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Language and culture in mathematical cognition

Language and culture in mathematical cognition

Biologists have known for decades that many traits involved in competition for mates or other resources and that influence mate choice are exaggerated, and their expression is influenced by the individuals’ ability to tolerate a variety of environmental and social stressors. Evolution of Vulnerability applies this concept of heightened sensitivity to humans for a host of physical, social, psychological, cognitive, and brain traits. By reframing the issue entirely, Geary demonstrates this principle can be used to identify children, adolescents, or populations at risk for poor long-term outcomes and identify specific traits in each sex and at different points in development that are most easily disrupted by exposure to stressors.

Evolution of Vulnerability begins by reviewing the expansive literature on traits predicted to show sex-specific sensitivity to environmental and social stressors, and details the implications for better assessing and understanding the consequences of exposure to these stressors. Next, the book reviews sexual selection—mate competition and choice—and the mechanisms involved in the evolution of condition dependent traits and the stressors that can undermine their development and expression, such as poor early nutrition and health, parasites, social stress, and exposure to man-made toxins. Then it reviews condition dependent traits (physical, behavioral, cognitive, and brain) in birds, fish, insects, and mammals to demonstrate the ubiquity of these traits in nature. The focus then turns to humans and covers sex-specific vulnerabilities in children and adults for physical traits, social behavior, psychological wellbeing, and brain and cognitive traits. The sensitivity of these traits is related to exposure to parasites, poor nutrition, social maltreatment and other stressors, environmental toxins, chemotherapy, and Alzheimer’s disease, among others. The book concludes with an implications chapter that outlines how to better assess vulnerabilities in children and adults and how to more fully understand how and why some types of environmental and social stressors are particularly harmful to humans.

Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts, Volume 3

Development of Mathematical Cognition, Volume 2: Neural Substrates and Genetic Influences

Like it or not, math matters and matters more than ever. In the United States and many other developed nations, as many as one in four adults are functionally innumerate. These individuals have difficulty managing the day-to-day demands of modern living, such as making informed medical decisions, and are typically under employed or frequently unemployed, independent of their intelligence or reading ability. The situation is likely to become worse as our information- and technology-based economy and society intensifies. Risk of long-term innumeracy is evident as early as kindergarten or 1st grade, as children who have a poor grasp of numbers, counting and other foundational skills at the beginning of schooling tend to remain behind their peers throughout schooling and therefore into adulthood. The nature of mathematics contributes to the long-term persistence of these early deficits. Any new mathematical content that we expect children to learn in school is based on an assumption that they already have a good grasp of the foundational knowledge and skills that came before it.  Competence with algebra is dependent on fluency with fractions and this in turn is dependent on a good grasp of whole number arithmetic that in turn is dependent on an understanding of Arabic numerals and the relations among them. Early difficulties create a shaky foundation that results in a mathematics education akin to a house of cards. It is only a matter of time before it collapses, and even if it could be rebuilt, their peers would move well beyond them during the process.

The key then is to identify how preschool children understand quantities and how they integrate this knowledge with the basic symbols of mathematics, number words and numerals. It is not enough to be able to count from one to ten. Children have to understand how many ‘one’ or ‘1 and ‘ten’ and ’10’ stand for. Making this connection can take several years and is the first and arguably the most important step toward numeracy. A stumble here or a late start can cascade into long-term issues with real consequences. This first volume of a five volume series on mathematical cognition and learning – from evolution to remedial intervention – addresses these first, critical steps to numeracy. To wit, we have assembled many of the most established and promising young scientists studying how nonhuman species and human infants and toddlers represent and understand non-symbolic (e.g., the relative magnitude of a collection of 3 items vs. a collection of 6 items) and symbolic (e.g., the quantity represented by the Arabic numeral ‘3’) number and magnitude. Many of these issues have been touched upon in a scattering of other edited books on animal cognition or early (human) cognitive development or here and there in scholarly journals, but none have pulled together the latest work in these areas into a single volume. We do so in this book. Across the chapters, the reader will find an integrative approach to the topic, providing not only a comprehensive treatment of relevant research with nonhuman species and human infants and toddlers but also a thorough yet comprehensible coverage of the prevailing methodological approaches used by leading researchers in the field.

