen
Grades einer Doktorin der Philosophie genehmigte Dissertation


vorgelegt von

Mag.rer.nat. Helga Krinzinger





Berichter: Univ.-Prof. Dr.rer.nat. Klaus Willmes-von Hinckeldey
Univ.-Prof. Dr.phil. Iring Koch


Tag der mündlichen Prüfung: 29. Oktober 2010





Diese Dissertation ist auf den Internetseiten der Hochschulbibliothek
online verfügbarThe role of multi-digit number processing in the development of numerical cognition

2 The role of multi-digit number processing in the development of numerical cognition




















“If you take care of the syntax of a representational system, the
semantics will take care of itself.”
(Haugeland, 1985, p. 106)
3 The role of multi-digit number processing in the development of numerical cognition

4 The role of multi-digit number processing in the development of numerical cognition

Table of Contents

1 General Introduction _________________________________________________ 15
1.1 Can adult models be used to describe the development of numeracy?________ 17
1.2 Is the transcoding process in children semantic or asemantic? ______________ 17
1.3 Are multi-digit number representations in children holistic or decomposed? ____ 19
1.4 Do visual-spatial abilities explain individual (and gender) differences in multi-digit
number processing in children? ____________________________________________ 20
1.5 General outline of the studies and specific research questions ______________ 21

2 Study 1: Comparison of one-, two-, and three-componential models of early
numeracy ______________________________________________________________ 23
2.1 Introduction______________________________________________________ 23
2.1.1 Adult models of numeracy ______________________________________ 23
2.1.2 Models based on subtypes of developmental dyscalculia ______________ 25
2.1.3 Developmental stage models ____________________________________ 28
2.1.4 Objectives of Study 1 __________________________________________ 30
2.2 Methods ________________________________________________________ 32
2.2.1 Participants __________________________________________________ 32
2.2.2 Dyscalculia test battery_________________________________________ 33
2.2.3 Procedure and tasks___________________________________________ 33
2.2.4 Modes of analysis _____________________________________________ 36
2.2.5 Structural models _____________________________________________ 37
2.2.6 Fit statistics __________________________________________________ 40
2.3 Results _________________________________________________________ 41
2.3.1 Descriptive statistics and gender differences in raw scores _____________ 41
2.3.2 One-componential model _______________________________________ 43
2.3.3 Two-componential model _______________________________________ 45
2.3.4 Model fit comparisons between one- and two-componential models ______ 47
2.3.5 Three-componential model ______________________________________ 48
2.4 Discussion ______________________________________________________ 51
2.4.1 Evaluation of the three-componential model ________________________ 51
2.4.2 Comparison of the one- and the two-componential model ______________ 53
2.4.3 Linking the two-componential model to previous theories of number
processing __________________________________________________________ 55
2.5 Conclusion ______________________________________________________ 58

3 Study 2: Differential linguistic effects on numerical tasks___________________ 59
3.1 Introduction______________________________________________________ 59
3.1.1 Language effects on the development of numeracy___________________ 60
3.1.2 Inversion effects on the development of numeracy ___________________ 61
3.1.3 Objectives of Study 2 __________________________________________ 63
3.2 Methods ________________________________________________________ 65
3.2.1 Participants __________________________________________________ 65
3.2.2 Procedure and tasks___________________________________________ 66
3.2.3 Analyses ____________________________________________________ 67
3.3 Results _________________________________________________________ 69
3.3.1 Writing Arabic numbers to dictation _______________________________ 69
3.3.2 Recognition of unit- and decade-digits _____________________________ 71
3.3.3 Subtraction __________________________________________________ 73
3.4 Discussion ______________________________________________________ 75
3.4.1 Inversion effects between language groups _________________________ 75
3.4.2 Specific vs. unspecific effects of inversion __________________________ 76
5 The role of multi-digit number processing in the development of numerical cognition

3.4.3 Positive effects of inversion on Subtraction _________________________ 78
3.4.4 No inversion effect on Recognition of unit- and decade-digits ___________ 78
3.5 Conclusion ______________________________________________________ 81

4 Study 3: Influence of gender equality on gender differences in numerical tasks 82
4.1 Introduction______________________________________________________ 82
4.1.1 Higher performance variability in males as a possible reason for gender
differences in mathematics______________________________________________ 83
4.1.2 Socio-cultural reasons for gender differences in mathematics ___________ 84
4.1.3 Fact retrieval advantage as a possible reason for gender differences in
mathematics _________________________________________________________ 85
4.1.4 Objectives of Study 3 __________________________________________ 86
4.2 Method _________________________________________________________ 87
4.2.1 Participants and tasks__________________________________________ 87
4.2.2 Gender Gap Index ____________________________________________ 87
4.2.3 Analysis ____________________________________________________ 88
4.3 Results _________________________________________________________ 89
4.3.1 Writing Arabic numbers to dictation _______________________________ 89
4.3.2 Recognition of unit- and decade-digits _____________________________ 90
4.3.3 Subtraction __________________________________________________ 91
4.3.4 Multiplication _________________________________________________ 92
4.4 Discussion ______________________________________________________ 94
4.5 Conclusion ______________________________________________________ 95

5 Study 4: What accounts for gender differences in multi-digit number processing?
____________________________________________________________________96
5.1 Introduction______________________________________________________ 96
5.1.1 The spatial cognition hypothesis of gender differences in mathematical
cognition ___________________________________________________________ 96
5.1.2 The psychobiosocial model of gender differences in mathematics________ 98
5.1.3 Objectives of Study 4 __________________________________________ 99
5.2 Methods _______________________________________________________ 100
5.2.1 Participants _________________________________________________ 100
5.2.2 General procedure ___________________________________________ 100
5.2.3 Stimuli and task procedures ____________________________________ 101
5.2.4 Model specification ___________________________________________ 105
5.2.5 Fit statistics _________________________________________________ 108
5.3 Results ________________________________________________________ 109
5.3.1 Descriptive statistics __________________________________________ 109
5.3.2 Longitudinal model ___________________________________________ 110
5.4 Discussion _____________________________________________________ 114
5.4.1 Why are visual-spatial abilities important for the acquisition of multi-digit
number processing?__________________________________________________ 115
5.4.2 Why is visual-spatial working memory capacity not a predictor for multi-digit
number processing?__________________________________________________ 116
5.5 Conclusion _____________________________________________________ 117

6 Study 5: Multi-digit number processing as predictor of multi-digit calculation
performance and an exact number magnitude representation: a longitudinal structural
equation model_________________________________________________________ 118
6.1 Introduction_____________________________________________________ 118
6.1.1 Models of number processing___________________________________ 118
6.1.2 The role of multi-digit number processing in the development of an exact,
linear number magnitude representation __________________________________ 121
6 The role of multi-digit number processing in the development of numerical cognition

6.1.3 The role of multi-digit number processing in learning multi-digit
calculation________________