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Subgame Consistent Cooperation
by David W.K. Yeung Leon A. PetrosyanStrategic behavior in the human and social world has been increasingly recognized in theory and practice. It is well known that non-cooperative behavior could lead to suboptimal or even highly undesirable outcomes. Cooperation suggests the possibility of obtaining socially optimal solutions and the calls for cooperation are prevalent in real-life problems. Dynamic cooperation cannot be sustainable if there is no guarantee that the agreed upon optimality principle at the beginning is maintained throughout the cooperation duration. It is due to the lack of this kind of guarantees that cooperative schemes fail to last till its end or even fail to get started. The property of subgame consistency in cooperative dynamic games and the corresponding solution mechanism resolve this "classic" problem in game theory. This book is a comprehensive treatise on subgame consistent dynamic cooperation covering the up-to-date state of the art analyses in this important topic. It sets out to provide the theory, solution techniques and applications of subgame consistent cooperation in a wide spectrum of paradigms for analysis which includes cooperative dynamic game models with stochastic state dynamics, with uncertain future payoffs, with asynchronous players' horizons, with random cooperation duration, with control spaces switching and with transferable and nontransferable payoffs. The book would be a significant research reference text for researchers in game theory, economists, applied mathematicians, policy-makers, corporate decision-makers, and graduate students in applied mathematics, game theory, decision sciences, economics and management sciences.
Subtraction Facts that Stick: Help Your Child Master the Subtraction Facts for Good in Just Eight Weeks
by Corrin Brewer Debra Pearson Kate SnowThe fun, engaging program that will help your child master the subtraction facts once and for all—without spending hours and hours drilling flash cards! Subtraction Facts That Stick will guide you, step-by- step, as you teach your child to understand and memorize the subtraction facts, from 1 - 1 through 9 - 9. Hands-on activities, fun games your child will love, and simple practice pages help young students remember the subtraction facts for good. In 15 minutes per day (perfect for after school, or as a supplement to a homeschool math curriculum) your child will master the subtraction facts, gain a greater understanding of how math works, and develop greater confidence, in just six weeks! Mastery of the math facts is the foundation for all future math learning. Lay that foundation now, and make it solid, with Subtraction Facts That Stick!
Summary and Analysis of The Signal and the Noise: Based on the Book by Nate Silver (Smart Summaries)
by Worth BooksSo much to read, so little time? This brief overview of The Signal and the Noise tells you what you need to know—before or after you read Nate Silver&’s book. Crafted and edited with care, Worth Books set the standard for quality and give you the tools you need to be a well-informed reader. This short summary and analysis of The Signal and the Noise by Nate Silver includes: Historical contextChapter-by-chapter summariesImportant quotesFascinating triviaGlossary of termsSupporting material to enhance your understanding of the original work About The Signal and the Noise by Nate Silver: Drawing on groundbreaking research, The Signal and the Noise, written by the founder and editor-in-chief of FiveThirtyEight.com, examines how data has been used in prediction and forecasting, and how to find the true signals—the points that indicate that something will happen—amidst noisy and distracting data. Addressing different fields of forecasting and predictions—from politics to earthquakes to poker—Silver explores the reasons why some things are easier to forecast, like the weather, while others are so difficult, such as terrorism. From one of the country&’s smartest thinkers. The Signal and the Noise provides vital insights into how to think about probability and predictions on the economy, climate change, sports, and other subjects that impact our lives. The summary and analysis in this ebook are intended to complement your reading experience and bring you closer to a great work of nonfiction.