As implied by the title, the scope is broad and deep, touching on the evolved functions of number systems, their potential evolutionary conservation across a wide variety of species, and how these competencies are expressed in nonhuman species and young children. Many of the chapters discuss the methods that are best used to study these competencies in infants, and several link these to specific brain regions and to children’s learning of school-based mathematics. The latter is intriguing and critical, as it suggests that these evolved number systems might provide the foundation upon which the first steps to numeracy are placed and thus have broad implications not only for helping children to take these first steps.

We have organized the volume into three sections. In the first are chapters that review number and magnitude systems in nonhuman species. Across these chapters, the reader is provided with cutting edge reviews of number competencies in fish, birds, and primates. A striking feature of these studies is the similarities in number competencies across a very diverse array of species. Perhaps more striking, or at least less intuitive to people unfamiliar with this research are the similarities between the number competencies of nonhuman animals and those of humans infants and young children before they acquire language; and, in some cases, the similarities in their brain systems that are sensitive to number and magnitude. The chapters in the second section focus on these similarities, as well as infants’ and young children’s sensitivity to and understand of number and magnitude more generally, and tie these to the learning of symbolic mathematics, that is, their understanding of the meaning of number words and numerals. The reader will be provided up-to-date reviews of the different ways in which infants and young children can represent number and magnitude, the implicit competencies built into the organization of these systems (e.g., sensitivity to additions and subtractions from collections of items), and the cues (e.g., sequence of tones) that shift attention to the numerical features of the world. The third section addresses related theoretical issues, including the nature of the core system for numerical representations and how to measure it, the contexts in which number systems evolved biologically and historically across human cultures, as well as a few thoughts on directions for future research.

Author Index

Amazon listing

Why do girls tend to earn better grades in school than boys? Why are men still far more likely than women to earn degrees in the fields of science, technology, engineering, and mathematics? And why are men on average more likely to be injured in accidents and fights than women? These and many other questions are the subject of both informal investigation in the media and formal investigation in academic and scientific circles.

In his landmark book Male, Female: The Evolution of Human Sex Differences, author David C. Geary provided the first comprehensive evolutionary model to explain human sex differences. Using the principles of sexual selection, such as female choice and male–male competition, Geary systematically reviewed and discussed the evolution of sex differences and their expression throughout the animal kingdom, as a means of not just describing but explaining the same process in Homo sapiens.      
Now, over 10 years since the first edition, Geary has completed a massive update, expansion, and theoretical revision of his classic text. New findings in brain and genetic research inform a wealth of new material, including a new chapter on sex differences in patterns of life history development; expanded coverage of genetic research (e.g., DNA fingerprinting to determine paternity as related to male–male competition in primates); fatherhood in humans; cross-cultural patterns of sex differences in choosing and competing for mates; and genetic, hormonal, and socio-cultural influences on the expression of sex differences. Finally, through his motivation to control framework (introduced in the first edition and expanded in The Origin of Mind, 2005), Geary presents a theoretical bridge linking parenting, mate choices, and competition with children’s development and sex differences in brain and cognition. The result is an even better book than the original—a lively and nuanced application of Darwin’s insight to help explain our heritage and our place in the natural world.

Portuguese translation of Chapter 1: https://www.homeyou.com/~edu/masculino-feminino-capitulo-1

Male, Female is a superb introduction to the science of sex differences, and one with a real difference: it seeks to explain the differences between women and men, rather than just describe them. The book is coherent, balanced, incisive, and well-written. It is both an invaluable resource for researchers and a pleasure to read.
Steven Pinker, Harvard College Professor of Psychology, Harvard University, and author of How the Mind Works and The Blank Slate.

