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An Introduction to Mathematical Cognition
The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavio...
Numerical Development - From cognitive functions to neural underpinnings
Living at the beginning of the 21st century requires being numerate, because numerical abilities are not only essential for life prospects of individuals but also for economic interests of post-industrial knowledge societies. Thus, numerical development is at the core of both individual as well as societal interests. There is the notion that we are already born with a very basic ability to deal with small numerosities. Yet, this often called “number sense” seems to be very restricted, approximate, and driven by perceptual constraints. During our numerical development in formal (e.g., school) but also informal contexts (e.g., family, street) we acquire culturally developed abstract symbol...
Handy numbers: finger counting and numerical cognition
We are born with a “number sense” - the ability to respond to numerosity, which we share with other vertebrates. This inherited numerosity representation is approximate and follows the Weber-Fechner law that governs sensory perception. As educated adults we can also use culturally developed abstract symbol systems to represent exact numerosities – in particular number words and Arabic numbers. This developmental stage is preceded by an apparently transient phase of finger counting and finger calculation. In fact, the use of fingers to represent number is ubiquitous across ages and cultures. Children use finger counting even if they are discouraged to do so, sometimes even before they a...
Linguistic Influences on Mathematical Cognition
For many years, an abstract, amodal semantic magnitude representation, largely independent of verbal linguistic representations, has been viewed as the core numerical or mathematical representation This assumption has been substantially challenged in recent years. Linguistic properties affect not only verbal representations of numbers,but also numerical magnitude representation, spatial magnitude representations, calculation, parity representation, place-value representation and even early number acquisition. Thus, we postulate that numerical and arithmetic processing are not fully independent of linguistic processing. This is not to say, that in patients, magnitude processing cannot functio...
The Wiley-Blackwell Handbook of Childhood Cognitive Development
This definitive volume is the result of collaboration by top scholars in the field of children's cognition. New edition offers an up-to-date overview of all the major areas of importance in the field, and includes new data from cognitive neuroscience and new chapters on social cognitive development and language Provides state-of-the-art summaries of current research by international specialists in different areas of cognitive development Spans aspects of cognitive development from infancy to the onset of adolescence Includes chapters on symbolic reasoning, pretend play, spatial development, abnormal cognitive development and current theoretical perspectives
The Oxford Handbook of Numerical Cognition
How do we understand numbers? Do animals and babies have numerical abilities? Why do some people fail to grasp numbers, and how we can improve numerical understanding? Numbers are vital to so many areas of life: in science, economics, sports, education, and many aspects of everyday life from infancy onwards. Numerical cognition is a vibrant area that brings together scientists from different and diverse research areas (e.g., neuropsychology, cognitive psychology, developmental psychology, comparative psychology, anthropology, education, and neuroscience) using different methodological approaches (e.g., behavioral studies of healthy children and adults and of patients; electrophysiology and b...
The Best Writing on Mathematics 2016
The year's finest mathematics writing from around the world This annual anthology brings together the year's finest mathematics writing from around the world. Featuring promising new voices alongside some of the foremost names in the field, The Best Writing on Mathematics 2016 makes available to a wide audience many articles not easily found anywhere else—and you don't need to be a mathematician to enjoy them. These writings offer surprising insights into the nature, meaning, and practice of mathematics today. They delve into the history, philosophy, teaching, and everyday occurrences of math, and take readers behind the scenes of today's hottest mathematical debates. Here Burkard Polster ...
An Introduction to Mathematical Cognition
The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavio...
