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How Children Learn Math: The Science of Math Learning in Research and Practice
by Nancy Krasa Karen Tzanetopoulos Colleen MaasWritten for pre-service and in-service educators of children in preschool through grade five, this book connects research in cognitive development and math education to offer an accessibly written and practical introduction to the science of elementary math learning. Structured according to children’s mathematical development, How Children Learn Math systematically reviews and synthesizes the latest developmental research on mathematical cognition into accessible sections that explain both the scientific evidence available and its practical classroom application. Written by an author team with decades of collective experience in cognitive learning research, clinical learning evaluations, and classroom experience working with both teachers and children, this amply illustrated text offers a powerful resource for understanding children’s mathematical development, from quantitative intuition to word problems, and helps readers understand and identify math learning difficulties that may emerge in later grades. Aimed at pre-service and in-service teachers and educators with little background in cognitive development, the book distills important findings in cognitive development into clear, accessible language and practical suggestions. The book therefore serves as an ideal text for pre-service early childhood, elementary, and special education teachers, as well as early career researchers, or as a professional development resource for in-service teachers, supervisors and administrators, school psychologists, homeschool parents, and other educators.
How Contagion Works: Science, Awareness and Community in Times of Global Crises - The short essay that helped change the Covid-19 debate
by Paolo Giordano'Lucid, calm, informed, directly helpful in trying to think about where we are now... The literature of the time after begins here' Evening Standard'Taking a breather from bewildering statistics and terrible tales of contagion to read Giordano's book was a jolt of brevity and simplicity... It takes concepts that have been dancing away in our minds, just out of reach, and lines them up neatly' The Times'Potent and original' Sunday Times'In one short hour, in the midst of this difficult moment, Giordano reinforced my sense of hope in humanity, in the one and the many' Philippe Sands, author of East West Street and The Rat LineThe Covid-19 pandemic is the most significant health emergency of our time.Writing from Italy in lockdown, physicist and novelist Paolo Giordano explains how disease spreads in our interconnected world: why it mattershow it impacts ushow we must reactExpanding his focus to include other forms of contagion - from the environmental crisis to fake news and xenophobia - Giordano shows us not just how the coronavirus crisis got so bad so quickly, but also how we can work together to create change.Paolo Giordano is a physicist and the author of four bestselling novels. His article 'The Mathematics of Contagion' - published in Italy at the beginning of the coronavirus emergency - was shared more than 4 million times and helped shift public opinion in the early stages of the epidemic.
How Data Can Manage Global Health Pandemics: Analyzing and Understanding COVID-19 (HIMSS Book Series)
by Rupa Mahanti"This book bridges the fields of health care and data to clarify how to use data to manage pandemics. Written while COVID-19 was raging, it identifies both effective practices and misfires, and is grounded in clear, research-based explanations of pandemics and data strategy….The author has written an essential book for students and professionals in both health care and data. While serving the needs of academics and experts, the book is accessible for the general reader." – Eileen Forrester, CEO of Forrester Leadership Group, Author of CMMI for Services, Guidelines for Superior Service "…Rupa Mahanti explores the connections between data and the human response to the spread of disease in her new book,... She recognizes the value of data and the kind of insight it can bring, while at the same time recognizing that using data to solve problems requires not just technology, but also leadership and courage. This is a book for people who want to better understand the role of data and people in solving human problems." -- Laura Sebastian-Coleman, Author of Meeting the Challenges of Data Quality Management In contrast to the 1918 Spanish flu pandemic which occurred in a non-digital age, the timing of the COVID-19 pandemic intersects with the digital age, characterized by the collection of large amounts of data and sophisticated technologies. Data and technology are being used to combat this digital age pandemic in ways that were not possible in the pre-digital age. Given the adverse impacts of pandemics in general and the COVID-19 pandemic in particular, it is imperative that people understand the meaning, origin of pandemics, related terms, trajectory of a new disease, butterfly effect of contagious diseases, factors governing the pandemic potential of a disease, strategies to combat a pandemic, role of data, data sharing, data strategy, data governance, analytics, and data visualization in managing pandemics, pandemic myths, critical success factors in managing pandemics, and lessons learned. How Data Can Manage Global Health Pandemics: Analyzing and Understanding COVID-19 discusses these elements with special reference to COVID-19. Dr. Rupa Mahanti is a business and data consultant and has expertise in different data management disciplines, business process improvement, regulatory reporting, quality management, and more. She is the author of Data Quality (ASQ Quality Press) and the series Data Governance: The Way Forward (Springer).
