Development of Mathematical Cognition: Neural Substrates and Genetic Influences

By Academic Press

Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities.

Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field.

• Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition
• Addresses recent work in quantitative and molecular genetics
• Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning
• Informs policy to help increase the level of mathematical proficiency among the general public

• Language: English
• Publisher: Academic Press
• Release date: Oct 3, 2015
• ISBN: 9780128019092

Book preview

2005:67–84.

Preface

Daniel B. Berch; Davis C. Geary; Kathleen Mann Koepke

Not a week goes by where there isn't at least one story in the news about mathematics learning, whether it's about the latest National Assessment of Educational Progress (NAEP) scores in the U.S., comparisons of performance by different countries on international tests such as the Trends in International Mathematics and Science Study (TIMSS) or the Program for International Student Assessment (PISA), or debates in op-ed pieces concerning the merits or shortcomings of the U.S. Common Core State Standards in Mathematics. Clearly, the myriad of opinions proffered by educators, administrators, teachers, journalists, and bloggers concerning the continuing difficulties experienced by many children in learning mathematics indicates there is still much to be learned. The science of the typical and atypical development of mathematical cognition and precisely what kinds of instructional interventions to improve mathematical fluency and achievement are best suited for each type of learner have yet to achieve a level of clarity that can settle the debates.

Although admirable progress has certainly been made with respect to our understanding of the basic cognitive operations, mental representations, and solution strategies used by children in various kinds of numerical and mathematical tasks, it is only fairly recently that the use of brain imaging tools have begun to reveal the neural underpinnings of developmental changes in mathematical thinking and learning. Furthermore, findings emerging from this research help to constrain cognitive theories of mathematical development, ensuring they remain neurobiologically plausible. Likewise, advances in molecular genetic methods when combined with more traditional quantitative genetic approaches are gradually providing us with a unique window on the relative contributions of heredity, shared environments, and nonshared environments to individual differences in mathematical ability and disability. The current volume, the second in the Mathematical Cognition and Learning Series, encompasses a unique blend of chapters that cover the landscape of these two domains. Taken together, they offer the reader not only comprehensive and insightful reviews of contemporary research in each of these domains, but also several nascent, neurocognitive models of numerical and arithmetic processing, along with the implications of this work for improving mathematics instruction. As such, this volume should be of particular interest to researchers and students in cognitive neuroscience, behavioral genetics, developmental psychology, educational psychology, special education, and mathematics education.

Although selected special issues of scholarly journals have occasionally covered brain imaging studies of children's mathematical development, no other edited books to date have focused exclusively on this topic nor included relevant work from behavioral and molecular genetics. Our volume aims to present the major biological evidences (genetic and neurobiologic) of mathematical development by including strong contributions from a group of leading North American and European researchers and scholars, as well as rising stars in the field who have already made important contributions to the literature. The resulting collection of chapters takes the reader on an interesting, unique, and informative tour of exciting ways in which contemporary as well as innovative brain imaging techniques and cutting-edge findings from modern genetic and genomic methods are being used to inform and illuminate our understanding of and ability to shape mathematical cognitive development through environmental and biologic means.

At issue in these pages are several theoretical debates, including how numerical symbols are linked to nonsymbolic representations of numerical quantity and how tightly these representations are connected in the brain (Chapter 2); how the malleable brains of children recruit different regions that will ultimately establish the mature neural system of arithmetic fact retrieval found in most adults (Chapter 4); what neurocognitive architecture is best suited to learning fractions (Chapter 6); whether mathematical proficiency is determined by a single unique, underlying cognitive factor or by multiple cognitive components such as memory, spatial processing, or executive function (Chapter 8); to what extent, if any, exogenous electrical stimulation of the brain can enhance numerical cognition and learning (Chapter 10); and the degree to which children presenting with different neurodevelopmental disorders differ in the specificity of their numerical and mathematical impairments (Chapter 12).

