The Number Sense How The Mind Creates Mathematics

Author by : Stanislas Dehaene Research Affiliate Institut National de la Sante et de la Recherche Medicale
Languange : en
Publisher by : Oxford University Press, USA
Format Available : PDF, ePub, Mobi
Total Read : 21
Total Download : 586
File Size : 42,5 Mb
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Description : Our understanding of how the human brain performs mathematical calculations is far from complete. But in recent years there have been many exciting scientific discoveries, some aided by new imaging techniques--which allow us for the first time to watch the living mind at work--and others by ingenious experiments conducted by researchers all over the world. There are still perplexing mysteries--how, for instance, do idiot savants perform almost miraculous mathematical feats?--but the picture is growing steadily clearer. In The Number Sense, Stanislas Dehaene offers general readers a first look at these recent stunning discoveries, in an enlightening exploration of the mathematical mind. Dehaene, a mathematician turned cognitive neuropsychologist, begins with the eye-opening discovery that animals--including rats, pigeons, raccoons, and chimpanzees--can perform simple mathematical calculations, and he describes ingenious experiments that show that human infants also have a rudimentary number sense (American scientist Karen Wynn, for instance, using just a few Mickey Mouse toys and a small puppet theater, proved that five-month-old infants already have the ability to add and subtract). Further, 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. But how then did the brain leap from this basic number ability to trigonometry, calculus, and beyond? Dehaene shows that it was the invention of symbolic systems of numerals that started us on the climb to higher mathematics, and in a marvelous chapter he traces the history of numbers, from early times when people indicated a number by pointing to a part of their body (even today, in many societies in New Guinea, the word for six is "wrist"), to early abstract numbers such as Roman numerals (chosen for the ease with which they could be carved into wooden sticks), to modern numbers. On our way, we also discover many fascinating facts: for example, because Chinese names for numbers are so short, Chinese people can remember up to nine or ten digits at a time--English-speaking people can only remember seven. Dehaene also explores the unique abilities of idiot savants and mathematical geniuses, asking what might explain their special mathematical talent. And we meet people whose minute brain lesions render their mathematical ability useless--one man, in fact, who is certain that two and two is three. Using modern imaging techniques (PET scans and MRI), Dehaene reveals exactly where in the brain numerical calculation takes place. But perhaps most important, The Number Sense reaches many provocative conclusions that will intrigue anyone interested in mathematics or the mind. Dehaene argues, for instance, that many of the difficulties that children face when learning math, and which may turn into a full-blown adult "innumeracy," stem from the architecture of our primate brain, which has not evolved for the purpose of doing mathematics. He also shows why the human brain does not work like a computer, and that the physical world is not based on mathematics--rather, mathematics evolved to explain the physical world the way that the eye evolved to provide sight. A truly 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.


Clothesline Math The Master Number Sense Maker

Author by : Chris Shore
Languange : en
Publisher by : Shell Education
Format Available : PDF, ePub, Mobi
Total Read : 54
Total Download : 796
File Size : 49,9 Mb
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Description : This must-have resource provides the theoretical groundwork for teaching number sense. Authored by Chris Shore, this e-book empowers teachers with the pedagogy, lessons, and detailed instructions to help them implement Clothesline Math in K-12 classrooms. Detailed, useful tips for facilitating the ensuing mathematical discourse are also included. At the elementary level, the hands-on lessons cover important math topics including whole numbers, place value, fractions, order of operations, algebraic reasoning, variables, and more. Implement Clothesline Math at the secondary level and provide students with hands-on learning and activities that teach advanced math topics including geometry, algebra, statistics, trigonometry, and pre-calculus. Aligned to state and national standards, this helpful resource will get students excited about learning math as they engage in meaningful discourse.


Mathematical Difficulties

Author by :
Languange : en
Publisher by : Elsevier
Format Available : PDF, ePub, Mobi
Total Read : 92
Total Download : 664
File Size : 45,6 Mb
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Description : This book examines the mathematical difficulties in typical and atypical populations. It discusses the behavioural, educational and neuropsychological characteristics of people with mathematical difficulties, and educational interventions to prevent, diagnose, treat or ameliorate such difficulties. The book brings together studies from different disciplines, including developmental psychology, neuroscience and education, and includes perspectives from practicing teachers. The book is divided into three major sections. The first includes chapters about the nature and characteristics of mathematical difficulties in the population as a whole, in relation to both psychology and education. The second deals with mathematical difficulties in children with other problems such as specific language impairment and dyslexia. The third discusses methods of interventions aimed at preventing, treating or ameliorating mathematical difficulties, and will include discussions of assessment and diagnosis.


