An introduction to mathematical cognition:
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
London ; New York
Routledge
2018
|
| Schriftenreihe: | International texts in developmental psychology
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | xv, 248 Seiten Illustrationen, Diagramme 24 cm |
| ISBN: | 9781138923959 9781138923942 |
Internformat
MARC
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Datensatz im Suchindex
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| adam_text | CONTENTS List offigures, tables and boxes Acknowledgements 1 Introduction 1.1 What is mathematical cognition? 1.2 The development of mathematical skills Nonsymbolic number 2.1 Introduction 2.2 Small exact system 2.2.1 The development of subitizing 2.2.2 Individual differences in subitizing ability and its relationship with mathematics 2.2.3 Theoretical models of subitizing 2.2.4 Subitizing in groups: ‘groupitizing’ 2.2.5 Summary: subitizing 2.3 Large approximate system 2.3.1 The Approximate Number System (ANS) 2.3.2 Brain bases of ANS: numerons and genes 2.3.3 The ANS in infants 2.3.4 The development of the ANS 2.3.5 The ANS and arithmetic 2.3.6 Influence of mathematics education on the ANS 2.3.7 ANS training 2.3.8 The ANS and space 2.3.9 Difficulties in studying the ANS 2.3.10 Is there really an ANS? x x¡v 1 1 3 6 7 7 7 8 9 11 12 12 14 16 18 19 19 21 21 23 23 25
vi Contents 2.4 3 4 2.3.11 Summary: estimation and the Approximate Number System (ANS) Summary Symbolic number 3.1 Introduction 3.2 Number words 3.2.1 Number word acquisition 3.2.2 Theories of children s acquisition of exact number concepts 3.2.3 Number words influence place-value understanding and exact calculation 3.2.4 Spontaneous Focusing on Numerosity (SFON) 3.2.5 Summary: number words 3.3 Arabic digits 3.3.1 Single digits 3.3.2 Multi-digit number processing 3.3.3 Summary: Arabic digits 3.4 The number line task 3.5 Transcoding: from number words to Arabic digits 3.5.1 Theories of number transcoding 3.5.2 Linguistic influences on transcoding 3.5.3 Summary: transcoding 3.6 The relationship between symbolic and nonsymbolic numerical systems 3.7 The relationship betweensymbolic number processing and mathematical performance 3.8 Summary The development of arithmetic skills 4.1 Early arithmetic skills 4.1.1 Arithmetic in infancy? 4.1.2 Nonverbal arithmetic in preschoolers 4.2 Symbolic arithmetic 4.2.1 Effects of problem representation 4.2.2 Arithmetic word problems 4.3 Arithmetic strategies 4.3.1 Strategies to solve arithmetic problems 4.3.2 Strategy choice 4.4 Domain-general influences on arithmetic development 4.4.1 Working memory 4.4.2 Inhibition and shifting 4.4.3 Language skills 4.5 Summary 26 Ή 29 30 30 30 33 34 36 36 37 37 42 44 44 45 46 47 47 47 49 49 51 51 51 53 54 55 56 59 59 64 67 68 69 70 ^
Contents 5 6 7 vii Understanding arithmetic concepts 5.1 Key concepts in arithmetic understanding 5.1.1 Additive composition 5.1.2 Commutativity and associativity 5.1.3 Inversion 5.1.4 Multiplicative reasoning 5.1.5 Summary 5.2 The relationship between conceptual and procedural knowledge 5.2.1 Defining conceptual and procedural knowledge 5.2.2 The development of conceptual and procedural knowledge 5.2.3 Individual differences in the development of conceptual and procedural knowledge 5.3 Summary 73 74 74 76 77 78 80 Individual differences and mathematical difficulties 6.1 Introduction 6.2 Mathematical difficulties 6.2.1 Diagnostic criteria 6.2.2 Severity 6.2.3 Genetic risk 6.2.4 Difficulties of children with developmental dyscalculia or mathematical learning disorder 6.2.5 Neural correlates of developmental dyscalculia 6.2.6 Current theories of developmental dyscalculia 6.2.7 Subtypes of developmental dyscalculia 6.2.8 Comorbidity with other developmental learning disorders 6.2.9 Summary: mathematical difficulties 6.3 Mathematics anxiety 6.3.1 How is mathematics anxiety measured? 6.3.2 The relationship between mathematics anxiety and mathematics achievement 6.3.3 Mathematics anxiety and working memory 6.3.4 Risk factors 6.3.5 Alleviating mathematics anxiety 6.3.6 Summary: mathematics anxiety 6.4 Attitudes towards mathematics 6.5 Summary 93 93 94 95 97 97 112 113 115 115 116 116 118 Number Systems 7.1 Going beyond the natural numbers 7.2 The theory of conceptual change 120 120 122 82 82 84 87 90 98 102 104 107 108 109 109 110
