Atnaujinkite slapukų nuostatas

Introduction to Mathematical Cognition [Kietas viršelis]

3.00/5 (4 ratings by Goodreads)
(Loughborough University, UK), (University of York, UK), (Loughborough University, UK)
  • Formatas: Hardback, 248 pages, aukštis x plotis: 234x156 mm, weight: 453 g, 9 Tables, black and white
  • Serija: International Texts in Developmental Psychology
  • Išleidimo metai: 05-Jun-2018
  • Leidėjas: Routledge
  • ISBN-10: 113892394X
  • ISBN-13: 9781138923942
Kitos knygos pagal šią temą:
Introduction to Mathematical CognitionDidesnis paveikslėlis
  • Formatas: Hardback, 248 pages, aukštis x plotis: 234x156 mm, weight: 453 g, 9 Tables, black and white
  • Serija: International Texts in Developmental Psychology
  • Išleidimo metai: 05-Jun-2018
  • Leidėjas: Routledge
  • ISBN-10: 113892394X
  • ISBN-13: 9781138923942
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9781138923942.html
Raktažodžiai:
The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.

Recenzijos

"Not only does this book provide up-to-date, accurate summaries of topics that have been well studied (basically aspects of mathematics acquired in the first decade of life among most children in Western and East Asian countries), it also examines less-studied topics that are likely to become increasingly important in the future, such as number systems, mathematical argumentation, and proof. Everyone interested in mathematical cognition will want to have this book." - Robert Siegler, Carnegie Mellon University, USA

"The field of mathematical cognition has grown tremendously over the past few decades. This book, written by three leading experts, provides a comprehensive summary and analysis of these advances. It represents an invaluable resource not only for those interested in mathematical cognition but also for instructors teaching courses on this field and their undergraduate and graduate students." Daniel Ansari, The University of Western Ontario, Canada

"An Introduction to Mathematical Cognition is a much-welcomed addition to this growing and important literature. The volume is written by three highly respected scientists and covers an impressive range of topics from our evolved number sense to students understanding of mathematical proofs. It will be of interest to experts in the field and students wanting to learn more about the field." David C. Geary, University of Missouri, USA

"An impressively coherent, systematic and clear introduction into the cognitive systems that underlie mathematical learning and performance from early childhood to adulthood, relying on a rich diversity of behavioural and neuroscientific methods. A vital book for students and researchers in mathematical cognition and adjacent fields." - Lieven Verschaffel, Katholieke Universiteit Leuven, Belgium

