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Fibonacci and Lucas Numbers with Applications, Volume 1
by Thomas KoshyPraise for the First Edition “ …beautiful and well worth the reading … with many exercises and a good bibliography, this book will fascinate both students and teachers.” Mathematics Teacher Fibonacci and Lucas Numbers with Applications, Volume I, Second Edition provides a user-friendly and historical approach to the many fascinating properties of Fibonacci and Lucas numbers, which have intrigued amateurs and professionals for centuries. Offering an in-depth study of the topic, this book includes exciting applications that provide many opportunities to explore and experiment. In addition, the book includes a historical survey of the development of Fibonacci and Lucas numbers, with biographical sketches of important figures in the field. Each chapter features a wealth of examples, as well as numeric and theoretical exercises that avoid using extensive and time-consuming proofs of theorems. The Second Edition offers new opportunities to illustrate and expand on various problem-solving skills and techniques. In addition, the book features: • A clear, comprehensive introduction to one of the most fascinating topics in mathematics, including links to graph theory, matrices, geometry, the stock market, and the Golden Ratio • Abundant examples, exercises, and properties throughout, with a wide range of difficulty and sophistication • Numeric puzzles based on Fibonacci numbers, as well as popular geometric paradoxes, and a glossary of symbols and fundamental properties from the theory of numbers • A wide range of applications in many disciplines, including architecture, biology, chemistry, electrical engineering, physics, physiology, and neurophysiology The Second Edition is appropriate for upper-undergraduate and graduate-level courses on the history of mathematics, combinatorics, and number theory. The book is also a valuable resource for undergraduate research courses, independent study projects, and senior/graduate theses, as well as a useful resource for computer scientists, physicists, biologists, and electrical engineers. Thomas Koshy, PhD, is Professor Emeritus of Mathematics at Framingham State University in Massachusetts and author of several books and numerous articles on mathematics. His work has been recognized by the Association of American Publishers, and he has received many awards, including the Distinguished Faculty of the Year. Dr. Koshy received his PhD in Algebraic Coding Theory from Boston University. “Anyone who loves mathematical puzzles, number theory, and Fibonacci numbers will treasure this book. Dr. Koshy has compiled Fibonacci lore from diverse sources into one understandable and intriguing volume, [interweaving] a historical flavor into an array of applications.” Marjorie Bicknell-Johnson
Fibonacci Numbers (Dover Books on Mathematics)
by Nikolai Nikolaevich Vorob'EvFibonacci numbers date back to an 800-year-old problem concerning the number of offspring born in a single year to a pair of rabbits. This book offers the solution and explores the occurrence of Fibonacci numbers in number theory, continued fractions, and geometry. A discussion of the "golden section" rectangle, in which the lengths of the sides can be expressed as a ration of two successive Fibonacci numbers, draws upon attempts by ancient and medieval thinkers to base aesthetic and philosophical principles on the beauty of these figures. Recreational readers as well as students and teachers will appreciate this light and entertaining treatment of a classic puzzle.
Field-based Tests for Soccer Players: Methodological Concerns and Applications (SpringerBriefs in Applied Sciences and Technology)
by Filipe Manuel Clemente Rafael Oliveira Rui Silva Zeki Akyildiz Halil Ibrahim Ceylan Javier Raya González Francisco Tomás Fernández Rui Araújo Hugo Sarmento Ricardo Lima Bruno Silva Sérgio Matos Yung-Sheng Chen José AfonsoThis book systematically summarizes the accuracy, precision, and repeatability levels of field-based tests applied in soccer. It considers such details as the effectiveness of tests for different age categories and sexes. In this book, the readers will be able to check all the field-based tests conceived for fitness assessment in soccer through a large systematic review made to the literature. In addition a brief characterization of each test and presentation of the concurrent validity and repeatability levels for each test will be provided. Finally, the book contains a general discussion of the implications of the tests for different methodological approaches to training. It will be use to sports scientists and practitioners.
