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E-raamat: Language and Culture in Mathematical Cognition

Edited by (National Institute of Child Health and Human Development, NIH, Rockville, MD, USA), Edited by (University of Missouri, Columbia, MO, USA), Edited by (University of Virginia, Charlottesville, VA, USA)
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Language and Culture in Mathematical Cognition, Fourth Edition focuses on the role of linguistic and cultural factors in math cognition and development. It covers a wide range of topics, including analogical mapping in numerical development, arithmetic fact retrieval in the bilingual brain, cross-cultural comparisons of mathematics achievement, the shaping of numerical processing by number word construction, the influence of Head Start programs, the mathematical skills of children with specific language impairments, the role of culture and language in creating associations between number and space, and electrophysiological studies of linguistic traces in core knowledge at the neural level.

  • Includes cutting-edge findings, innovative measures, recent methodological advances and groundbreaking theoretical developments
  • Synthesizes research from various subdomains of math cognition research
  • Covers the full complement of research in mathematical thinking and learning
  • Informs researchers, scholars, educators, students and policymakers
Contributors xiii
Foreword: Mathematical Cognition, Language, and Culture: Understanding the Links xv
John Towse
Preface xxi
1 Introduction: Language and Culture in Mathematical Cognitive Development
1(30)
Daniel B. Berch
David C. Geary
Kathleen Mann Koepke
Introduction
1(1)
A Brief Historical Review of Research on the Roles of Language and Culture in Mathematical Cognition
2(1)
Specific Linguistic Levels of Influence on Numerical Processing
3(9)
Lexical: The Composition of Number Words
3(2)
Semantic: The Meaning of Words
5(2)
Syntactic: The Grammatical Structure of Languages Beyond Word-Level Influences
7(1)
Phonological: The Structure and Sequencing of Speech Sounds
8(1)
Visuo-Spatial-Orthographic: Conventions for Writing and Reading Directions of Languages
8(1)
Conceptual: Conceptual Properties of Language
9(2)
Other Language-Related Skills: Verbal Working Memory and Other Cognitive Skills Related to Language Representations
11(1)
A Key Question Driving Research on Numerical Development
12(2)
How Do Children Learn the Meaning of Number Words?
12(2)
Other Considerations in Studying Linguistic Influences on Numerical Processing
14(3)
Language and Number in the Brain
14(1)
Domain-General and Domain-Specific Influences of Bilingualism on Cognition
15(2)
The Role of Culture in Mathematical Cognition
17(5)
Five Myths of Cultural Psychology
19(3)
Disentangling Linguistic and Cultural Influences on Numerical Processing and Mathematics Achievement
22(1)
Conclusions
23(1)
References
24(7)
2 Analogical Mapping in Numerical Development
31(18)
Elisabeth Marchand
David Barner
Introduction
31(1)
Analogical Mapping in Integer Learning
32(1)
Acquisition of Natural Numbers
32(1)
Analogical Mapping in Acquiring Natural Numbers
33(2)
Problems With the Current Account of Analogical Mapping in Integer Learning
35(4)
Analogical Mapping in Magnitude Estimation
39(1)
Analogical Mapping in Estimation: Evidence From the Flexibility and Interdependence of Estimates
40(3)
Analogical Mapping in Estimation: The Role of Ordinality
43(1)
Other Evidence of Analogy as a Source of Representational Changes
44(1)
General Conclusion
45(1)
References
45(4)
3 Linguistic and Experiential Factors as Predictors of Young Children's Early Numeracy Skills
49(24)
Jo-Anne LeFevre
Ozlem Cankaya
Chang Xu
Carolina Jimenez Lira
Number Language and Early Numeracy Performance
52(1)
Comparisons of Counting Across Languages
53(7)
English- Vs Chinese-Speaking Canadian Children
53(1)
English- Vs French-Speaking Canadian Children
54(3)
English-Speaking Canadian Vs Spanish-Speaking Mexican Children
57(2)
Turkish- and Chinese-Speaking Canadian Children
59(1)
Correlation Vs Causation in Comparisons Across Languages
60(1)
Other Approaches to Exploring Language Effects
60(7)
English-Speaking Children Learning to Speak French
61(2)
Training Study I: Guided Practice Counting for English-and Turkish-Speaking Children
63(3)
Training Study II: Structured Counting Practice for English-Speaking Children
66(1)
Conclusions
67(2)
Acknowledgments
69(1)
References
69(3)
Further Reading
72(1)
4 Effects of Mathematics Language on Children's Mathematics Achievement ana Central Conceptual Knowledge
73(26)
Yukari Okamoto
Mathematics Language and Achievement
74(12)
Mathematics Language
75(2)
Cognitive Organization of Numbers
77(2)
Numerical Language and Estimation of Numerical Magnitudes
79(1)
Relation of Numerical Language to Mathematics Achievement
80(1)
Place-Value Understanding
80(2)
Numerical Language and Instructional Methods
82(1)
Fraction Terms
83(1)
Terms for Geometric Shapes
84(2)
Mathematics Achievement, Central Conceptual Knowledge, and Numerical Language
86(7)
Development of Core Conceptual Knowledge
86(2)
Cultural Comparisons of Central Conceptual Knowledge and Specific Skills
88(5)
Conclusions
93(1)
References
94(5)
5 How Does the "Learning Gap" Open? A Cognitive Theory of Nation Effects on Mathematics Proficiency
99(32)
John E. Opfer
Dan Kim
Jike Qin
The Traditional Approach: Differences in Input, Differences in Output
100(4)
Quantity of Math Instruction
101(1)
Quality of Math Instruction
101(1)
Quality of Teacher Knowledge
102(1)
Cultural Differences in Math Attitudes
102(1)
Beyond Habits of Highly Successful Educational Systems
103(1)
A Cognitive Theory on How the Learning Gap Opens
104(11)
Why Numerical Magnitude Judgments?
105(1)
Varieties of Numerical Magnitude Judgments
106(5)
Connections Between Numerical Magnitude Judgments and Math Proficiency
111(2)
Cross-National Differences in Numerical Magnitude Judgments
113(2)
Do Numerical Magnitude Judgments Mediate Nation Effects on Math Proficiency?
115(5)
Comparing Sets and Numbers: U.S. Vs Chinese Children
117(1)
Estimating the Placement of Sets and Numbers on a Number Line: U.S. Vs Chinese Children
118(1)
Approximately Adding Sets and Numbers: U.S. Vs Chinese Children
118(1)
Cognitive Mechanisms of Nation Effects on Mathematics Proficiency
119(1)
Conclusions
120(2)
Acknowledgments
122(1)
References
122(7)
Further Reading
129(2)
6 Mathematical Skills of Children With Specific Language Impairments: Testing Developmental Theory
131(14)
Chris Donlan
Introduction
131(1)
Background to Specific Language Impairment
132(2)
Definition
132(1)
Causes of SLI
132(1)
Mathematical Attainments of Children With SLI
133(1)
Linguistic and Nonlinguistic Contributions to Mathematical Development
134(4)
The Approximate Number System
134(1)
The Importance of Number Symbols
135(1)
The Integration of Symbolic Representations
135(1)
Natural Language as a Support for Learning Number Meanings
136(1)
Pragmatics
137(1)
Summary
138(1)
Evidence From Children With Specific Language Impairments (SLI)
138(2)
Challenges Presented by the Number Word Sequence and Transcoding
138(2)
Effects of Cognitive Factors
140(1)
Conclusions
140(1)
References
141(4)
7 Arithmetic in the Bilingual Brain
145(28)
Nicole Y. Wicha
Danielle S. Dickson
Amanda Martinez-Lincoln
Introduction
145(1)
Bilingualism and Retrieval of Mathematical Facts
146(18)
How Bilinguals Process Arithmetic
146(1)
Relevant Models of Mathematical Cognition
147(3)
Behavioral Evidence From Bilinguals as Tests of the TMC and ECM Models
150(2)
Review of Brain Evidence in Bilingual Arithmetic Processing
152(12)
Conclusions and Future Directions
164(3)
References
167(6)
8 Linguistic Traces in Core Numerical Knowledge: An Approach From Bilingualism
173(24)
Elena Salillas
Alejandro Martinez
Introduction
173(1)
Numbers Without Language
174(2)
Language and Symbol Acquisition
176(2)
Bilingualism as a Window to Numerical Cognition
178(3)
The Case of Basque
181(1)
The Language of Learning Mathematics
181(5)
New Evidence: Bilingual Dyscalculia
186(4)
Conclusions
190(1)
Acknowledgments
191(1)
References
191(5)
Further Reading
196(1)
9 Early Number Knowledge in Dual-Language Learners From Low-SES Households
197(32)
Barbara W. Sarnecka
James Negen
Meghan C. Goldman
Introduction
197(1)
Does Bilingualism Matter for Early Numeracy?
198(2)
Ways for Young Children to Represent Numbers
200(6)
The Innate, Approximate Number System
200(2)
Spoken Numbers
202(4)
Written Numbers
206(1)
Our Study
206(15)