Beyond these kinds of issues, the other chapters deal with such matters as distinct ways in which two core, cognitive and brain systems contribute to symbolic numerical and mathematical development (Chapter 3); the use of fingers in the development of numerical representations and arithmetic processing (Chapter 5); evidence suggesting that at least some forms of developmental dyscalculia are associated with alterations in brain structure and function as well as metabolism and fiber connections in the parietal cortex (Chapter 7); the possible role of phonological processing and the recruitment of a widespread brain network in children's developing, arithmetic fact-retrieval skills (Chapter 9); and how both genes and environments influence the origins and development of mathematical ability and disability (Chapter 11). In the introductory chapter, we discuss some of the fundamental issues concerning the interpretation of findings from brain imaging and behavioral genetics research, and how these play out in the study of mathematical cognitive development.

Finally, we thank the Child Development and Behavior Branch of the Eunice Kennedy Shriver National Institute of Child Health and Human Development (NICHD), NIH for the principal funding to support the conference on which this volume is based, and we are likewise grateful to the Institute of Education Sciences (IES) of the U.S. Department of Education for their continuing monetary and substantive support of this conference series.

Chapter 1

Introduction

How the Study of Neurobiological and Genetic Factors Can Enhance Our Understanding of Mathematical Cognitive Development

Daniel B. Berch¹; David C. Geary²; Kathleen Mann Koepke³    ¹ Curry School of Education, UVA Cognitive Science Program, University of Virginia, Charlottesville, Virginia, USA

² Department of Psychological Sciences, Interdisciplinary Neuroscience Program, University of Missouri, Columbia, Missouri, USA

³ NICHD/CDBB, Rockville, Maryland, USA

Abstract

In this introductory chapter, we examine some of the basic issues concerning the use of brain imaging methods and interpretations of the data they generate, as well as the ways in which these considerations may influence the study of mathematical cognitive development. We begin by providing a brief history of brain imaging research in this field, followed by a discussion of the importance of adopting a developmental perspective. Then we review various criticisms of functional magnetic resonance imaging (fMRI), the dominant technique employed by the authors in this volume, and summarize a recent analysis that reveals the major limitations of these claims. Next, we describe some specific ways in which neuroimaging can inform cognitive theories. Finally, we chronicle major developments in the field of genetics, describe some of the interpretive challenges associated with behavioral genetic designs, and make recommendations concerning how cognitive science and behavioral genetics can best move forward in the age of molecular genetics and neuroscience.

Keywords

Triple-code model

Brain imaging methods

Reverse inference

Modularity

Localization

Neurovascular changes

Adaptation paradigm

Multi-voxel pattern analysis

Developmental perspective

Behavioral and molecular genetics

Epigenetics

Introduction

Our understanding of developmental changes in mathematical cognition has advanced significantly over the past 40 plus years. A variety of innovative tasks have been used to study the intuitive number sense of preverbal human infants, toddlers, and preschoolers (see Geary, Berch, & Mann Koepke, 2015 for reviews), as well as the formal mathematical learning of school-age children and adolescents. The findings that have emerged from the use of these paradigms and the consistent effects they have generated are so numerous that it would be challenging to list them all here, much less to explain their significance with respect to achieving a comprehensive understanding of both the typical and atypical development of mathematical thinking and learning. That being said, it is worth providing the reader with a representative set of topics that have been studied to date. These include subitizing (i.e., the rapid and accurate apprehension of the quantity of small collections of items); magnitude comparison of nonsymbolic quantities (e.g., random dot arrays) and symbolic quantities (e.g., Arabic numerals); transcoding (i.e., translating from one numerical format to another); other relations between nonsymbolic and symbolic numerical skills; the development of counting skills, single-digit arithmetic, and multidigit arithmetic processing; the acquisition of place value; conceptual and procedural knowledge of fractions; proportional reasoning; mathematical equivalence; and the role of domain general processes (e.g., working memory, processing speed) in mathematical cognitive development. Furthermore, some findings have been so robust that they have attained the status of effects, such as the numerical distance effect (Moyer & Landauer, 1967); the problem-size effect (Ashcraft & Guillaume, 2009; Zbrodoff & Logan, 2005), the Spatial-Numerical Association of Response Codes (SNARC) effect (see Fischer & Shaki, 2014 for a review), and the operational momentum effect (also reviewed by Fischer & Shaki,