Field Experiments and Their Critics
by Dawn Langan TeeleIn recent years, social scientists have engaged in a deep debate over the methods appropriate to their research. Their long reliance on passive observational collection of information has been challenged by proponents of experimental methods designed to precisely infer causal effects through active intervention in the social world. Some scholars claim that field experiments represent a new gold standard and the best way forward, while others insist that these methods carry inherent inconsistencies, limitations, or ethical dilemmas that observational approaches do not. This unique collection of essays by the most influential figures on every side of this debate reveals its most important stakes and will provide useful guidance to students and scholars in many disciplines.
Field Guide to Compelling Analytics (Chapman and Hall/CRC Focus Case Studies in Analytics and OR)
by Walter DeGrange Lucia DarrowField Guide to Compelling Analytics is written for Analytics Professionals (APs) who want to increase their probability of success in implementing analytical solutions. In the past, soft skills such as presentation and persuasive writing techniques have been the extent of teaching junior APs how to effectively communicate the value of analytical products. However, there are other aspects to success such as trust and experience that may play a more important role in convincing fellow APs, clients, advisors, and leadership groups that their analytic solutions will work. This book introduces the formula ‘Analytics + Trust + Communication + Experience > Convince Them’ to illustrate an AP’s ability to convince a stakeholder. The ‘Convince Me’ stakeholders might be an analytics team member, team lead, decision-maker, or senior leader that are either internal or external to the AP’s organization. Whoever they are, this formula represents a concise, digestible, and above all practical means to increase the likelihood that you will be able to persuade them of the value of your analytical product. Features Includes insight questions to support class discussion. Written in broadly non-mathematical terms, designed to be accessible to any level of student or practicing AP to read, understand, and implement the concepts. Each section introduces the ideas through real-life case studies.
A Field Guide to Lies: Critical Thinking in the Information Age
by Daniel J. LevitinFrom The New York Times bestselling author of THE ORGANIZED MIND and THIS IS YOUR BRAIN ON MUSIC, a primer to the critical thinking that is more necessary now than ever. We are bombarded with more information each day than our brains can process--especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports revealing the ways lying weasels can use them. It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, distortions, and outright lies from reliable information? Levitin groups his field guide into two categories--statistical infomation and faulty arguments--ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning--not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some lying weasels in their tracks!
A Field Guide to Lies: Critical Thinking with Statistics and the Scientific Method
by Daniel J. LevitinWinner of the National Business Book AwardFrom the New York Times bestselling author of The Organized Mind and This Is Your Brain on Music, a primer to the critical thinking that is more necessary now than ever We are bombarded with more information each day than our brains can process—especially in election season. It's raining bad data, half-truths, and even outright lies. New York Times bestselling author Daniel J. Levitin shows how to recognize misleading announcements, statistics, graphs, and written reports, revealing the ways lying weasels can use them. It's becoming harder to separate the wheat from the digital chaff. How do we distinguish misinformation, pseudo-facts, and distortions from reliable information? Levitin groups his field guide into two categories—statistical information and faulty arguments—ultimately showing how science is the bedrock of critical thinking. Infoliteracy means understanding that there are hierarchies of source quality and bias that variously distort our information feeds via every media channel, including social media. We may expect newspapers, bloggers, the government, and Wikipedia to be factually and logically correct, but they so often aren't. We need to think critically about the words and numbers we encounter if we want to be successful at work, at play, and in making the most of our lives. This means checking the plausibility and reasoning—not passively accepting information, repeating it, and making decisions based on it. Readers learn to avoid the extremes of passive gullibility and cynical rejection. Levitin's charming, entertaining, accessible guide can help anyone wake up to a whole lot of things that aren't so. And catch some weasels in their tracks!
Field Solutions on Computers
by Stanley Humphries Jr.Field Solutions on Computers covers a broad range of practical applications involving electric and magnetic fields. The text emphasizes finite-element techniques to solve real-world problems in research and industry. After introducing numerical methods with a thorough treatment of electrostatics, the book moves in a structured sequence to advanced topics. These include magnetostatics with non-linear materials, permanent magnet devices, RF heating, eddy current analysis, electromagnetic pulses, microwave structures, and wave scattering. The mathematical derivations are supplemented with chapter exercises and comprehensive reviews of the underlying physics. The book also covers essential supporting techniques such as mesh generation, interpolation, sparse matrix inversions, and advanced plotting routines.