How Data Quality Affects our Understanding of the Earnings Distribution
by Reza Che DanielsThis open access book demonstrates how data quality issues affect all surveys and proposes methods that can be utilised to deal with the observable components of survey error in a statistically sound manner. This book begins by profiling the post-Apartheid period in South Africa's history when the sampling frame and survey methodology for household surveys was undergoing periodic changes due to the changing geopolitical landscape in the country. This book profiles how different components of error had disproportionate magnitudes in different survey years, including coverage error, sampling error, nonresponse error, measurement error, processing error and adjustment error. The parameters of interest concern the earnings distribution, but despite this outcome of interest, the discussion is generalizable to any question in a random sample survey of households or firms. This book then investigates questionnaire design and item nonresponse by building a response propensity model for the employee income question in two South African labour market surveys: the October Household Survey (OHS, 1997-1999) and the Labour Force Survey (LFS, 2000-2003). This time period isolates a period of changing questionnaire design for the income question. Finally, this book is concerned with how to employee income data with a mixture of continuous data, bounded response data and nonresponse. A variable with this mixture of data types is called coarse data. Because the income question consists of two parts -- an initial, exact income question and a bounded income follow-up question -- the resulting statistical distribution of employee income is both continuous and discrete. The book shows researchers how to appropriately deal with coarse income data using multiple imputation. The take-home message from this book is that researchers have a responsibility to treat data quality concerns in a statistically sound manner, rather than making adjustments to public-use data in arbitrary ways, often underpinned by undefensible assumptions about an implicit unobservable loss function in the data. The demonstration of how this can be done provides a replicable concept map with applicable methods that can be utilised in any sample survey.
How Did You Count?: Picture Book
by Christopher DanielsonFrom the author of the award-winning Which One Doesn’t Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson’s collection that is sure to spark conversation, questioning and wondering amongst both younger and older students alike.This listing is for a hard cover copy of the children's picture book.
How Did You Count?: Teacher's Guide
by Christopher Danielson“I hope that this Teacher’s Guide supports your own inquiry into children’s mathematics, and I hope that the images elicit brilliance from the children you do math with—wherever you and they may count.”From the author of the award-winning Which One Doesn’t Belong? and How Many? comes How Did You Count?, the latest title in Christopher Danielson’s collection that is sure to spark conversation, questioning, and wondering amongst both younger and older students alike.In this innovative Teacher’s Guide, Danielson gives you the tools you need to both begin and dig deeper into the How Did You Count? routine. In clear, accessible language, Danielson discusses the mathematical ideas likely to emerge on each page of the How Did You Count? picture book and helps you anticipate and understand your students’ likely answers. Through classroom stories, he models listening to, talking about, and delighting in students’ ideas around counting, numbers, and operations.Reading this Teacher’s Guide alongside your copy of the How Did You Count? children’s picture book will help you and your students discover together how the beauty of counting and numerical relationships and structure extends far beyond 1, 2, 3.Note: This Teacher's Guide is currently available as part of the Teacher's Guide and How Did You Count? picture book bundle.
How Do Dinosaurs Count to Ten?
by Jane Yolen Mark TeagueCome along for some BIG fun as your favorite dinosaurs delight young readers with their playful antics. How do dinosaurs count to ten? Over and over and over again! Image descriptions present
How Do You Spend? A Moneybunny Book (A Moneybunny Book)
by Cinders McLeodCelebrate the many different ways a little bunny can spend her savings, and learn about opposites too!Bun has been saving her carrots, and now it&’s time to spend some—but HOW will she spend them? Well, she could spend fast and buy a lot of things all at once, or she could take her time and spend slowly on something unique. She could buy something ordinary like a toothbrush, or something exciting like a mini sports car. Then there are things to buy for herself and things to buy for others, as well as things she needs and some that she wants. There are so many options, and little bunnies will have a ball considering them all!