What We Measured and What We Found
207(11)
Overall Conclusions of the Study
218(3)
Acknowledgment
221(1)
References
222(7)
10 How Culturally Predominant Reading Direction and Number Word Construction Influence Numerical Cognition and Mathematics Performance
229(28)
Silke M. Gobel
Introduction
229(1)
Effects of Reading Direction
230(11)
Counting Direction
232(6)
Number Generation
238(2)
Summary of the Effects of Reading Direction
240(1)
Effects of Number Word Construction
241(8)
Number Word Inversion
243(1)
Number Word Inversion and the Carry Effect in Addition
244(1)
Carry Effect and Mathematical Performance
244(1)
Effects of Reading Direction and Number Word Construction Can interact
245(2)
Compatibility Effect and Mathematical Performance
247(1)
Summary of Effects of Number Word Construction
248(1)
Conclusions and Future Directions
249(1)
Acknowledgments
250(1)
References
250(7)
11 Language, Culture, and Space: Reconstructing Spatial-Numerical Associations
257(18)
Samuel Shaki
Martin H. Fischer
Verbal Components of Language-Related Spatial-Numerical Associations
258(5)
Do Space-Number Associations Require Directional Harmony?
258(3)
Longstanding Cultural Habits or Recent Experience?
261(2)
Non-Verbal Language-Related Behavior and Spatial-Numerical Associations
263(6)
Reading Observation
264(1)
Finger Counting
265(2)
Object Counting
267(2)
Evolutionary Predispositions to SNARC
269(1)
Summary and Conclusions
270(2)
References
272(3)
12 Cultural Processes in Elementary Mathematics: Studies in a Remote Papua New Guinea Community
275(22)
Geoffrey B. Saxe
Dichotomous Approaches to Analyzing Relations Between Culture and the Development of Numerical Understandings
275(2)
Intrinsic Relations Approaches to Analyzing Relations Between Culture and the Development of Numerical Understandings
277(5)
Cultural Dimension of the Framework: A Focus on Collective Practices
277(5)
The Interplay Between Cultural and Developmental Processes in Mathematical Understandings: A Program of Research in Remote Oksapmin Communities
282(12)
Oksapmin Communities
282(1)
Studies Conducted in 1978 and
1980. Form-Function Shifts in Children's Developing Use and Knowledge of the Body System
283(1)
Studies of Unschooled Children's Use of the Body System: A Focus on Ontogeny of Numerical Representations With the Body System
284(5)
Studies on Children Attending School in 1980: A Focus on Genetic Processes in Form-Function Relations in Collective Practices of Schooling
289(5)
Concluding Remarks
294(1)
References
295(2)
13 Numeration Systems as Cultural Tools for Numerical Cognition
297(24)
Andrea Bender
Sieghard Beller
Introduction
297(1)
Properties of Numeration Systems and Their Implications
298(9)
Modality
300(1)
Dimensionality
300(1)
Dimensional Representation
301(1)
Base Size
302(1)
Regularity
303(3)
Extent
306(1)
Inconsistencies Between Representational Systems
307(6)
Learning the Verbal System
308(1)
Support by Fingers
309(1)
Mapping on Arabic Digits
310(2)
Possible Benefits of Inconsistencies and Mismatches
312(1)
Conclusion
313(3)
Acknowledgments
316(1)
References
316(5)
Index 321
Daniel B. Berch is Professor of Educational Psychology and Applied Developmental Science at the University of Virginias Curry School of Education. Prior to this position, he was Associate Dean for Research and Faculty Development at the Curry School. Before coming to the University of Virginia, Professor Berch served as Associate Chief of the Child Development and Behavior Branch at the National Institute of Child Health and Human Development, NIH. His previous federal service included a year spent as a Senior Research Associate at the U. S. Department of Education, advising the Assistant Secretary for Educational Research and Improvement. Professor Berch is a cognitive developmental psychologist with interests ranging from the development of numerical cognition and mathematical learning disabilities (MLD) to evolutionary perspectives on education. He has published articles on childrens magnitude representations, the development of number sense, and the role of working memory in MLD. He is senior editor of the book, Why is math so hard for some children? The nature and origins of mathematical learning difficulties and disabilities (co-edited by Michele Mazzocco).

Among other honors, he received the NIH Award of Merit, was elected Fellow of the American Psychological Associations Division of Experimental Psychology, served as an ex officio member of the U.S. Department of Educations National Mathematics Advisory Panel commissioned by President George W. Bush, was elected to the Evolution Institutes Scientific Advisory Board (and chairs its Education Subcommittee), was appointed to the AIM Academys Research Advisory Board, and served as a member of the Professional Advisory Board of the National Center for Learning Disabilities for six years. During the past several years, Professor Berch has been working on the implications of evolutionary theory for educational research and practice, publishing a book chapter on instructing evolved minds, serving as one of the Evolution Institutes primary organizers of a 2013 conference on evolutionary perspectives in educational research funded by the American Educational Research Association, and is co-author (with David Geary) of an article entitled Evolutionary Approaches to Understanding Childrens Academic Achievement” to be published in Wileys forthcoming online reference work, Emerging Trends in the Social and Behavioral Sciences.

David C. Geary is a cognitive developmental and evolutionary psychologist at the University of Missouri. He has wide ranging interests but his primary areas of research and scholarly work are childrens mathematical cognition and learning and Darwins sexual selection as largely but not solely related to human sex differences.

Professor Geary directed a 10-year longitudinal study of childrens mathematical development from kindergarten to ninth grade, with a focus on identifying the core deficits underlying learning disabilities and persistent low achievement in mathematics. The study was funded by the National Institutes of Health (US), including through a MERIT award to professor Geary. One result has been the identification of the school-entry number knowledge that predicts economically-relevant mathematical competencies in adolescence. As a follow-up, professor Geary is directing a second longitudinal study, funded by the National Science Foundation (US), to identify the preschool quantitative competencies that predict this school-entry number knowledge. Professor Geary has also published conceptual and theoretical articles on individual differences in childrens mathematical learning, as well as a book published by the American Psychological Association, Childrens mathematical development (1994); recently translated into Korean. Professor Geary has also contributed to applied and policy related work on this topic, serving, for instance, on the Presidents National Mathematics Advisory Panel, and chairing its learning processes task group.

Professor Gearys interests in evolution are reflected in two of his other books published by the American Psychological Association, The origin of mind: Evolution of brain, cognition, and general intelligence (2005), and Male, female: The evolution of human sex differences (1998, 2010 second edition). The corresponding empirical work ranges from the study of changes in brain volume during hominid evolution to human mate choices to hormonal responses to simulated (video game) competition. Professor Gearys current interests in this area follow from several of his collaborative studies on the effects of prenatal toxin exposure on sex differences in cognition and behavior in mice. Specifically, traits related to Darwins sexual selection are often exaggerated relative to other traits. These would include, for example, the bright plumage of the males of many species of bird that in turn is a good indicator of their behavioral and genetic health. These traits are particularly sensitive to environmental disruption, even in healthy individuals. Professor Gearys in progress book, The evolution of vulnerability, is focused on these traits in humans and how they can be used to identify at-risk populations and individuals.

Kathleen Mann Koepke, Ph.D., is Director of the Math and Science Cognition and Learning, Development & Disorders Program in the Child Devlopment and Behavior Branch (CDBB) of the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), National Institutes of Health (NIH), Rockville, MD (kmk@nih.gov).

Dr. Mann Koepke oversees a research program focused on developing and supporting research and training initiatives to increase knowledge relevant to the development of math and science cogniton, reasoning, knowledge, and abilities, both in animals and in humans from birth through all years of formal education in diverse learners with and without disabilities. This research focus recently lead to her serving as co-Guest Editor of a special journal issue regarding the co-occurrence of math and reading disabilities (Mann Koepke, K and Miller, B. (Eds.) At the Intersection of Math & Reading Disabilities. Journal of Learning Disabilities. 2013: 46(6)).

She is a lifecourse developmental cognitive neuroscientist/psychologist with a passion to serve the cognitively challenged and/or disabled via promoting new and innovative basic research and theoretically-grounded evidence-based intervention strategies to maximuze function. Dr. Mann Koepke has served in the Division of Extramural Programs across the National Institute on Aging (NIA), the National Institute of Nursing Research (NINR), and now NICHD, overseeing research on cognitive and neurological development and disorders, including neurobiological, behavioral and caregiving research foci. She has served on numerous federal and national committees aimed at advancing research and services for young learners and persons with cognitive and/or physical disability or differences, co-authoring numerous calls for new research to close significant gaps, as well as peer-reviewed publications. Prior to coming to NIH, she was faculty in Neurology (Psychology) at Washington University-St. Louis School of Medicine where she managed the universitys Alzheimers Disease Research Center (supported in part by grant P50AG05681), and served as Director of its Education Core and its Rural Outreach Satellite. While there, expanding on her enthusiasm for the use of newly developed technologies as tools for cognition, she developed and regularly contributed to the first-ever freely available web-based online educational support system for anyone interested in Alzheimers disease (AD) and for formal and informal dementia patient caregivers; the cite has garnered numerous national and international awards. This early online educational service has been used & replicated around the globe as a model for online disease/disabilty-focused educational support service.