Field Theoretic Method in Phase Transformations
by Alexander UmantsevThe main subject of the book is the continuum, field theoretic method of study of phase transformations in material systems. The method, also known as "phase field", allows one to analyze different stages of transformations on the unified platform. It has received significant attention in the materials science community recently due to many successes in solving or illuminating important problems. The book will address fundamentals of the method starting from the classical theories of phase transitions, the most important theoretical and computational results, and some of the most advanced recent applications.
The Field Theoretic Renormalization Group in Critical Behavior Theory and Stochastic Dynamics (Frontiers in Physics)
by null A.N. Vasil'evThis volume provides a general field-theoretical picture of critical phenomena and stochastic dynamics and helps readers develop a practical skill for calculations. This education on the practical skill sets this book apart: it is the first to give a full technical introduction to the field. Both general ideas and ...hard... calculations are presen
The Fielding Bible
by John Dewan Ben JedlovecThe Fielding Bible—Volume III is a thorough compilation of the latest breakthroughs in defensive analytics from Baseball Info Solutions. With information previously exclusive to major league teams, Volume III is 100% new material that builds on the well received Volumes I and II. Included are comprehensive defensive evaluations, a study on the effectiveness of the "Ted Williams shift", the new Timer Plus/Minus system, and updated Defensive Runs Saved numbers that estimate the value of each fielder in Major League Baseball. The Fielding Bible—Volume III will include: Defensive Runs Saved— the most comprehensive defensive evaluations are back and better than ever, with significant enhancements to the eight-component system first introduced in Volume II. Timer Plus/Minus—the revolutionary Plus/Minus system, which measures each fielder’s ability to turn batted balls into outs, gets a facelift to incorporate the brand new battedball timer information, creating the most objective fielding evaluations ever. Good Play/Misplay Runs Saved—turns Bill James’ in-depth Good Fielding Plays and Defensive Misplays system into a new component of Defensive Runs Saved, adding previously-unrecorded aspects of defense like scooped throws and pitch blocks. Total Runs—adding Pitching Runs Created to offensive, defensive, and baserunning ratings to combine every aspect of the game into one tell-all number for every player The latest essay from Bill James on defense. Defensive scouting reports and player commentaries on every regular and semi-regular position player in baseball. New studies on crucial aspects of fielding, including defensive positioning, the "Ted Williams shift", bunts, double plays, outfielder arms and catcher defense.
Fiesta!
by Ginger Foglesong GuyBilingual text describes a children's party and provides practice counting in English and Spanish.
Fifty Challenging Problems in Probability with Solutions (Dover Books on Mathematics)
by Frederick MostellerCan you solve the problem of "The Unfair Subway"? Marvin gets off work at random times between 3 and 5 p.m. His mother lives uptown, his girlfriend downtown. He takes the first subway that comes in either direction and eats dinner with the one he is delivered to. His mother complains that he never comes to see her, but he says she has a 50-50 chance. He has had dinner with her twice in the last 20 working days. Explain. Marvin's adventures in probability are one of the fifty intriguing puzzles that illustrate both elementary ad advanced aspects of probability, each problem designed to challenge the mathematically inclined. From "The Flippant Juror" and "The Prisoner's Dilemma" to "The Cliffhanger" and "The Clumsy Chemist," they provide an ideal supplement for all who enjoy the stimulating fun of mathematics. Professor Frederick Mosteller, who teaches statistics at Harvard University, has chosen the problems for originality, general interest, or because they demonstrate valuable techniques. In addition, the problems are graded as to difficulty and many have considerable stature. Indeed, one has "enlivened the research lives of many excellent mathematicians." Detailed solutions are included. There is every probability you'll need at least a few of them.