Summing It Up: From One Plus One to Modern Number Theory
by Avner Ash Robert GrossWe use addition on a daily basis--yet how many of us stop to truly consider the enormous and remarkable ramifications of this mathematical activity? Summing It Up uses addition as a springboard to present a fascinating and accessible look at numbers and number theory, and how we apply beautiful numerical properties to answer math problems. Mathematicians Avner Ash and Robert Gross explore addition's most basic characteristics as well as the addition of squares and other powers before moving onward to infinite series, modular forms, and issues at the forefront of current mathematical research. Ash and Gross tailor their succinct and engaging investigations for math enthusiasts of all backgrounds. Employing college algebra, the first part of the book examines such questions as, can all positive numbers be written as a sum of four perfect squares? The second section of the book incorporates calculus and examines infinite series--long sums that can only be defined by the concept of limit, as in the example of 1+1/2+1/4+. . .=? With the help of some group theory and geometry, the third section ties together the first two parts of the book through a discussion of modular forms--the analytic functions on the upper half-plane of the complex numbers that have growth and transformation properties. Ash and Gross show how modular forms are indispensable in modern number theory, for example in the proof of Fermat's Last Theorem.Appropriate for numbers novices as well as college math majors, Summing It Up delves into mathematics that will enlighten anyone fascinated by numbers.
The Super Age: Decoding Our Demographic Destiny
by Bradley SchurmanA demographic futurist explains the coming Super Age—when there will be more people older than sixty-five than those under the age of eighteen—and explores what it could mean for our collective future. Societies all over the world are getting older, the result of the fact that we are living longer and having fewer children. At some point in the near future, much of the developed world will have at least twenty percent of their national populations over the age of sixty-five. Bradley Schurman calls this the Super Age. Today, Italy, Japan, and Germany have already reached the Super Age, and another ten countries will have gone over the tipping point in 2021. Thirty-five countries will be part of this club by the end of the decade. This seismic shift in the world population can portend a period of tremendous growth—or leave swaths of us behind. Schurman explains how changing demographics will affect government and business and touch all of our lives. Fewer people working and paying income taxes, due to outdated employment and retirement practices, could mean less money feeding popular programs such as Social Security and Medicare—with greater numbers relying on them. The forced retirement or redundancy of older workers could impact business by creating a shortage of workers, which would likely drive wages up and result in inflation. Corporations, too, must rethink marketing strategies—older consumers are already purchasing the majority of new cars, and they are a growing and vitally important market for health technologies and housing. Architects and designers must re-create homes and communities that are more inclusive of people of all ages and abilities.If we aren’t prepared for the changes to come, Schurman warns, we face economic stagnation, increased isolation of at-risk populations, and accelerated decline of rural communities. Instead, we can plan now to harness the benefits of the Super Age: extended and healthier lives, more generational cooperation at work and home, and new markets and products to explore. The choice is ours to make.
Supermathematics and its Applications in Statistical Physics
by Franz WegnerThis text presents the mathematical concepts of Grassmannvariables and the method of supersymmetry to a broad audience of physicistsinterested in applying these tools to disordered and critical systems, as wellas related topics in statistical physics. Based on many courses and seminarsheld by the author, one of the pioneers in this field, the reader is given asystematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables ispresented in part I. The mathematics of these variables is applied to a randommatrix model, path integrals for fermions, dimer models and the Ising model intwo dimensions. Supermathematics - the use of commuting and anticommutingvariables on an equal footing - is the subject of part II. The properties ofsupervectors and supermatrices, which contain both commuting and Grassmanncomponents, are treated in great detail, including the derivation of integraltheorems. In part III, supersymmetric physical models are considered. Whilesupersymmetry was first introduced in elementary particle physics as exactsymmetry between bosons and fermions, the formal introduction of anticommutingspacetime components, can be extended to problems of statistical physics, and,since it connects states with equal energies, has also found its way intoquantum mechanics. Several models are considered in the applications, afterwhich the representation of the random matrix model by the nonlinearsigma-model, the determination of the density of states and the levelcorrelation are derived. Eventually, the mobility edge behavior is discussedand a short account of the ten symmetry classes of disorder, two-dimensionaldisordered models, and superbosonization is given.
