L'apprentissage des nombres naturels et rationnels

Sommaire

Introduction générale 13
Chapitre 1. Les nombres naturels et le transcodage 19
1 Représentations des nombres naturels 21
1.1 Les premiers systèmes de numération et la représentation analogique 21
1.2 Les systèmes numériques écrits et la représentation arabe de nombre 22
1.1 La représentation verbale du nombre 25
2. Le transcodage et le langage 26
2.1 Le transcodage 26
2.2 Le transcodage et les spécificités du langage 31
Chapitre 2. Enseignement des fractions et décimaux 37
1. Enseignement des fractions et décimaux en Communauté
française de Belgique 40
1.1 Les « Socles de Compétences » 40
1.2 Programme des études d'enseignement fondamental 44
1.3 Les manuels scolaires : 4 et 5 « Archi m’aide » 46
2. Enseignement des fractions et décimaux au Vietnam. 50
3. L’expression verbale du nombre rationnel 53
3.1 Le langage vietnamien du décimal 53
3.2 L’expression verbale du décimal en Belgique 54
Chapter 3. Rational number construct and whole number bias 57
1. Rational number construct 60
1.1 Process of partitioning 61
1.2 The part-whole sub-construct 61
1.3 The ratio sub-construct 64
1.4 The operator sub-construct 65
1.5 The quotient sub-construct 65
1.6 The measure sub-construct 66
2. Whole number bias 67
2.1 The innate constraint 68
L‟apprentissage des nombres naturels et rationnels
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2.2 The Undifferentiated Amount Hypothesis 70
2.3 Learning accounts 72
Conclusion 77
Chapter 4. When 5004 is Said "Five Thousand Zero Hundred
Remainder Four": The Influence of Language on Natural Number
Transcoding: Cross-National Comparison 83
1. Introduction 85
1.1 The process of number transcoding and the two types of zero 86
1.2 Impact of language characteristics on mathematical thinking and
performances 87
1.3 The Vietnamese verbal number 88
2. Method 89
2.1 Participants 89
2.2 Task and stimuli 90
3. Results 90
3.1 Overall analysis 90
3.2 The impact of language 91
3.3 The impact of syntactic zero 93
3.4 Nature of errors and cluster analyses 95
4. Discussion 98
4.1 Impact of structural characteristics of numerical languages on a
transcoding task 98
4.2 The impact of the syntactic zero and the nature of errors 99
4.3 Perspectives and future studies 101
Chapter 5. Belgian and Vietnamese children’s comprehension
of the natural number system: a re-examination of cross-national
differences 103
1. Introduction 105
1.1 The impact of language on understanding and performance in
mathematics 105
1.2 Vietnamese number word systems and transcoding tasks 106
1.3 Limitation of language influence on cross-national studies and
the present study 107
2. Method 109
2.1 Participants 109
2.2 Task 109
2.3 Procedure 110
3. Results 111
Table des matières
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3.1 Boys and girls performances 111
3.2 Overall analysis 111
3.3 The zero in the digit identification task 113
3.4 The nature of errors 114
4. Discussion 118
4.1 The influence of language: the task related to the number-name system 118
4.2 Misunderstanding of the positional number system and the
impact of zero. 120
Chapter 6. Arabic representation of the decimal numbers: from
natural to decimal numbers 123
1. Introduction 125
1.1 The generalization process 126
1.2 Impact of preexisting knowledge on the construction of the
decimal number concept 126
1.3 The effect of the curriculum and language systems 130
1.4 Present study 132
2. Method 133
2.1 Participants 133
2.2 Procedure and Materials 133
2.3 Data analysis 134
3. Results 135
3.1 Overall analysis (achievement in the conceptual decimal) 135
3.2 The generalization process for decimal number representation 136
3.3 Cluster analysis 139
3.4 The case of the integer part that equaled zero 142
4. Discussion 143
Chapter 7. The misunderstanding of the part-whole relationship: a
didactic obstacle 147
1. Introduction 149
1.1 The role of the part-whole relationship in rational number knowledge 150
1.2 Action of partitioning 151
1.3 The present study 151
2. Method 152
2.1 Participants 152
2.2 Measure and Procedure 153
3. Results 156
3.1 The first task: to determine the fraction symbol corresponding
to the given graphical presentation. 156
L‟apprentissage des nombres naturels et rationnels
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3.2 The second task: to determine the graphical presentation associated
with the given fraction symbol 157
4. Discussion 161
Chapter 8. From natural number to decimal number 165
1. Introduction 167
2. Method 170
2.1 Participants 170
2.2 Measures 170
2.3 Procedure 174
2.4 Data analysis 174
3. Results 175
3.1 Descriptive statistics 175
3.2 Preliminary analyses 176
3.3 Structural equation modeling 178
4. Discussion 180
General conclusion 183
Références bibliographiques 197
Annexes 213