Geary demonstrates in Male, Female just how much understanding of sex differences can be achieved by looking at human development through evolutionary lenses. Confusion turns into insight when the most powerful scientific paradigm ever developed in the life sciences replaces ideology. Any student, teacher, or even layperson fascinated by why we humans behave the way we do will find this exhaustively researched volume highly informative, to say nothing of fascinating.
- Jay Belsky, PhD, Director, Institute for the Study of Children, Families and Social Issues, Birkbeck University of London, England

Warning! If you still insist that sex differences have little to do with evolution and don’t want your cherished nostrums shattered, then avoid this book. For this new edition is testimony to the rapid burgeoning of the science of such differences and to Geary’s unrivaled command of it. From genes and hormones, to physiology and psychology, to brains and behavior, Male, Female is a comprehensive, authoritative guide to Darwin’s fundamental explanation and to the cornucopia of stunning new findings that it continues to inspire. Human nature is revealed as distinct male and female natures—an insight with profound implications for natural and social science, for public policy, and for our view of ourselves. This is a must-read for experts, novices, and anyone else who cares about today’s science and tomorrow’s agenda.
- Helena Cronin, PhD, Co-Director, Centre for Philosophy of Natural and Social Science, London School of Economics, London, England

Earlier in my career as a developmental psychologist, I had little interest in sex differences for their own sake. Sex differences only make sense when you have a theory about why they should exist. Evolutionary psychology provides that theory, and nowhere is it better articulated than in Geary’s Male, Female. This comprehensive yet highly accessible book is a must-read for anyone interested in sex differences, their evolution, and their development.
- David F. Bjorklund, PhD, Department of Psychology, Florida Atlantic University, Boca Raton

This richly illustrated second edition documents hundreds of ways the sexes differ, and it persuasively argues that most of the differences are not simply the result of sex role training and gender stereotypes. For anyone interested in better comprehending male and female cognition and behavior, I cannot think of a better book to read.
- Lee Ellis, PhD, Department of Anthropology and Sociology, University of Malaya, Kuala Lumpur, Malaysia

The origin of mind: Evolution of brain, cognition, and general intelligence.

David Geary’s The Origin of Mind is a remarkable book. As suggested by its subtitle, it ambitiously addresses many of the oldest questions of science (and society)… These are profound questions to ask and (to varying degrees in different chapters) Geary’s work does an extraordinary job in answering them. American Journal of Psychiatry. [read review]

Geary, D. C. (2005). The origin of mind: Evolution of brain, cognition, and general intelligence. Washington, DC: American Psychological Association. [Amazon listing]

This is a work of massive and wide ranging scholarship … The Origin of Mind will be of fundamental importance for developing an evolutionary psychology that integrates all of contemporary behavioral science. Geary has made a ground-breaking contribution…   Human Ethology Bulletin. [read review]

This book is a tour de force of current thinking and research in evolutionary psychology, neuroscience, and decision science.  The Journal of Behavioral Finance

The Origin of Mind… is an impressive effort to make the case for a modern interdisciplinary study of brain and cognition that views cognitive processes as biological adaptations…  PsycCRITIQUES

This book develops several lines of thought about issues that are crucial to understanding human nature.  Readers will find this a rewarding experience.  MetaPsychology

All Reviews

Sample excerpted chapter

Sex Differences

Ellis, L., Hershberger, S., Field, E., Wersinger, S., Sergio, P., Geary, D., Palmer, C., Hoyenga, K., Hetsroni, A., & Karadi, K. (2008). Sex differences: Summarizing more than a century of scientific research. New York: Francis & Taylor. [Amazon listing]


Geary, D. C. (1998). Male, female: The evolution of human sex differences. Washington, DC: American Psychological Association.
ISBN: 1-555798-527-8

Male, female is now available in French

Honorable mention, Best sciences books of the 1990s, Lingua franca


Table of Contents
Chapter One

Chapter Seven


Geary, D. C. (1994). Children's mathematical development: Research and practical applications. Washington, DC: American Psychological Association.

Table of Contents

Children's mathematical development is a monumental book and an exciting one -- an encyclopedia that will end one era and begin another. Robert B. Davis, Journal for Research in Mathematics Education (1995).