Surfaces in Classical Geometries
by Gary R. Jensen Emilio Musso Lorenzo NicolodiDesigned for intermediate graduate studies, this text will broaden students' core knowledge of differential geometry providing foundational material to relevant topics in classical differential geometry. The method of moving frames, a natural means for discovering and proving important results, provides the basis of treatment for topics discussed. Its application in many areas helps to connect the various geometries and to uncover many deep relationships, such as the Lawson correspondence. The nearly 300 problems and exercises range from simple applications to open problems. Exercises are embedded in the text as essential parts of the exposition. Problems are collected at the end of each chapter; solutions to select problems are given at the end of the book. Mathematica®, Matlab(tm), and Xfig are used to illustrate selected concepts and results. The careful selection of results serves to show the reader how to prove the most important theorems in the subject, which may become the foundation of future progress. The book pursues significant results beyond the standard topics of an introductory differential geometry course. A sample of these results includes the Willmore functional, the classification of cyclides of Dupin, the Bonnet problem, constant mean curvature immersions, isothermic immersions, and the duality between minimal surfaces in Euclidean space and constant mean curvature surfaces in hyperbolic space. The book concludes with Lie sphere geometry and its spectacular result that all cyclides of Dupin are Lie sphere equivalent. The exposition is restricted to curves and surfaces in order to emphasize the geometric interpretation of invariants and other constructions. Working in low dimensions helps students develop a strong geometric intuition. Aspiring geometers will acquire a working knowledge of curves and surfaces in classical geometries. Students will learn the invariants of conformal geometry and how these relate to the invariants of Euclidean, spherical, and hyperbolic geometry. They will learn the fundamentals of Lie sphere geometry, which require the notion of Legendre immersions of a contact structure. Prerequisites include a completed one semester standard course on manifold theory.
Surveys in Differential-Algebraic Equations IV
by Timo Reis Achim IlchmannThe present volume comprises survey articles on various fields of Differential-Algebraic Equations (DAEs) which have widespread applications in controlled dynamical systems, especially in mechanical and electrical engineering and a strong relation to (ordinary) differential equations. The individual chapters provide reviews, presentations of the current state of research and new concepts in - History of DAEs - DAE modelling of mechanical multibody systems - Model reduction of DAEs - Observability for DAEs - Numerical Analysis for DAEs The results are presented in an accessible style, making this book suitable not only for active researchers but also for graduate students (with a good knowledge of the basic principles of DAEs) for self-study.
A Survival Guide to the Misinformation Age: Scientific Habits of Mind
by David HelfandWe live in the Information Age, with billions of bytes of data just two swipes away. Yet how much of this is mis- or even disinformation? A lot of it is, and your search engine can't tell the difference. As a result, an avalanche of misinformation threatens to overwhelm the discourse we so desperately need to address complex social problems such as climate change, the food and water crises, biodiversity collapse, and emerging threats to public health. This book provides an inoculation against the misinformation epidemic by cultivating scientific habits of mind. Anyone can do it—indeed, everyone must do it if our species is to survive on this crowded and finite planet.This survival guide supplies an essential set of apps for the prefrontal cortex while making science both accessible and entertaining. It will dissolve your fear of numbers, demystify graphs, and elucidate the key concepts of probability, all while celebrating the precise use of language and logic. David Helfand, one of our nation's leading astronomers and science educators, has taught scientific habits of mind to generations in the classroom, where he continues to wage a provocative battle against sloppy thinking and the encroachment of misinformation.
Swarm Intelligence Based Optimization
by Patrick Siarry Lhassane Idoumghar Julien LepagnotThis book constitutes the thoroughly refereed post-conference proceedings of the 1st International Conference on Swarm Intelligence Based Optimization, ICSIBO 2014, held in Mulhouse, France, in May 2014. The 20 full papers presented were carefully reviewed and selected from 48 submissions. Topics of interest presented and discussed in the conference focuses on the theoretical progress of swarm intelligence metaheuristics and their applications in areas such as: theoretical advances of swarm intelligence metaheuristics, combinatorial, discrete, binary, constrained, multi-objective, multi-modal, dynamic, noisy, and large-scale optimization, artificial immune systems, particle swarms, ant colony, bacterial foraging, artificial bees, fireflies algorithm, hybridization of algorithms, parallel/distributed computing, machine learning, data mining, data clustering, decision making and multi-agent systems based on swarm intelligence principles, adaptation and applications of swarm intelligence principles to real world problems in various domains.