List of figures, tables and boxes
x
Acknowledgements xiv
1 Introduction
1(5)
1.1 What is mathematical cognition?
1(2)
1.2 The development of mathematical skills
3(3)
2 Nonsymbolic number
6(23)
2.1 Introduction
7(1)
2.2 Small exact system
7(5)
2.2.1 The development of subitizing
7(1)
2.2.2 Individual differences in subitizing ability and its relationship with mathematics
8(1)
2.2.3 Theoretical models of subitizing
9(2)
2.2.4 Subitizing in groups: `groupitizing'
11(1)
2.2.5 Summary: subitizing
12(1)
2.3 Large approximate system
12(15)
2.3.1 The Approximate Number System (ANS)
14(2)
2.3.2 Brain bases of ANS: numerons and genes
16(2)
2.3.3 The ANS in infants
18(1)
2.3.4 The development of the ANS
19(1)
2.3.5 The ANS and arithmetic
19(2)
2.3.6 Influence of mathematics education on the ANS
21(1)
2.3.7 ANS training
21(2)
2.3.8 The ANS and space
23(1)
2.3.9 Difficulties in studying the ANS
23(2)
2.3.10 Is there really an ANS?
25(1)
2.3.11 Summary: estimation and the Approximate Number System (ANS)
26(1)
2.4 Summary
27(2)
3 Symbolic number
29(22)
3.1 Introduction
30(1)
3.2 Number words
30(7)
3.2.1 Number word acquisition
30(3)
3.2.2 Theories of children's acquisition of exact number concepts
33(1)
3.2.3 Number words influence place-value understanding and exact calculation
34(2)
3.2.4 Spontaneous Focusing on Numerosity (SFON)
36(1)
3.2.5 Summary: number words
36(1)
3.3 Arabic digits
37(7)
3.3.1 Single digits
37(5)
3.3.2 Multi-digit number processing
42(2)
3.3.3 Summary: Arabic digits
44(1)
3.4 The number line task
44(1)
3.5 Transcoding: from number words to Arabic digits
45(2)
3.5.1 Theories of number transcoding
46(1)
3.5.2 Linguistic influences on transcoding
47(1)
3.5.3 Summary: transcoding
47(1)
3.6 The relationship between symbolic and nonsymbolic numerical systems
47(2)
3.7 The relationship between symbolic number processing and mathematical performance
49(1)
3.8 Summary
49(2)
4 The development of arithmetic skills
51(22)
4.1 Early arithmetic skills
51(3)
4.1.1 Arithmetic in infancy?
51(2)
4.1.2 Nonverbal arithmetic in preschoolers
53(1)
4.2 Symbolic arithmetic
54(5)
4.2.1 Effects of problem representation
55(1)
4.2.2 Arithmetic word problems
56(3)
4.3 Arithmetic strategies
59(8)
4.3.1 Strategies to solve arithmetic problems
59(5)
4.3.2 Strategy choice
64(3)
4.4 Domain-general influences on arithmetic development
67(4)
4.4.1 Working memory
68(1)
4.4.2 Inhibition and shifting
69(1)
4.4.3 Language skills
70(1)
4.5 Summary
71(2)
5 Understanding arithmetic concepts
73(20)
5.1 Key concepts in arithmetic understanding
74(8)
5.1.1 Additive composition
74(2)
5.1.2 Commutativity and associativity
76(1)
5.1.3 Inversion
77(1)
5.1.4 Multiplicative reasoning
78(2)
5.1.5 Summary
80(2)
5.2 The relationship between conceptual and procedural knowledge
82(8)
5.2.1 Defining conceptual and procedural knowledge
82(2)
5.2.2 The development of conceptual and procedural knowledge
84(3)
5.2.3 Individual differences in the development of conceptual and procedural knowledge
87(3)
5.3 Summary
90(3)
6 Individual differences and mathematical difficulties
93(27)
6.1 Introduction
93(1)
6.2 Mathematical difficulties
94(15)
6.2.1 Diagnostic criteria
95(2)
6.2.2 Severity
97(1)
6.2.3 Genetic risk
97(1)
6.2.4 Difficulties of children with developmental dyscalculia or mathematical learning disorder
98(4)
6.2.5 Neural correlates of developmental dyscalculia
102(2)
6.2.6 Current theories of developmental dyscalculia
104(3)
6.2.7 Subtypes of developmental dyscalculia
107(1)
6.2.8 Comorbidity with other developmental learning disorders
108(1)
6.2.9 Summary: mathematical difficulties
109(1)
6.3 Mathematics anxiety
109(7)
6.3.1 How is mathematics anxiety measured?
110(2)
6.3.2 The relationship between mathematics anxiety and mathematics achievement
112(1)
6.3.3 Mathematics anxiety and working memory
113(2)
6.3.4 Risk factors
115(1)
6.3.5 Alleviating mathematics anxiety
115(1)
6.3.6 Summary: mathematics anxiety
116(1)
6.4 Attitudes towards mathematics
116(2)
6.5 Summary
118(2)
7 Number Systems
120(18)
7.1 Going beyond the natural numbers
120(2)
7.2 The theory of conceptual change
122(1)
7.3 Zero: a special number?
123(2)
7.4 Negative numbers
125(1)
7.5 The transition to rational numbers
125(5)
7.5.1 Density
126(1)
7.5.2 Size
126(1)
7.5.3 Operations
127(1)
7.5.4 The developmental trajectory of the natural number bias
127(3)
7.6 Teaching and the natural number bias
130(1)
7.7 Rational number arithmetic
131(2)
7.8 Real numbers and cardinal numbers
133(3)
7.9 Summary
136(2)
8 Algebra and equivalence
138(16)
8.1 Moving from arithmetic to algebra
139(1)
8.2 The concept of a variable
140(3)
8.3 Early algebra
143(1)
8.4 Equivalence
144(8)
8.4.1 The development of equivalence understanding
145(3)
8.4.2 Influences on children's equivalence understanding
148(2)
8.4.3 Interventions to support equivalence understanding
150(2)
8.5 Summary
152(2)
9 Mathematical argumentation and proof
154(13)
9.1 What is a mathematical proof?
155(2)
9.2 What difficulties do students have with proof?
157(4)
9.2.1 Proof construction
157(1)
9.2.2 Proof validation
158(1)
9.2.3 Proof comprehension
159(2)
9.3 Why do students have these difficulties?
161(4)
9.3.1 Epistemic cognition and mathematical proof
161(3)
9.3.2 Strategic failure
164(1)
9.3.3 Logical problems
165(1)
9.4 Summary
165(2)
10 Logic, conditional reasoning and mathematics
167(15)
10.1 Logic in proofs
167(3)
10.2 Conditional reasoning
170(7)
10.2.1 The Wason selection task
170(2)
10.2.2 Evans's conditional inference task
172(5)
10.3 The relationship between reasoning and mathematics
177(3)
10.4 Summary
180(2)
11 Where next for mathematical cognition?
182(13)
11.1 Mathematical cognition as an interdisciplinary field?
183(2)
11.2 Methodological developments
185(6)
11.2.1 The replication crisis in psychology
185(4)
11.2.2 A replication crisis in mathematical cognition?
189(2)
11.3 Future research directions
191(4)
References 195(43)
Index 238
Camilla Gilmore is a Reader in Mathematical Cognition in the Mathematics Education Centre at Loughborough University. Her research explores the development of numerical skills in children and adults.

Silke Göbel is a Senior Lecturer in Psychology at the University of York. She teaches courses on Numerical Cognition, Dyscalculia, Mathematics Anxiety and Neuroscience of Numbers and Arithmetic. Her current research focuses on predictors of mathematical development.

Matthew Inglis is a Reader in Mathematical Cognition in the Mathematics Education Centre at Loughborough University. He is interested in understanding the processes involved in numerical and mathematical reasoning, and how these can be promoted through education.