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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: Simple Effective Number Sense Experiences / Grades 6-8
by Alistair McIntosh (Author), Barbara Reys (Author), Robert Reys (Author), Joan Gideon (Editor), Rachel Gage (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 4-6
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Number Sense: Simple Effective Number Sense Experiences Grade 1-2
by Barbara Reys (Author), Robert Reys (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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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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Teaching Number Sense, Grade 1
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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Young Mathematicians at Work: Constructing Number Sense, Addition, and Subtraction
by Catherine Twomey Fosnot (Author), Maarten Dolk (Author)
The first in a three-volume set, Young Mathematicians at Work focuses on young children between the ages of four and eight as they construct a deep understanding of number and the operations of addition and subtraction.
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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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Teaching Number Sense: Grade 2
by Susan Scharton (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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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 and Nonsense: Building Math Creativity and Confidence Through Number Play
by Claudia Zaslavsky (Author)
These 80-plus math activities and number games help kids to think intuitively about math instead of just memorizing rules. The emphasis is on the underlying relationships between numbers and the process of manipulating them, not in coming up with the right answer every time. Kids get together and play games with odd and even numbers, prime and composite numbers, factors, divisors, and multiples of numbers, common and decimal fractions. Children learn the history of numbers-finger counting, number symbols in various cultures, and different ways of calculating. The book is full of riddles, puzzles, number tricks, and calculator games. Kids develop skills in estimation and computation as they become familiar with the characteristics and behavior of numbers. They will gain math confidence and...
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