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 : 72
Total Download : 887
File Size : 47,7 Mb
pdf pdf

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 : 67
Total Download : 880
File Size : 46,8 Mb
pdf pdf

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 : 62
Total Download : 610
File Size : 45,9 Mb
pdf pdf

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.


Analysis Of Arithmetic For Mathematics Teaching

Author by : Gaea Leinhardt
Languange : en
Publisher by : Psychology Press
Format Available : PDF, ePub, Mobi
Total Read : 82
Total Download : 745
File Size : 52,9 Mb
pdf pdf

Description : This volume emerges from a partnership between the American Federation of Teachers and the Learning Research and Development Center at the University of Pittsburgh. The partnership brought together researchers and expert teachers for intensive dialogue sessions focusing on what each community knows about effective mathematical learning and instruction. The chapters deal with the research on, and conceptual analysis of, specific arithmetic topics (addition, subtraction, multiplication, division, decimals, and fractions) or with overarching themes that pervade the early curriculum and constitute the links with the more advanced topics of mathematics (intuition, number sense, and estimation). Serving as a link between the communities of cognitive researchers and mathematics educators, the book capitalizes on the recent research successes of cognitive science and reviews the literature of the math education community as well.


Mathsemantics

Author by : Edward MacNeal
Languange : en
Publisher by : Viking Adult
Format Available : PDF, ePub, Mobi
Total Read : 72
Total Download : 216
File Size : 42,8 Mb
pdf pdf

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.


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 : 16
Total Download : 277
File Size : 49,6 Mb
pdf pdf

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.


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 : 73
Total Download : 923
File Size : 51,6 Mb
pdf pdf

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!


Beads And Shoes Making Twos

Author by : Madeline Chang
Languange : en
Publisher by : Firsthand
Format Available : PDF, ePub, Mobi
Total Read : 45
Total Download : 556
File Size : 42,8 Mb
pdf pdf

Description : Beads and Shoes, Making Twos: Extending Number Sense is one of eight units in the Contexts for Learning Mathematics' Investigating Number Sense, Addition, and Subtraction (K - 3) This unit begins with the context of walking in line - two lines of children holding hands. The context encourages children to explore doubles while also strengthening their understanding of one-to-one correspondence. As the unit progresses, children explore containers that could hold doubles (such as egg cartons, English muffin packages, and juice boxes). Then the context shifts to an examination of pairs of shoes for varying numbers of people. As children investigate these situations, they explore both pairing and doubling - for instance, how six pairs of shoes can also be seen as six right shoes plus six left shoes (six sets of two or two sets of six). Later children work with larger numbers and the terminology of odds and evens is introduced. In the second week, the story Grandma's Necklaces is used to develop a context for several investigations related to patterns made with two colors. The first necklace (one blue/one green repeating) can only be made with an even number of objects, because the unit that repeats has two objects. The second necklace (five blue/five green repeating) and the third necklace (three blue/three green repeating) challenge children to see a group of objects doubled as the unit that repeats. Minilessons in the unit are crafted to support the automatizing of doubles and their use in solving near doubles - for example, using 6 + 6 to solve 6 + 7, or 10 + 10 to solve 9 + 10. Quick images and the arithmetic rack are both used with strings of related problems. The unit also includes the Shoe Game. This game can be played throughout the year for further support in developing the use of doubles as an addition strategy. To learn more visit http://www.contextsforlearning.com


Daily Routines To Jump Start Math Class Middle School

Author by : John J. SanGiovanni
Languange : en
Publisher by : Corwin Press
Format Available : PDF, ePub, Mobi
Total Read : 54
Total Download : 956
File Size : 47,5 Mb
pdf pdf

Description : Kickstart your middle school math class! Kickstart your class with 20 different routines, all of which include content examples, extensions, and variations for grades 6–8. Offering a year’s worth of daily instructional material that you can use each class period to promote student reasoning and number sense, this resource will help students Frequently revisit essential mathematical concepts Foster and shore up conceptual understanding Engage in mental mathematics, leading to efficiency and fluency Engage in mathematical discourse by constructing viable arguments and critiquing the reasoning of others Reason mathematically, which can improve performance on high-stakes assessments Move learning beyond “correctness” by valuing mistakes and discourse to encourage a growth mindset


Unpacking Fractions

Author by : Monica Neagoy
Languange : en
Publisher by : ASCD
Format Available : PDF, ePub, Mobi
Total Read : 98
Total Download : 745
File Size : 49,5 Mb
pdf pdf

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.