Symmetries in Graphs, Maps, and Polytopes
by Jozef Širáň Robert JajcayThis volume contains seventeen of the best papers delivered at the SIGMAP Workshop 2014, representing the most recent advances in the field of symmetries of discrete objects and structures, with a particular emphasis on connections between maps, Riemann surfaces and dessins d'enfant. Providing the global community of researchers in the field with the opportunity to gather, converse and present their newest findings and advances, the Symmetries In Graphs, Maps, and Polytopes Workshop 2014 was the fifth in a series of workshops. The initial workshop, organized by Steve Wilson in Flagstaff, Arizona, in 1998, was followed in 2002 and 2006 by two meetings held in Aveiro, Portugal, organized by Antonio Breda d'Azevedo, and a fourth workshop held in Oaxaca, Mexico, organized by Isabel Hubard in 2010. This book should appeal to both specialists and those seeking a broad overview of what is happening in the area of symmetries of discrete objects and structures. iv>
Systems Biology
by Stefan Hohmann Sang Yup Lee Jens Nielsen J. Nielsen Gregory StephanopoulosComprehensive coverage of the many different aspects of systems biology, resulting in an excellent overview of the experimental and computational approaches currently in use to study biological systems. Each chapter represents a valuable introduction to one specific branch of systems biology, while also including the current state of the art and pointers to future directions. Following different methods for the integrative analysis of omics data, the book goes on to describe techniques that allow for the direct quantification of carbon fluxes in large metabolic networks, including the use of 13C labelled substrates and genome-scale metabolic models. The latter is explained on the basis of the model organism Escherichia coli as well as the human metabolism. Subsequently, the authors deal with the application of such techniques to human health and cell factory engineering, with a focus on recent progress in building genome-scale models and regulatory networks. They highlight the importance of such information for specific biological processes, including the ageing of cells, the immune system and organogenesis. The book concludes with a summary of recent advances in genome editing, which have allowed for precise genetic modifications, even with the dynamic control of gene expression. This is part of the Advances Biotechnology series, covering all pertinent aspects of the field with each volume prepared by eminent scientists who are experts on the topic in question.
Systems Dependability Assessment
by Nicolae Brinzei Jean-François Aubry Mohammed-Habib MazouniPresents recent developments of probabilistic assessment of systems dependability based on stochastic models, including graph theory, finite state automaton and language theory, for both dynamic and hybrid contexts.
Systems Medicine
by Ulf Schmitz Olaf WolkenhauerThis volume guides readers through the field of systems medicine by defining the terminology, and describing how established computational methods form bioinformatics and systems biology can be taken forward to an integrative systems medicine approach. Chapters provide an outlook on the role that systems medicine may or should play in various medical fields, and describe different facets of the systems medicine approach in action. Ultimately it introduces tools, resources and methodologies from bioinformatics and systems biology, and how to apply these in a systems medicine project. Written for the Methods in Molecular Biology series, chapters include introductions to their respective topics, and discuss experimental and computational approaches, methods, and tools that should be considered for a successful systems medicine project. Systems Medicine aims to motivate and provide guidance for collaborations across disciplines to tackle today's challenges related to human health and well-being.
Tableau Your Data!
