Atnaujinkite slapukų nuostatas

El. knyga: Introduction to Mathematical Cognition [Taylor & Francis e-book]

(Loughborough University, UK), (University of York, UK), (Loughborough University, UK)
Kitos knygos pagal šią temą:
  • Taylor & Francis e-book
  • Kaina: 161,57 €*
  • * this price gives unlimited concurrent access for unlimited time
  • Standartinė kaina: 230,81 €
  • Sutaupote 30%
Introduction to Mathematical CognitionDidesnis paveikslėlis
Kitos knygos pagal šią temą:
Taylor & Francis e-booksMore info about Taylor & Francis e-books
Partnerių interneto svetainė: https://www.taylorfrancis.com/books/9781315684758
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.
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.
Pastovi nuoroda: https://www.kriso.lt/db/9781315684758_pe.html
Raktažodžiai: