Neuroscience of Mathematical Cognitive Development

155 Pages·2018·5.26 MB·English

by  Rhonda Douglas Brown

Rhonda Douglas Brown
Neuroscience of
Mathematical
Cognitive
Development
From Infancy Through Emerging
Adulthood
Neuroscience of Mathematical Cognitive
Development
Rhonda Douglas Brown
Neuroscience of
Mathematical Cognitive
Development
From Infancy Through Emerging Adulthood
Rhonda Douglas Brown
Developmental & Learning Sciences Research Center
School of Education
University of Cincinnati
Cincinnati, OH, USA
ISBN 978-3-319-76408-5 ISBN 978-3-319-76409-2 (eBook)
https://doi.org/10.1007/978-3-319-76409-2
Library of Congress Control Number: 2018935253
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To Russ, Ainsley, and Paige Brown
and Theresa Douglas
In loving memory of Ronald Douglas
and Virgil and Martha Brown
Preface
This book examines the neuroscience of mathematical cognitive development from
infancy through emerging adulthood, addressing both biological and environmental
influences on brain development and plasticity. It was written as a resource for pro-
fessors, researchers, clinicians, educators, and graduate students in the fields of
developmental, cognitive, child clinical, educational, and school psychology; neu-
roscience and neuropsychology; and mathematics education and intervention. It
was also designed to serve as a text for advanced undergraduate and graduate
courses covering mathematical cognition. It includes background information on
developmental psychology theory, brain development, and cognitive neuroscience
research methods to make the volume more accessible to graduate students and
professionals from other fields and to facilitate understanding and application of
research results.
The book begins by presenting major theories for interpreting neuroscience stud-
ies of mathematical cognitive development and achievement, including evolution-
ary developmental psychology, a developmental systems approach, and the
triple-code model of numerical processing. These theories provide a cohesive
framework that is revisited throughout the text. A general paradigm for conducting
studies using multiple levels of analysis to examine interactions between neural
activity, behavior, and environmental contexts and experiences is discussed. Then,
the book describes brain development and cutting-edge neuroscience research
methods, including functional Magnetic Resonance Imaging (fMRI), Diffusion
Tensor Imaging (DTI), Event-Related Potentials (ERP), and Transcranial Magnetic
Stimulation (TMS), at a level that is comprehensible to those who may be unfamil-
iar with these neuroimaging techniques. The book includes chapters that discuss
existing studies and new research findings from my work with colleagues at the
University of Cincinnati using neuroscience research methods to examine quantity
representation, calculation, and visuospatial cognition. Furthermore, it also presents
neuroscience models and research for understanding mathematical difficulties and a
diversity of exceptionalities, such as autism spectrum disorder and Turner’s syn-
drome. A review of mathematics intervention programs is included that relates them
to neuroscience theory and research to provide information to researchers, practitio-
vii
viii Preface
ners, and educators seeking strategies for improving developmental trajectories,
individual outcomes, and educational practices for students experiencing mathe-
matical difficulties. The book ends with a summary of conclusions that can cur-
rently be drawn from neuroscience studies of mathematical cognitive development
and recommendations for future research.
This book is a product of the work of many scholars and researchers dedicated to
understanding mathematical cognitive development so that we may, ultimately,
improve children’s learning and their success in life. Their names are too numerous
to list here, but the references to each chapter provide some acknowledgement. I am
especially inspired by the work of David F. Bjorklund, David C. Geary, Stanislas
Dehaene, Daniel B. Berch, Robert Siegler, Douglas H. Clements, Ted Hasselbring,
Lynn Fuchs, and Sharon Griffin. I am grateful to my colleagues Scott Holland, Peter
Chiu, and Tzipi Horowitz-Kraus at the University of Cincinnati and Cincinnati
Children’s Hospital Medical Center for engaging me in neuroimaging research. I
feel especially privileged to have Vincent J. Schmithorst as a long-t ime collaborator
on the research presented in this book. I offer my sincere gratitude to David
F. Bjorklund for reviewing and providing feedback on portions of the text; Bethany
Reeb-Sutherland for providing a photograph from her lab; Ted Hasselbring for
assisting with permissions for the figures from the FASTT Math program; Sharon
Griffin for providing figures from the Number Worlds program; and Vicki Plano-
Clark for her publication advice. I would especially like to thank Cheri Williams for
mentoring and motivating me through the process of writing this book and for her
friendship. I am also grateful for the camaraderie and support of my colleagues at
the University of Cincinnati, especially Vicki Carr, Tina Stanton-Chapman, Heidi
Kloos, and Cathy Maltbie; Jonathan Thomas at the University of Kentucky; and the
graduate students who participated in my courses over the years, including
Mathematics Cognition, especially Lori Kroeger, Nicole Hammons, Gail Headley,
Laura Kelley, Lori Foote, Mindy Victor, Kate Doyle, Sammie Marita, Lindsay