by Daniel G. MurrayTransform your organization's data into actionable insights with Tableau Tableau is designed specifically to provide fast and easy visual analytics. The intuitive drag-and-drop interface helps you create interactive reports, dashboards, and visualizations, all without any special or advanced training. This all new edition of Tableau Your Data! is your Tableau companion, helping you get the most out of this invaluable business toolset.Tableau Your Data! shows you how to build dynamic, best of breed visualizations using the Tableau Software toolset. This comprehensive guide covers the core feature set for data analytics, and provides clear step-by-step guidance toward best practices and advanced techniques that go way beyond the user manual. You'll learn how Tableau is different from traditional business information analysis tools, and how to navigate your way around the Tableau 9.0 desktop before delving into functions and calculations, as well as sharing with the Tableau Server. Analyze data more effectively with Tableau Desktop Customize Tableau's settings for your organization's needs with detailed real-world examples on data security, scaling, syntax, and more Deploy visualizations to consumers throughout the enterprise - from sales to marketing, operations to finance, and beyond Understand Tableau functions and calculations and leverage Tableau across every link in the value chain Learn from actual working models of the book's visualizations and other web-based resources via a companion website Tableau helps you unlock the stories within the numbers, and Tableau Your Data! puts the software's full functionality right at your fingertips.
Taking Stock: Cultures of Enumeration in Contemporary Jewish Life
by Michal Kravel-Tovi Deborah Dash MooreTaking Stock is a collection of lively, original essays that explore the cultures of enumeration that permeate contemporary and modern Jewish life. Speaking to the profound cultural investment in quantified forms of knowledge and representation--whether discussing the Holocaust or counting the numbers of Israeli and American Jews--these essays reveal a social life of Jewish numbers. As they trace the uses of numerical frameworks, they portray how Jews define, negotiate, and enact matters of Jewish collectivity. The contributors offer productive perspectives into ubiquitous yet often overlooked aspects of the modern Jewish experience.
Tales from the Atlanta Braves Dugout: A Collection of the Greatest Braves Stories Ever Told (Tales from the Team)
by Cory McCartneyThe newest addition to the Tales from the Team series, Tales from the Atlanta Braves Dugout includes stories on the greatest players and coaches to don the Braves uniform. Author Cory McCartney includes stories about Hank Aaron, Dale Murphy, Phil Niekro, Chipper Jones, Andruw Jones, Greg Maddux, Tom Glavine, John Smoltz, Bobby Cox, and so many others.Recall the harrowing experience of Atlanta-Fulton County Stadium catching fire on July 21, 1993, overshadowing the debut of Fred McGriff, and read all about Sid Bream's slide and the worst-to-first season of 1991. From the run of 14 consecutive division titles and the 1995 World Series title, to Kent Mercker's 1994 no-hitter; from the arrival of the Baby Braves in Brian McCann, Jeff Francoeur, and others, to the 2014 Hall of Fame-induction of Tom Glavine, Greg Maddux, and Bobby Cox, the on and off-the-field stories are all here.This is the perfect addition to a Braves fan’s shelf!Skyhorse Publishing, as well as our Sports Publishing imprint, are proud to publish a broad range of books for readers interested in sports-books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.Whether you are a New York Yankees fan or hail from Red Sox nation; whether you are a die-hard Green Bay Packers or Dallas Cowboys fan; whether you root for the Kentucky Wildcats, Louisville Cardinals, UCLA Bruins, or Kansas Jayhawks; whether you route for the Boston Bruins, Toronto Maple Leafs, Montreal Canadiens, or Los Angeles Kings; we have a book for you. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Tales from the Baltimore Orioles Dugout: A Collection of the Greatest Orioles Stories Ever Told (Tales from the Team)