viii Contents 7.3 7.4 7.5 7.6 7.7 7.8 7.9 Zero: a special number? Negative numbers The transition to rational numbers 7.5.1 Density 7.5.2 Size 7.5.3 Operations 7.5.4 The developmental trajectory of the natural ґ number bias Teaching and the natural number bias Rational number arithmetic Real numbers and cardinal numbers Summary 8 Algebra and equivalence 8.1 Moving from arithmetic to algebra 8.2 The concept of a variable 8.3 Early algebra 8.4 Equivalence 8.4.1 The development of equivalence understanding 8.4.2 Influences on children’s equivalenceunderstanding 8.4.3 Interventions to support equivalence understanding 8.5 Summary 9 Mathematical argumentation and proof 9.1 What is a mathematical proof? 9.2 What difficulties do students have with proof? 9.2.1 Proof construction 9.2.2 Proof validation 9.2.3 Proof comprehension 9.3 Why do students have these difficulties? 9.3.1 Epistemic cognition and mathematicalproof 9.3.2 Strategic failure 9.3.3 Logical problems 9.4 Summary 10 Logic, conditional reasoning and mathematics 10.1 Logic in proofs 10.2 Conditional reasoning 10.2.1 The Wason selection task 10.2.2 Evans’s conditional inference task 10.3 The relationship between reasoning and mathematics 10.4 Summary 123 125 125 126 126 127 1Դ1 130 131 I33 136 33^ 139 ^ ^4 145 148 I39 I32 l3^ I33 I37 I37 158 159 161 161 164 165 165 16? 167 170 170 172 177 180
Contents 11 Where next for mathematical cognition? 11.1 Mathematical cognition as an interdisciplinary field? 11.2 Methodological developments 11.2.1 The replication crisis in psychology 11.2.2 A replication crisis in mathematical cognition? 11.3 Future research directions ix 182 183 185 185 189 191 References 195 Index 238
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| language | English |
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| spelling | Gilmore, Camilla Verfasser (DE-588)1162075112 aut An introduction to mathematical cognition Camilla Gilmore, Silke M. Göbel and Matthew Inglis London ; New York Routledge 2018 xv, 248 Seiten Illustrationen, Diagramme 24 cm txt rdacontent n rdamedia nc rdacarrier International texts in developmental psychology Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Rechenfähigkeit (DE-588)4671320-7 gnd rswk-swf Kognition (DE-588)4031630-0 gnd rswk-swf Mathematische Begabung (DE-588)4169099-0 gnd rswk-swf Kognitiver Prozess (DE-588)4140177-3 gnd rswk-swf Mathematics / Study and teaching Mathematical ability Cognition Kognition (DE-588)4031630-0 s Kognitiver Prozess (DE-588)4140177-3 s Mathematikunterricht (DE-588)4037949-8 s Mathematische Begabung (DE-588)4169099-0 s Rechenfähigkeit (DE-588)4671320-7 s DE-604 Göbel, Silke M. Verfasser (DE-588)1163125075 aut Inglis, Matthew Verfasser (DE-588)1121597157 aut 9781315684758 Erscheint auch als Online-Ausgabe 978-1-315-68475-8 Digitalisierung UB Bamberg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=030587509&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Gilmore, Camilla Göbel, Silke M. Inglis, Matthew An introduction to mathematical cognition Mathematikunterricht (DE-588)4037949-8 gnd Rechenfähigkeit (DE-588)4671320-7 gnd Kognition (DE-588)4031630-0 gnd Mathematische Begabung (DE-588)4169099-0 gnd Kognitiver Prozess (DE-588)4140177-3 gnd |
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| title | An introduction to mathematical cognition |
| title_auth | An introduction to mathematical cognition |
| title_exact_search | An introduction to mathematical cognition |
| title_full | An introduction to mathematical cognition Camilla Gilmore, Silke M. Göbel and Matthew Inglis |
| title_fullStr | An introduction to mathematical cognition Camilla Gilmore, Silke M. Göbel and Matthew Inglis |
| title_full_unstemmed | An introduction to mathematical cognition Camilla Gilmore, Silke M. Göbel and Matthew Inglis |
| title_short | An introduction to mathematical cognition |
| title_sort | an introduction to mathematical cognition |
| topic | Mathematikunterricht (DE-588)4037949-8 gnd Rechenfähigkeit (DE-588)4671320-7 gnd Kognition (DE-588)4031630-0 gnd Mathematische Begabung (DE-588)4169099-0 gnd Kognitiver Prozess (DE-588)4140177-3 gnd |
| topic_facet | Mathematikunterricht Rechenfähigkeit Kognition Mathematische Begabung Kognitiver Prozess |
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