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# Math Cognition and Learning

Controversies if not outright polemics have characterized mathematics education in the U.S. and other countries for more than a quarter of a century, since the National Council of Teachers of Mathematics (NCTM) published its first Curriculum and Evaluation Standards (1989), triggering what eventually became known as the “The Math Wars.” And just when it appeared that these wars were abating, if not devolving into more minor skirmishes, a report by the National Mathematics Advisory Panel (2008) set off a backlash by many prominent mathematics educators (see the Educational Researcher, 2008) that re-ignited these wars. Since that time, with the periodic rise of initiatives such as the U.S. Common Core State Standards in Mathematics, arguments often as contentious as the earlier math wars have resurfaced, both with respect to what aspects of mathematics our children should learn and how these should be taught.

All the while, and seemingly behind the scenes, research on the origins and early development of basic numerical competencies has been accruing that is destined to provide a strong evidentiary foundation for the design of effective instructional strategies for teaching mathematics in general and interventions for moderating the difficulties experienced by low-achieving students and those with learning disabilities in particular. In Volume 1 of this series on mathematical cognition and learning, we provided a unique collection of chapters that explored the evolutionary origins and early development of basic number skills in nonhuman species, human infants and toddlers. It turns out that much of the progress that has been made to date with respect to our understanding of mathematical cognitive development has focused on the fundamental cognitive operations, mental representations, and solution strategies used by children when engaging in various kinds of numerical and arithmetic tasks.

More recently, however, the application of modern brain imaging tools to the study of numerical cognition has 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 that they remain neurobiologically plausible—that is, not incompatible with what we have learned about the developing brain. Likewise, advances in molecular genetic methods when combined with more traditional quantitative genetic approaches are gradually providing us with a window on the unique contributions of both heredity and environment to individual differences in mathematical ability and disability.

The current volume, the second in this series, encompasses a distinctive blend of chapters authored by leading North American and European researchers along with rising stars in the field, offering the reader comprehensive and insightful reviews of contemporary research on both the neural substrates of and genetic influences on mathematical cognitive development. These chapters take the reader on an interesting and informative tour of exciting ways in which contemporary and 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.

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.

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. At issue in other chapters are several theoretical considerations concerning: how numerical symbols are linked to nonsymbolic representations of numerical quantity and how tightly these representations are connected in the brain; 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; what neurocognitive architecture is best suited to learning fractions; whether mathematical proficiency is determined by a single unique, underlying cognitive factor or by multiple cognitive components; to what extent, if any, electrical stimulation of the brain can enhance numerical cognition and learning; and the degree to which children presenting with different neurodevelopmental disorders differ in the specificity of their numerical and mathematical impairments.

Beyond these kinds of issues, the remaining chapters deal with such matters as the use of fingers and their neural substrates in the development of numerical representations and arithmetic processing; 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; the role of phonological processing and the recruitment of a widespread brain network in children’s developing, arithmetic fact-retrieval skills; and how both genes and environments interact to influence the origins and development of mathematical ability and disability.

**References**

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.

National Mathematics Advisory Panel. (2008). Foundations for success: The final report of the National Mathematics Advisory Panel. Washington, DC: U.S. Department of Education.

Kelly, A. E. (Ed.). (2008). Special Issue on Foundations for Success: The Final Report of the National Mathematics Advisory Panel. [Special issue]. Educational Researcher, 37(9).

**About the Mathematical Cognition and Learning series:**

The *Mathematical Cognition and Learning* series integrates the latest in innovative measures and methodological advances from the top researchers in the field. The first volume of the ground-breaking series, *Evolutionary Origins and Early Development of Number Processing**,* focuses on the origins and early development of numerical cognition in non-human primates, lower vertebrates, human infants, and preschool children. The text will help readers understand the nature and complexity of these foundational quantitative concepts and skills along with evolutionary precursors and early developmental trajectories. The second volume, *Development of Mathematical Cognition**, *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.

Both books are available for purchase via the Elsevier Store at up to 30% off the list price and free global shipping. Simply enter the discount code STC315 at checkout and receive your discount on either of these ground-breaking volumes.

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.

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