by Louis BerneyFor several decades, the Baltimore Orioles were the envy of every Major League Baseball team. Stars like Rick Dempsey and Cal Ripken, Jr. brought life and power to a team full of dedication and fun. Since 2012, the team has regained momentum under Buck Showalter, boasting winning seasons and clinching their division title for the 2014 playoffs. Now fans of this indomitable team can walk into the glory of Camden Yards and onto the field with Louis Berney’s newly revised edition of Tales from the Baltimore Orioles Dugout. Berney provides countless stories of players, filling the pages with both memorable moments on the field and silly anecdotes from in the clubhouse or on the road. Individually, these stories are funny, poignant, and eccentric. Collectively, they offer a portrait of a team that is as much a family and a community treasure as it is a professional sports organization. Tales from the Baltimore Orioles Dugout is truly a must-have for any Orioles fan.Skyhorse Publishing, as well as our Sports Publishing imprint, are proud to publish a broad range of books for readers interested in sports-books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.Whether you are a New York Yankees fan or hail from Red Sox nation; whether you are a die-hard Green Bay Packers or Dallas Cowboys fan; whether you root for the Kentucky Wildcats, Louisville Cardinals, UCLA Bruins, or Kansas Jayhawks; whether you route for the Boston Bruins, Toronto Maple Leafs, Montreal Canadiens, or Los Angeles Kings; we have a book for you. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Tales from the Detroit Tigers Dugout: A Collection of the Greatest Tigers Stories Ever Told (Tales from the Team)
by Jack Ebling Richard KincaideThe Detroit Tigers Old English "D” is one of the most recognized symbols in sports. A team rich with legends and history, the Tigers have endured in the hearts of fans and continue to up the ante of competition against rivals like the Cleveland Indians and Chicago White Sox. The Tigers have been a constant presence in the MLB playoffs for the last four years. Three of those years resulted in ALCS appearances, and in 2012 the Tigers captured the ALCS title that sent them to another exciting World Series.Now fans of this indomitable franchise can relive the passion and excitement that has come to define the Tigers in this newly updated edition of Tales from the Detroit Tigers Dugout. Veteran sportswriter Jack Ebling brings to life a vision of what drives the Detroit Tigers franchise. Ebling highlights baseball stars, managers, and games that have come to define the Tigers over the years. Readers will experience the excitement of four World Championships, five other World Series appearances, and so much more.Skyhorse Publishing, as well as our Sports Publishing imprint, are proud to publish a broad range of books for readers interested in sports-books about baseball, pro football, college football, pro and college basketball, hockey, or soccer, we have a book about your sport or your team.Whether you are a New York Yankees fan or hail from Red Sox nation; whether you are a die-hard Green Bay Packers or Dallas Cowboys fan; whether you root for the Kentucky Wildcats, Louisville Cardinals, UCLA Bruins, or Kansas Jayhawks; whether you route for the Boston Bruins, Toronto Maple Leafs, Montreal Canadiens, or Los Angeles Kings; we have a book for you. While not every title we publish becomes a New York Times bestseller or a national bestseller, we are committed to publishing books on subjects that are sometimes overlooked by other publishers and to authors whose work might not otherwise find a home.
Taylor Coefficients and Coefficient Multipliers of Hardy and Bergman-Type Spaces
by Miroljub Jevtić Dragan Vukotić Miloš ArsenovićThis book provides a systematic overview of the theory of Taylor coefficients of functions in some classical spaces of analytic functions and especially of the coefficient multipliers between spaces of Hardy type. Offering a comprehensive reference guide to the subject, it is the first of its kind in this area. After several introductory chapters covering the basic material, a large variety of results obtained over the past 80 years, including the most recent ones, are treated in detail. Several chapters end with discussions of practical applications and related topics that graduate students and experts in other subjects may find useful for their own purposes. Thus, a further aim of the book is to communicate to non-specialists some concrete facts that may be of value in their own work. The book can also be used as a textbook or a supplementary reference for an advanced graduate course. It is primarily intended for specialists in complex and functional analysis, graduate students, and experts in other related fields.