Fifty Years of Fuzzy Logic and its Applications
by Dan E. Tamir Naphtali D. Rishe Abraham KandelThis book presents a comprehensive report on the evolution of Fuzzy Logic since its formulation in Lotfi Zadeh's seminal paper on "fuzzy sets," published in 1965. In addition, it features a stimulating sampling from the broad field of research and development inspired by Zadeh's paper. The chapters, written by pioneers and prominent scholars in the field, show how fuzzy sets have been successfully applied to artificial intelligence, control theory, inference, and reasoning. The book also reports on theoretical issues; features recent applications of Fuzzy Logic in the fields of neural networks, clustering, data mining and software testing; and highlights an important paradigm shift caused by Fuzzy Logic in the area of uncertainty management. Conceived by the editors as an academic celebration of the fifty years' anniversary of the 1965 paper, this work is a must-have for students and researchers willing to get an inspiring picture of the potentialities, limitations, achievements and accomplishments of Fuzzy Logic-based systems.
Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM (Association for Women in Mathematics Series #28)
by Cathy Kessel Janet L. Beery Sarah J. GreenwaldThe Assocation for Women in Mathematics (AWM), the oldest organization in the world for women in mathematics, had its fiftieth anniversary in 2021. This collection of refereed articles, illustrated by color photographs, reflects on women in mathematics and the organization as a whole. Some articles focus on the situation for women in mathematics at various times and places, including other countries. Others describe how individuals have shaped AWM, and, in turn, how the organization has impacted individuals as well as the broader mathematical community. Some are personal stories about careers in mathematics. Fifty Years of Women in Mathematics: Reminiscences, History, and Visions for the Future of AWM covers a span from AWM’s beginnings through the following fifty years. The volume celebrates AWM and its successes but does not shy away from its challenges.The book is designed for a general audience. It provides interesting and informative reading for people interested in mathematics, gender equity, or organizational structures; teachers of mathematics; students at the high school, college, and graduate levels; and members of more recently established organizations for women in mathematics and related fields or prospective founders of such organizations.
Fighting the Silent Killer: How Men and Women Can Prevent and Cope with Heart Disease Today
by Dr Peter Cohn Dr Joan CohnAmericais number-one killer, heart disease, can exist in the absence of symptoms. Calledlent heart disease,�ts first manifestations can be catastrophic. This no-nonsense guide now addresses this and other new issues in a clear, non-technical way and examines old concerns from a fresh perspective. The text moves easily from the role of smoking, st
Figure It Out, Henri Weldon
by Tanita S. DavisTanita S. Davis, author of Partly Cloudy and Serena Says, has written another funny, warm story featuring middle school and family life—all about the complex calculations it takes for everyone to balance the equations of their lives and what it takes to be part of a team while handling a learning disability. This middle grade novel is perfect for fans of From the Desk of Zoe Washington and A Good Kind of Trouble.Seventh grader Henrietta Weldon gets to switch schools—finally! She’ll be “mainstreaming” into public school, leaving her special education school behind. She can’t wait for her new schedule, new friends, and new classes.Henri’s dyscalculia, a learning disability that makes math challenging to process and understand, is what she expects to give her problems. What she doesn’t expect is a family feud with her sister over her new friends, joining the girls’ soccer team, and discovering poetry. Henri’s tutor and new friend, Vinnie, reminds her to take it slow. One problem at a time.If Henri Weldon has twenty-four hours in a day, and she has two siblings who dislike her four new friends, two hours of soccer practice, seven hours of classes, and three hours of homework . . . she has:A. No free timeB. No idea how to make everyone happyC. No time to figure it out, Henri Weldon!
