Constructing Number

Constructing Number

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  • Author: Anderson Norton
  • Publisher: Springer
  • ISBN: 3030004910
  • Category : Education
  • Languages : en
  • Pages : 377

The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.


Young Mathematicians at Work

Young Mathematicians at Work

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  • Author: Catherine Twomey Fosnot
  • Publisher: Heinemann Educational Books
  • ISBN:
  • Category : Education
  • Languages : en
  • Pages : 196

Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.


Making Number Talks Matter

Making Number Talks Matter

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  • Author: Cathy Humphreys
  • Publisher:
  • ISBN: 9781760016524
  • Category :
  • Languages : en
  • Pages : 196


Making Sense of Number

Making Sense of Number

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  • Author: Annette Hilton
  • Publisher: Cambridge University Press
  • ISBN: 1009007521
  • Category : Education
  • Languages : en
  • Pages : 215

Making Sense of Number is a concise introduction to personal and professional numeracy skills, helping readers to become more mathematically competent. It includes relevant content to assist pre-service teachers to improve numeracy for the classroom or to prepare for LANTITE, as well as support for practising teachers to develop their understanding and skills in numeracy. Making Sense of Number focuses on number sense as a conceptual framework for understanding mathematics, covering foundational areas of mathematics that often cause concern such as multiplication, fractions, ratio, rate and scale. The authors use real-world examples to explain mathematical concepts in an accessible and engaging way. Written by authors with over 30 years' experience teaching mathematics at primary, secondary and tertiary levels, Making Sense of Number is an essential guide for both pre-service teachers and those looking to improve their understanding of numeracy.


Number Fun

Number Fun

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  • Author: Isabel Thomas
  • Publisher: Raintree
  • ISBN: 1406282316
  • Category : Juvenile Nonfiction
  • Languages : en
  • Pages : 24

With this book, children can learn the numbers 1 to 20 while getting "e;in shape"e;! Each page shows children using their bodies to make the shape of numbers, alongside simple printed versions of each number. The book complements the similar Alphabet Fun title.


Making Transcendence Transparent

Making Transcendence Transparent

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  • Author: Edward B. Burger
  • Publisher: Springer Science & Business Media
  • ISBN: 1475741146
  • Category : Mathematics
  • Languages : en
  • Pages : 266

This is the first book that makes the difficult and important subject of transcendental number theory accessible to undergraduate mathematics students. Edward Burger is one of the authors of The Heart of Mathematics, winner of a 2001 Robert W. Hamilton Book Award. He will also be awarded the 2004 Chauvenet Prize, one of the most prestigious MAA prizes for outstanding exposition.


Digging Deeper

Digging Deeper

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  • Author: Ruth Parker
  • Publisher: Taylor & Francis
  • ISBN: 1003843212
  • Category : Education
  • Languages : en
  • Pages : 172

Making the transition to student-centered learning begins with finding ways to get students to share their thinking, something that can be particularly challenging for older learners. Authors Ruth Parker and Cathy Humphreys return with Digging Deeper: Making Number Talks Matter Even More, Grades 3-10, taking the readers into classrooms where their Number Talks routines are taught.In this comprehensive sequel to their best-selling book, Making Number Talks Matter, Parker and Humphreys apply their 15 minute lessons to older grade levels to inspire and initiate math talks. Through vignettes in the book, you'll meet other teachers learning how to listen closely to students and how to prompt them into figuring out solutions to problems. You will learn how to make on-the-spot decisions, continually advancing and deepening the conversation. Digging Deeper includes: Sample Problems: Digging Deeper is filled with a range of Number Talks problems, 10-15 minute warm-up routines that lend themselves to mental math and comparison of strategies Navigating Rough Spots: Learn how to create a safe environment for tricky, problematic, or challenging student discussions that can arise when talking through problems and sharing ideas Responding to Mistakes: Ways to handle misconceptions and mathematical errors that come up during the course of Number Talk conversations Digging Deeper is filled with teaching tips for using wait time between problems more efficiently, honoring student contributions while still correcting errors, and teaching concepts while nudging independent thinking. Through daily practice and open conversation, you can make Number Talks matter more.


Constructing Number

Constructing Number

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  • Author: Anderson Norton
  • Publisher: Springer
  • ISBN: 9783030004903
  • Category : Education
  • Languages : en
  • Pages : 0

The book synergizes research on number across two disciplines—mathematics education and psychology. The underlying problem the book addresses is how the brain constructs number. The opening chapter frames the problem in terms of children’s activity, including mental and physical actions. Subsequent chapters are organized into sections that address specific domains of number: natural numbers, fractions, and integers. Chapters within each section address ways that children build upon biological primitives (e.g., subitizing) and prior constructs (e.g., counting sequences) to construct number. The book relies on co-authored chapters and commentaries at the end of each section to create dialogue between junior faculty and senior researchers, as well as between psychologists and mathematics educators. The final chapter brings this work together around the framework of children’s activity and additional themes that arise in the collective work. The book is aimed to appeal to mathematics educators, mathematics teacher educators, mathematics education researchers, educational psychologists, cognitive psychologists, and developmental psychologists.


Young Mathematicians at Work

Young Mathematicians at Work

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  • Author: Catherine Twomey Fosnot
  • Publisher: Heinemann Educational Books
  • ISBN: 9780325003559
  • Category : Education
  • Languages : en
  • Pages : 0

Explains how children between the ages of four and eight construct a deep understanding of numbers and the operations of addition and subtraction.


Radical Uncertainty: Decision-Making Beyond the Numbers

Radical Uncertainty: Decision-Making Beyond the Numbers

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  • Author: John Kay
  • Publisher: W. W. Norton & Company
  • ISBN: 1324004789
  • Category : Business & Economics
  • Languages : en
  • Pages : 407

Much economic advice is bogus quantification, warn two leading experts in this essential book, now with a preface on COVID-19. Invented numbers offer a false sense of security; we need instead robust narratives that give us the confidence to manage uncertainty. “An elegant and careful guide to thinking about personal and social economics, especially in a time of uncertainty. The timing is impeccable." — Christine Kenneally, New York Times Book Review Some uncertainties are resolvable. The insurance industry’s actuarial tables and the gambler’s roulette wheel both yield to the tools of probability theory. Most situations in life, however, involve a deeper kind of uncertainty, a radical uncertainty for which historical data provide no useful guidance to future outcomes. Radical uncertainty concerns events whose determinants are insufficiently understood for probabilities to be known or forecasting possible. Before President Barack Obama made the fateful decision to send in the Navy Seals, his advisers offered him wildly divergent estimates of the odds that Osama bin Laden would be in the Abbottabad compound. In 2000, no one—not least Steve Jobs—knew what a smartphone was; how could anyone have predicted how many would be sold in 2020? And financial advisers who confidently provide the information required in the standard retirement planning package—what will interest rates, the cost of living, and your state of health be in 2050?—demonstrate only that their advice is worthless. The limits of certainty demonstrate the power of human judgment over artificial intelligence. In most critical decisions there can be no forecasts or probability distributions on which we might sensibly rely. Instead of inventing numbers to fill the gaps in our knowledge, we should adopt business, political, and personal strategies that will be robust to alternative futures and resilient to unpredictable events. Within the security of such a robust and resilient reference narrative, uncertainty can be embraced, because it is the source of creativity, excitement, and profit.