Teaching and Learning About Whole Numbers in Primary School
by Terezinha Nunes Beatriz Vargas Dorneles Pi-Jen Lin Elisabeth Rathgeb-SchniererThis book offers a theory for the analysis of how children learn and are taught about whole numbers. Two meanings of numbers are distinguished - the analytical meaning, defined by the number system, and the representational meaning, identified by the use of numbers as conventional signs that stand for quantities. This framework makes it possible to compare different approaches to making numbers meaningful in the classroom and contrast the outcomes of these diverse aspects of teaching. The book identifies themes and trends in empirical research on the teaching and learning of whole numbers since the launch of the major journals in mathematics education research in the 1970s. It documents a shift in focus in the teaching of arithmetic from research about teaching written algorithms to teaching arithmetic in ways that result in flexible approaches to calculation. The analysis of studies on quantitative reasoning reveals classifications of problem types that are related to different cognitive demands and rates of success in both additive and multiplicative reasoning. Three different approaches to quantitative reasoning education illustrate current thinking on teaching problem solving: teaching reasoning before arithmetic, schema-based instruction, and the use of pre-designed diagrams. The book also includes a summary of contemporary approaches to the description of the knowledge of numbers and arithmetic that teachers need to be effective teachers of these aspects of mathematics in primary school. The concluding section includes a brief summary of the major themes addressed and the challenges for the future. The new theoretical framework presented offers researchers in mathematics education novel insights into the differences between empirical studies in this domain. At the same time the description of the two meanings of numbers helps teachers distinguish between the different aims of teaching about numbers supported by diverse methods used in primary school. The framework is a valuable tool for comparing the different methods and identifying the various assumptions about teaching and learning.
Teaching and Learning of Calculus
by David Bressoud Imène Ghedamsi Victor Martinez-Luaces Günter TörnerThis survey focuses on the main trends in the field of calculus education. Despite their variety, the findings reveal a cornerstone issue that is strongly linked to the formalism of calculus concepts and to the difficulties it generates in the learning and teaching process. As a complement to the main text, an extended bibliography with some of the most important references on this topic is included. Since the diversity of the research in the field makes it difficult to produce an exhaustive state-of-the-art summary, the authors discuss recent developments that go beyond this survey and put forward new research questions.
The Teaching and Learning of Statistics
by Dani Ben-Zvi Katie MakarThis book presents the breadth and diversity of empirical and practical work done on statistics education around the world. A wide range of methods are used to respond to the research questions that form it's base. Case studies of single students or teachers aimed at understanding reasoning processes, large-scale experimental studies attempting to generalize trends in the teaching and learning of statistics are both employed. Various epistemological stances are described and utilized. The teaching and learning of statistics is presented in multiple contexts in the book. These include designed settings for young children, students in formal schooling, tertiary level students, vocational schools, and teacher professional development. A diversity is evident also in the choices of what to teach (curriculum), when to teach (learning trajectory), how to teach (pedagogy), how to demonstrate evidence of learning (assessment) and what challenges teachers and students face when they solve statistical problems (reasoning and thinking).
Teaching Elementary Mathematics to Struggling Learners
by Bradley S. Witzel Mary E. LittlePacked with effective instructional strategies, this book explores why certain K-5 students struggle with math and provides a framework for helping these learners succeed. The authors present empirically validated practices for supporting students with disabilities and others experiencing difficulties in specific areas of math, including problem solving, early numeracy, whole-number operations, fractions, geometry, and algebra. Concrete examples, easy-to-implement lesson-planning ideas, and connections to state standards, in particular the Common Core standards, enhance the book's utility. Also provided is invaluable guidance on planning and delivering multi-tiered instruction and intervention.
Teaching for Mathematical Understanding: Practical ideas for outstanding primary lessons
by Tony CottonTeaching for Mathematical Understanding develops the subject knowledge support and practical ideas from Tony Cotton's Understanding and Teaching Primary Mathematics into resources for full lessons. With an emphasis on developing outstanding lessons using a problem-solving approach, this highly practical guide is packed with activities that all trainee and practising teachers can use in the primary classroom. Covering each area of mathematics, every activity offers helpful step-by-step guidance, including teaching and learning objectives; resources; lesson outlines; ideas for differentiation; assessment for learning and key probing questions. Also featured in this text are call-outs to the information contained in the book's companion website, a shared site with a range of relevant resources to support and consolidate your learning. Teaching for Mathematical Understanding is an essential text for all trainee and practising teachers looking for inspiration and guidance towards outstanding mathematics teaching. Companion website features include: Video clips in which primary school teachers demonstrate concepts covered in the book through teaching to a real class PowerPoint presentations which provide support for those using the book as part of a teacher training course updated weblinks to external sites with useful teaching information and resources.