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Pre-verbal number sense common to monkeys, babies, college kids
February 13, 2009
Elizabeth Brannon to speak at AAAS CHICAGO -- Basic arithmetic and "number sense" appear to be part of the shared evolutionary past of many primates; it's the use of language to explain abstractions that apparently takes human math to a higher level. Elizabeth Brannon, an assistant professor of psychology and neuroscience at Duke University, studies how human adults and infants, lemurs, and monkeys think about numbers without using language. She's looking for the brain systems that support number sense and trying to figure out how this cognitive skill develops. "Number is one of the more abstract domains of cognition: three coins and three loaves of bread are very different concepts," says Brannon, who appears on a Friday afternoon panel at the AAAS annual meeting called "Comparative Cognition: The Science of Mental Evolution. "Yet, many studies show that babies, even in the first year of life, can tell the difference between quantities." She runs about 500 babies per year through her testing lab at Duke, as well as macaques, lemurs and the odd undergraduate. Most of the experiments involve computer touch-screens and sets of brightly colored dots. After seeing the same number of objects repeated in different-looking sets, infants recognize the novelty of a new number of objects. So do macaques. And both college kids and macaques can do a rough sort of math by summing sets of objects without actually counting them. Their speed and accuracy are about the same, in fact. That the evolved brain has some fundamental sense of number without language should come as little surprise, Brannon says. "There are all sorts of reasons why number would be useful for nonhuman animals in the wild. In foraging situations animals need to make decisions about how long to stay in a given patch of food and when to move on," Brannon says. "Territorial animals may need to assess the number of individuals in their own group relative to competing groups to decide whether to stand their ground or retreat." Understanding the biological basis of our number sense might also help early childhood educators. Brannon's latest work is aimed at understanding how the human brain changes to accommodate symbolism as a child learns the names of numbers and begins to grasp more abstract manipulations. "If the nonverbal number sense is really providing a critical foundation for math achievement, then this will suggest teaching methods that provide more grounding in the nonverbal quantity system." Brannon is also exploring the macaque's sense of an empty set, what we'd call zero with our linguistically intensive sense of number. The monkeys are more likely to confuse an empty set with a 1 or a 2 than they are to confuse it with an 8 or a 9, she says, which shows they're putting zero in the proper place on the number line. "We're trying to understand how the animal mind works. How much of human thought is dependent on language?" Duke University

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The Number Sense: How the Mind Creates Mathematics
by Stanislas Dehaene (Author)
The Number Sense is an enlightening exploration of the mathematical mind. Describing experiments that show that human infants have a rudimentary number sense, Stanislas Dehaene suggests that this sense is as basic as our perception of color, and that it is wired into the brain. Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics. A fascinating look at the crossroads where numbers and neurons intersect, The Number Sense offers an intriguing tour of how the structure of the brain shapes our mathematical abilities, and how our mathematics opens up a window on the human mind.
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Number Sense Routines: Building Numerical Literacy Every Day in Grades K-3
by Jessica F. Shumway (Author), Lucy West (Foreword)
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The Number Sense: How the Mind Creates Mathematics, Revised and Updated Edition
by Stanislas Dehaene (Author)
Our understanding of how the human brain performs mathematical calculations is far from complete, but in recent years there have been many exciting breakthroughs by scientists all over the world. Now, in The Number Sense, Stanislas Dehaene offers a fascinating look at this recent research, in an enlightening exploration of the mathematical mind. Dehaene begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and that human infants also have a rudimentary number sense. Dehaene suggests that this rudimentary number sense is as basic to the way the brain understands the world as our perception of color or of objects in space, and, like these other abilities, our number sense is wired into the brain....
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Building Number Sense - Games & Activities to Practice Combinations to 10 (Grades K-1)
by Catherine Jones Kuhns (Author), Diane Lyons (Editor), Joyce Rainville (Editor)
Students are guaranteed to enjoy the activities in this book. But more than having fun, they will be engaged in the critical practice they need to learn by heart - the number combinations to 10.
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Number Sense, Grades 1 Through 2 Simple Effective Number Sense Experiences
by Barbara Reys (Author), Robert Reys (Author), Alistair McIntosh (Author), Joan Gideon (Editor)
These 10-minute activities help students develop a sense of what numbers represent and how to use them by, exploring relationships and patterns, encouraging mental computation, recognizing equivalent representations of a number, establishing benchmarks, improving estimation skills, and exploring the idea of reasonableness. Includes activity masters, teacher's notes, and ideas for extending the activity. Grades 1-2
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It Makes Sense!: Using Ten-frames to Build Number Sense, Grades K-2
by Melissa Conklin (Author)
From Look, Quick! to Mystery Sums, the 20 classroom-tested lessons in this resource provide friendly, meaningful support for using ten-frames. Many state standards require students to solve addition and subtraction problems using models. Ten-frames are one of the most important models that teachers can use to help students anchor to the landmark number ten and develop all aspects of number sense. Additionally, state standards expect that students be fluent and flexible in their ability to compute numbers. Ten-frames help students develop the skills they need to become flexible and fluent problem solvers.
The step-by-step lessons are presented in three categories:
* routines * games * problem-solving activities
The lessons are designed to provide students with...
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Developing Number Sense, Grades 3-6
by Rusty Bresser (Author), Caren Holtzman (Author)
Imaginative lessons give students practice with mental computation, basic operations, navigating the number system, and estimation. Content is crafted to show that number sense is not a specific skill, but encompasses a student's ability to think and reason flexibly, make sound numerical judgments, and see numbers as useful. Both new and experienced teachers will find this book a valuable resource.
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Number Sense and Number Nonsense: Understanding the Challenges of Learning Math
by Nancy Krasa (Author), Sara Shunkwiler (Author)
How do children learn math -- and why do some children struggle with it? The answers are in Number Sense and Number Nonsense, a straightforward, reader-friendly book for education professionals and an invaluable multidisciplinary resource for researchers. More than a first-ever research synthesis, this highly accessible book brings math difficulties into clear focus, helping educators and psychologists get inside students' heads so they can devise the best way to help children learn. Clinical psychologist Nancy Krasa and middle-school teacher Sara Shunkwiler combine their expertise for an eye-opening exploration of how the brain works during the many complex facets of math learning. Readers will gain a complete, research-based understanding of what it means when students struggle with...
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Number Sense: Simple Effective Number Sense Experiences, Grades 3-4
by Barbara Reys (Author), Robert Reys (Author), Alistair McIntosh (Author), Rachel Gage (Illustrator)
These 10-minute activities help students develop a sense of what numbers represent and how to use them by, exploring relationships and patterns, encouraging mental computation, recognizing equivalent representations of a number, establishing benchmarks, improving estimation skills, and exploring the idea of reasonableness. Includes activity masters, teacher's notes, and ideas for extending the activity. Grades 3-4
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Teaching Number Sense: Kindergarten
by Chris Confer (Author)
This title is part of a three-book Teaching Number Sense series that focuses on the critical role that number sense plays in developing mathematical understanding. Number sense encompasses a wide range of abilities, including being able to make reasonable estimates and to think and reason flexibly. These lessons help students develop good number intuition and the ability to see numbers as tools, not barriers. By encouraging young children to reason their way to solutions, teachers help students form a solid foundation upon which all of their later mathematical understanding will be built. Lessons in this book are organized in an accessible, easy-to-read format that includes an overview, a materials list, the lesson duration, step-by-step teaching directions, and vignettes of how the...
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