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Like It or Not: Math Matters
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.
In the United States and many other developed nations, as many as one in four adults are functionally innumerate. – David C. Geary
The first volume of a five volume series, 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, Evolutionary Origins and Early Development of Number Processing. 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 for helping children 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 even more noteworthy, or at least less intuitive for people unfamiliar with this research, are the similarities between the number competencies of nonhuman animals and those of humans infants and 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.
Evolutionary Origins and Early Development of Number Processing is available for purchase on the Elsevier Store. Use discount code “STC215” at checkout and save up to 30% on your very own copy!
About the Author
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 children’s mathematical cognition and learning and Darwin’s sexual selection as largely but not solely related to human sex differences. Professor Geary directed a 10-year longitudinal study of children’s 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.
Professor Geary’s 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 Geary’s 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 Darwin’s 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 Geary’s 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.
Mathematics & Statistics
It has been said that “math is the language of science,” a common basis for understanding the world around us, no matter where in the world we are. From the most rudimentary measurements to the most sophisticated computational modeling, mathematics and statistical analysis are fundamental not only to pure scientific investigation, but to business, financial markets, health care, and more. In addition to providing core textbooks in algebra, calculus, analysis, probability, and statistics (including software such as R and BUGS), we publish valuable applied math reference content for professionals and researchers in all areas of physical and life science, finance, economics, engineering, and computing.