How Energy Considerations Have Shaped Our Fundamental Modern Theories of Physics: Theory and Key Historical Moments
by E. B. ManoukianAt long last, with sufficient technical details, emphasizing key historical moments, a book that develops all of fundamental modern theoretical physics from energy considerations in a compact form. Starting with a few electron-volts of atoms in the quantum world at low energies extending up to quantum gravity and beyond to the birth of the Universe, readers will experience the entire spectrum of fundamental modern theoretical physics, with one theory leading to another in an integrated unified manner. Energy considerations lead to the development of special and general relativity, quantum field theory, renormalization theory, modern quantum electrodynamics, electro-weak theory, the standard model of particle physics, grand unified theories, string theory, the current standard model of inflationary big bang theory, and even to the birth of the Higgs field, and in developments of quantum gravity. Unfortunately, due to strong specialization within theirfields, students and many practicing physicists are exposed only to parts of the beautiful story of modern fundamental physics. Here the entire story is told! This is a must-read book for graduate students, advanced undergraduate students, instructors and professionals who are interested in all aspects of fundamental modern theoretical physics and key historical moments in its development.
How Far It Is to Tomorrow...: Reflections of an Eminent Russian Applied Mathematician 1917-2000
by Nikita N. MoiseevThis is a translated autobiography of applied mathematician N. N. Moiseev, providing an insider’s view of the history of the Soviet Union from its founding in 1917 to its collapse in 1991, as well as a little of the aftermath.We see vividly the precariousness of life just after the October Revolution; his happy family life during the years 1921-28 of Lenin’s New Economic Policy; the subsequent destruction of his family by Stalin’s regime; his trials as a social outcast; his student days at Moscow State University; his experiences as a Soviet Air Force Engineer in World War II, including sorties as a gunner and a brush with an NKVD agent; post-war euphoria, marriage, and another round of ostracism; and then the vicissitudes of a highly varied academic career. Here we meet many famous Soviet and Western engineers and scientists. The last several chapters are devoted more to wide-ranging reflections on God, philosophy, science, communism, modelling the biosphere, and the threat of nuclear winter. His thoughts concerning the impending and then final collapse of the USSR, as well as hopes for Russia’s future, conclude the journey through Moiseev's life.
How Groups Grow--
by Avinoam MannGrowth of groups is an innovative new branch of group theory. This is the first book to introduce the subject from scratch. It begins with basic definitions and culminates in the seminal results of Gromov and Grigorchuk and more. The proof of Gromov's theorem on groups of polynomial growth is given in full, with the theory of asymptotic cones developed on the way. Grigorchuk's first and general groups are described, as well as the proof that they have intermediate growth, with explicit bounds, and their relationship to automorphisms of regular trees and finite automata. Also discussed are generating functions, groups of polynomial growth of low degrees, infinitely generated groups of local polynomial growth, the relation of intermediate growth to amenability and residual finiteness, and conjugacy class growth. This book is valuable reading for researchers, from graduate students onward, working in contemporary group theory.
How Humans Learn to Think Mathematically
by David TallHow Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
How James Watt Invented the Copier
by René SchilsFeatures 25 different scientists and the ideas which may not have made them famous, but made history...Typically, we remember our greatest scientists from one single invention, one new formula or one incredible breakthrough. This narrow perspective does not give justice to the versatility of many scientists who also earned a reputation in other areas of science. James Watt, for instance, is known for inventing the steam engine, yet most people do not know that he also invented the copier. Alexander Graham Bell of course invented the telephone, but only few know that he invented artificial breathing equipment, a prototype of the 'iron lung'. Edmond Halley, whose name is associated with the comet that visits Earth every 75 years, produced the first mortality tables, used for life insurances. This entertaining book is aimed at anyone who enjoys reading about inventions and discoveries by the most creative minds. Detailed illustrations of the forgotten designs and ideas enrich the work throughout.
How Labor Powers the Global Economy: A Labor Theory of Capitalism (New Economic Windows)
by Moshé Machover Emmanuel D. Farjoun David ZachariahThis book presents a probabilistic approach to studying the fundamental role of labor in capitalist economies and develops a non-deterministic theoretical framework for the foundations of political economy. By applying the framework to real-world data, the authors offer new insights into the dynamics of growth, wages, and accumulation in capitalist development around the globe. The book demonstrates that a probabilistic political economy based on labor inputs enables us to describe central organizing principles in modern capitalism. Starting from a few basic assumptions, it shows that the working time of employees is the main regulating variable for determining strict numerical limits on the rate of economic growth, the range of wages, and the pace of accumulation under the present global economic system. This book will appeal to anyone interested in how the capitalist mode of production works and its inherent limitations; in particular, it will be useful to scholars and students of Marxian economics.“Emmanuel Farjoun and Moshé Machover, follow up their pathbreaking work on the application of statistical physics methods to political economy in this book with David Zachariah, in which they develop methods for making educated and structured estimates of stylized facts applicable to capitalist economies. There’s a lot for economists and anyone interested in the political economy of capitalism to learn from their reasoning on these issues, including their novel and challenging suggestion of bounds on the rates of increase of use-value productivity of labor, and on the range of variation of the wage share.”Duncan K. Foley, Leo Model Professor of Economics, New School for Social Research
How Likely is it? Understanding Probability
by Glenda Lappan James T. Fey William M. Fitzgerald Susan N. Friel Elizabeth Difanis PhillipsNIMAC-sourced textbook
How Many Dolphins In a Pod?: Counting By 10's (Nature Numbers)
by Ruth MusgraveIn Nature Numbers, math is beautiful, recognizable, and all around us! Highly engaging pictures of animals and nature scenes, along with cool chalk illustrations, are used to introduce basic math concepts and encourage kids to see a world of numbers all around them.K-2 math concepts include power of 10. This book encourages kids to learn about multiples of 10 as schools of fish swim by and coral polyps build reefs, all with amazing nature pictures and chalk illustrations!
How Many Fish? (I Can Read! #My First Shared Reading)
by Caron Lee CohenA story of six fish and six feet interact underneath the water. When one fish gets lost under a bucket, the feet unknowingly saves the fish.
How Many Licks?: Or, How to Estimate Damn Near Anything
by Aaron SantosHow many licks to the center of a Tootsie Pop? How many people are having sex at this moment? How long would it take a monkey on a typewriter to produce the plays of Shakespeare? For all those questions that keep you up at night, here's the way to answer them. And the beauty of it is that it's all approximate!Using Enrico Fermi's theory of approximation, Santos brings the world of numbers into perspective. For puzzle junkies and trivia fanatics, these 70 word puzzles will show the reader how to take a bit of information, add what they already know, and extrapolate an answer.Santos has done the impossible: make math and the multiple possibilities of numbers fun and informative. Can you really cry a river? Is it possible to dig your way out of jail with just a teaspoon and before your life sentence is up?Taking an academic subject and using it as the prism to view everyday off-the-wall questions as math problems to be solved is a natural step for the lovers of sudoku, cryptograms, word puzzles, and other thought-provoking games.
How Many Penguins?: Counting Animals 0-100 (Nature Numbers)
by Jill EsbaumIn Nature Numbers, math is beautiful, recognizable, and all around us! Highly engaging pictures of animals and nature scenes, along with cool chalk illustrations, are used to introduce basic math concepts and encourage kids to see a world of numbers all around them.K-2 math concepts include counting 1-100. This book encourages kids to count groups of 10 animals with amazing nature pictures and chalk illustrations!
How Many Pennies Make A Dollar?
by Rebecca Wingard-NelsonHow many pennies are in a dollar? How many nickels make a dime? In this great book of money combinations, young readers can learn how all of the different denominations of money relate to each other. Free worksheets along with full-color photos and easy-to-read text make this a great way to reinforce math concepts.