Nimble With Numbers Grades 5 6 Engaging Math Experiences To Enhance Number Sense And Promote Practice

Author by : Leigh Childs
Languange : en
Publisher by :
Format Available : PDF, ePub, Mobi
Total Read : 58
Total Download : 923
File Size : 43,5 Mb
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Description : These lively and interesting math activities provide meaningful practice of those high priority skills necessary for number sense, operation sense, and number competency! Games, computational skill checks, and independent activities - all in fun formats that will attract and hold kids' interest! Includes activities for individuals and groups as well as a home-connection for each section, and an answer key in the back of the book!


Activities For A Differentiated Classroom Level 5

Author by : Wendy Conklin
Languange : en
Publisher by : Teacher Created Materials
Format Available : PDF, ePub, Mobi
Total Read : 92
Total Download : 896
File Size : 41,9 Mb
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Description : Easily implement grade appropriate lessons suitable for Grade 5 classrooms. Based on current research, these easy-to-use lessons are based on a variety of strategies to differentiate your instruction. Activities are included to allow access to all learners. Includes interactive whiteboard-compatible Resource CD with sample projects, templates, and assessment rubrics. 160pp. plus Teacher Resource CD.


Unpacking Fractions

Author by : Monica Neagoy
Languange : en
Publisher by : ASCD
Format Available : PDF, ePub, Mobi
Total Read : 49
Total Download : 422
File Size : 50,9 Mb
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Description : For years, the teaching and learning of fractions has been associated with rote memorization. But this mechanical approach to instruction—which strips students of an ability to reason or make sense of math—has resulted in a failure of understanding. Author Monica Neagoy, drawing on decades of research studies, evidence from teacher practice, and 25 years of experience working around the world with teachers, students, and parents, addresses seven big ideas in the teaching and learning of fractions in grades 2–6. Each idea is supported by a vignette from a real classroom, common misconceptions, a thorough unpacking of productive mathematical thinking, and several multistep and thought-provoking problems for teachers to explore. She offers three fundamental reasons why it’s imperative for us to take a closer look at how we teach fractions: 1. Fractions play a key role in students’ feelings about mathematics. 2. Fractions are fundamental to school math and daily life. 3. Fractions are foundational to success in algebra. While a solid grounding in algebra is necessary for a STEM career, the worthy goal of “algebra for all” will not be possible until “fractions for all” is a reality. Unpacking Fractions provides teachers with concrete strategies for achieving that reality—in short, helping all students gain the knowledge they need to feel at ease with fractions.


Mathsemantics

Author by : Edward MacNeal
Languange : en
Publisher by : Viking Adult
Format Available : PDF, ePub, Mobi
Total Read : 17
Total Download : 385
File Size : 51,9 Mb
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Description : An entertaining, anecdotal elucidation of math shows readers how numbers have inherent semantic content and attempts to cure readers of math blocks acquired in school. 20,000 first printing. $20,000 ad/promo.


Introduction To Number Theory

Author by : Mathew Crawford
Languange : en
Publisher by : Aops Incorporated
Format Available : PDF, ePub, Mobi
Total Read : 20
Total Download : 100
File Size : 51,6 Mb
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Description :


Supporting The Whole Child

Author by : Marge Scherer
Languange : en
Publisher by : ASCD
Format Available : PDF, ePub, Mobi
Total Read : 13
Total Download : 676
File Size : 52,5 Mb
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Description : This e-book, a collection of articles from Educational Leadership and other ASCD publications explores what it means to "support the whole child." In these articles, authors ponder the various meanings of support in the classroom, school, and community. This third in a four-book series exploring whole child education ends by emphasizing another maxim of good teaching: Hold high expectations for your students. Our authors agree: With the right supports, students are capable of doing more than even they think they can.


Making Sense Of Word Problems

Author by : Eric de Corte
Languange : en
Publisher by : CRC Press
Format Available : PDF, ePub, Mobi
Total Read : 76
Total Download : 339
File Size : 48,9 Mb
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Description : Word problems have been a staple of mathematics instruction for centuries, yet the rationale for their use has remained largely unexamined. A range of findings have shown how students consistently answer them in ways that fail to take account of the reality of the situations described. This monograph reports on studies carried out to investigate this "suspension of sense-making" in answering word problems. In Part One, a wide range of examples documenting the strength of the phenomenon is reviewed. Initial surprise at the findings was replaced by a conviction that the explanation lies in the culture of the mathematics classroom, specifically the rules implicitly governing the nature and interpretation of the word problem genre. This theoretical shift is reflected in Part Two. A detailed analysis of the way in which word problems are currently taught in typical mathematical classrooms is followed by reviews of design experiments illustrating how, by immersing students in a fundamentally changed learning environment, they can acquire what the authors consider to be more appropriate conceptions about, and strategies for doing, word problems. Part Three turns to a wider discussion of theoretical issues, a further analysis of the features of the educational system considered responsible for outcomes detrimental to many students' understanding and conception of mathematics, and suggestions for rethinking the role of word problems within the curriculum.