Owens, Rachel Lindberg, Jonathan Buening, Leslie Kochanowski, Sue Schlembach,
Ann Rossmiller, and Ashley Vaughn. At Springer, I am grateful to Garth Haller,
Judy Jones, and Michelle Tam for the opportunity to write this book and for their
enthusiasm and assistance during this process. Finally, to my husband Russ, my
daughters Ainsley and Paige, and my mother Theresa, I offer my deepest gratitude
for their ever-present love, encouragement, and support.
Cincinnati, OH, USA Rhonda Douglas Brown
Contents
1 Theories for Understanding the Neuroscience of Mathematical
Cognitive Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Rhonda Douglas Brown
The Importance of Mathematics in Human Development . . . . . . . . . . . . . 2
Theoretical Frameworks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
Evolutionary Developmental Psychology . . . . . . . . . . . . . . . . . . . . . . . . 5
Developmental Systems Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
Biologically Primary and Secondary Mathematical Abilities . . . . . . . . . 8
Triple-Code Model of Number Processing . . . . . . . . . . . . . . . . . . . . . . . 10
A Place for Neuroscience in Cognitive Development . . . . . . . . . . . . . . . . 12
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2 B rain Development and Cognitive Neuroscience Research
Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Rhonda Douglas Brown
Brain Development, Structure, and Function . . . . . . . . . . . . . . . . . . . . . . . 22
Cognitive Neuroscience Research Methods . . . . . . . . . . . . . . . . . . . . . . . . 28
Lesion Studies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
Transcranial Magnetic Stimulation (TMS) . . . . . . . . . . . . . . . . . . . . . . . 29
Functional Magnetic Resonance Imaging (fMRI) . . . . . . . . . . . . . . . . . 30
Diffusion Tensor Imaging (DTI) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Event-Related Potentials (ERP) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
Functional Near-Infrared Spectroscopy (fNIRS) . . . . . . . . . . . . . . . . . . 36
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3 Quantity Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Rhonda Douglas Brown and Vincent J. Schmithorst
Cognitive Systems for Quantity Representation . . . . . . . . . . . . . . . . . . . . . 45
Neural Basis of Quantity Representation . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Relationships Between Neural Correlates of Quantity
Representation and Mathematics Achievement . . . . . . . . . . . . . . . . . . . . . 48
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
ix
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4 Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
Rhonda Douglas Brown, Vincent J. Schmithorst, and Lori Kroeger
Cognitive Systems and Neural Basis Related for Mathematics
Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
Relationships Between Neural Correlates of Calculation
and Mathematics Achievement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Exact Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
Approximate Calculation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Error Detection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Fractions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5 Visuospatial Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
Jonathan Buening and Rhonda Douglas Brown
Neural Basis of Visuospatial Cognition . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Visual Attention and Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Visual Perception and Judgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Visual Imagery and Mental Rotation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
Visuospatial Working Memory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
6 M athematical Difficulties and Exceptionalities . . . . . . . . . . . . . . . . . . . 97
Rachel Lindberg and Rhonda Douglas Brown
Mathematical Difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Cognitive Processing Difficulties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Exceptionalities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
Neurodevelopmental Disorders, Syndromes, and Conditions . . . . . . . . 103
Individual Differences in Language and Reading . . . . . . . . . . . . . . . . . . 107
Giftedness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
Considerations and Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
7 Enhancing Mathematical Cognitive Development Through
Educational Interventions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
Lori Kroeger and Rhonda Douglas Brown
Mathematical Intervention Programs Related to Neuroscience
Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
The Number Race . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
Fluency and Automaticity Through Systematic Teaching
with Technology (FASTT Math) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123
SRA Number Worlds® with Building Blocks® . . . . . . . . . . . . . . . . . . . . 128
Other Intervention Programs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133
Conclusions and Future Directions for Research . . . . . . . . . . . . . . . . . . . . 133
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
Contents xi
8 Conclusions and Future Directions for the Neuroscience
of Mathematical Cognitive Development . . . . . . . . . . . . . . . . . . . . . . . . 137
Rhonda Douglas Brown
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143