How Many Seeds in a Pumpkin?
by Margaret Mcnamara"How many seeds in a pumpkin?" Mr. Tiffin asks his class as they gather around the big, medium, and small pumpkins on his desk. Robert, the biggest kid, guesses that the largest one has a million seeds; Elinor, sounding like she knows what she's talking about, guesses the medium one has 500 seeds; and Anna, who likes even numbers better than odd ones, guesses that the little one has 22. Charlie, the smallest boy in the class, doesn't have a guess. Counting pumpkin seeds is messy business, but once the slimy job is done, to everyone's surprise, the smallest pumpkin has the most seeds! As Charlie happily exclaims, "Small things have a lot going on inside of them."
How Many Zeroes?: Counting Solutions of Systems of Polynomials via Toric Geometry at Infinity (CMS/CAIMS Books in Mathematics #2)
by Pinaki MondalThis graduate textbook presents an approach through toric geometry to the problem of estimating the isolated solutions (counted with appropriate multiplicity) of n polynomial equations in n variables over an algebraically closed field. The text collects and synthesizes a number of works on Bernstein’s theorem of counting solutions of generic systems, ultimately presenting the theorem, commentary, and extensions in a comprehensive and coherent manner. It begins with Bernstein’s original theorem expressing solutions of generic systems in terms of the mixed volume of their Newton polytopes, including complete proofs of its recent extension to affine space and some applications to open problems. The text also applies the developed techniques to derive and generalize Kushnirenko's results on Milnor numbers of hypersurface singularities, which has served as a precursor to the development of toric geometry. Ultimately, the book aims to present material in an elementary format, developing all necessary algebraic geometry to provide a truly accessible overview suitable to second-year graduate students.
How Many? (Talking Math Ser.)
by Christopher DanielsonTalking math with your child is fun and easy with this better approach to counting!Written by a math educator, this innovative book encourages critical thinking and sparks memorable mathematical conversations. You and your child decide what to count on each page. You have many choices, and the longer you look, the more possibilities you'll notice. There are no wrong answers in this book. As long as you're talking about what you see, think, and wonder, you're talking math!
How Math Explains the World: A Guide to the Power of Numbers, from Car Repair to Modern Physics
by James D. Stein&“Explores the application of math to problem solving in the everyday. . . . [W]ill appeal to both casual and serious fans of math or physics.&” —Publishers Weekly In How Math Explains the World, mathematician Stein reveals how seemingly arcane mathematical investigations and discoveries have led to bigger, more world-shaking insights into the nature of our world. In the four main sections of the book, Stein tells the stories of the mathematical thinkers who discerned some of the most fundamental aspects of our universe. From their successes and failures, delusions, and even duels, the trajectories of their innovations—and their impact on society—are traced in this fascinating narrative. Quantum mechanics, space-time, chaos theory and the workings of complex systems, and the impossibility of a &“perfect&” democracy are all here. Stein's book is both mind-bending and practical, as he explains the best way for a salesman to plan a trip, examines why any thought you could have is imbedded in the number p, and—perhaps most importantly—answers one of the modern world's toughest questions: why the garage can never get your car repaired on time. Friendly, entertaining, and fun, How Math Explains the World is the first book by one of California's most popular math teachers, a veteran of both &“math for poets&” and Princeton's Institute for Advanced Studies. And it's perfect for any reader wanting to know how math makes both science and the world tick.
How Mathematicians Think: Using Ambiguity, Contradiction, and Paradox to Create Mathematics
by William ByersTo many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results. Nonlogical qualities, William Byers shows, play an essential role in mathematics. Ambiguities, contradictions, and paradoxes can arise when ideas developed in different contexts come into contact. Uncertainties and conflicts do not impede but rather spur the development of mathematics. Creativity often means bringing apparently incompatible perspectives together as complementary aspects of a new, more subtle theory. The secret of mathematics is not to be found only in its logical structure. The creative dimensions of mathematical work have great implications for our notions of mathematical and scientific truth, and How Mathematicians Think provides a novel approach to many fundamental questions. Is mathematics objectively true? Is it discovered or invented? And is there such a thing as a "final" scientific theory? Ultimately, How Mathematicians Think shows that the nature of mathematical thinking can teach us a great deal about the human condition itself.