Figures for Fun: Stories, Puzzles and Conundrums
by Yakov Perelman"Does your brain need a workout? Are you wondering what to do? Well this could be the book for you! This is a great book for anyone who is looking for a challenge and, if you get too stuck, the author kindly also provided the answers at the end of each chapter!" -- Splashes Into BooksGive your mind a playful workout with this collection of more than 100 inventive puzzles. Finding the solutions requires only minimal mathematical knowledge and will test your imagination as well as your brainpower. The motley collection ranges from conundrums and mathematical stunts to practical situations involving counting and measuring. Chess problems, magic squares, and a host of other intriguing scenarios will amuse and challenge puzzle enthusiasts and fans of recreational mathematics. Answers appear at the end of each chapter.These puzzles are the inventions of a gifted Soviet mathematician, Yakov Perelman, whose popular science books on astronomy, physics, and mathematics inspired generations of readers. Perelman's distinctive style, abounding in wit and ingenuity, adds a special flair to his timeless riddles and brainteasers.
Figures of the Future: Latino Civil Rights and the Politics of Demographic Change
by Michael Rodríguez-MuñizAn in-depth look at how U.S. Latino advocacy groups are using ethnoracial demographic projections to bring about political change in the presentFor years, newspaper headlines, partisan speeches, academic research, and even comedy routines have communicated that the United States is undergoing a profound demographic transformation—one that will purportedly change the “face” of the country in a matter of decades. But the so-called browning of America, sociologist Michael Rodríguez-Muñiz contends, has less to do with the complexion of growing populations than with past and present struggles shaping how demographic trends are popularly imagined and experienced. Offering an original and timely window into these struggles, Figures of the Future explores the population politics of national Latino civil rights groups.Based on eight years of ethnographic and qualitative research, spanning both the Obama and Trump administrations, this book investigates how several of the most prominent of these organizations—including UnidosUS (formerly NCLR), the League of United Latin American Citizens, and Voto Latino—have mobilized demographic data about the Latino population in dogged pursuit of political recognition and influence. In census promotions, get-out-the-vote campaigns, and policy advocacy, this knowledge has been infused with meaning, variously serving as future-oriented sources of inspiration, emblems for identification, and weapons for contestation. At the same time, Rodríguez-Muñiz considers why these political actors have struggled to translate this demographic growth into tangible political gain and how concerns about white backlash have affected how they forecast demographic futures.Figures of the Future looks closely at the politics surrounding ethnoracial demographic changes and their rising influence in U.S. public debate and discourse.
Figurierte Zahlen: Veranschaulichung als heuristische Strategie
by Jochen ZiegenbalgDieses Buch behandelt die Visualisierung als Methode des mathematischen Problemlösens, Begründens und Beweisens: Konkrete Beispiele zur Veranschaulichung durch mathematische Figuren und Bilder bieten einen faszinierenden Einblick in das Argumentieren anhand strukturierter und strukturierender Figuren zur Betrachtung von Zahlen und Zahlenfolgen. Die historischen Wurzeln dieses mathematischen Handwerkszeugs werden dabei so weit wie möglich einbezogen. Die Beispiele sind in der Regel konstruktiver Natur; gelegentlich wird, wo angebracht, die algorithmische Erschließung durch Hinweise auf die Programmierung mit Hilfe von Computeralgebra Systemen ergänzt. Das Buch richtet sich an Studierende und Lehrende an Schulen und Hochschulen, sowie an alle an der Elementarmathematik interessierten Nichtspezialisten, die das mathematische Arbeiten einmal außerhalb der von den Bildungsinstitutionen vorgezeichneten Pfade kennenlernen wollen. Es liefert insbesondere Lehrkräften und Lehramtsstudierenden wertvolle Anregungen, etwa zur Förderung mathematisch interessierter Schülerinnen und Schüler. In der 2. Auflage ist mit den mathematisch fundamentalen und historisch bedeutsamen Themen Wechselwegnahme, Teilbarkeit, Euklidischer Algorithmus, Inkommensurabilität und Kettenbrüche ein neues, für Visualisierungen gut geeignetes Kapitel hinzugekommen. Bereits bestehende Kapitel wurde durch Abschnitte über Trapezzahlen, ungerade Quadratzahlen und zentrierte Polygonalzahlen ergänzt.
Figuring It Out
by Nuno CratoThis is a book of mathematical stories -- funny and puzzling mathematical stories. They tell of villains who try to steal secrets, heroes who encode their messages, and mathematicians who spend years on end searching for the best way to pile oranges. There are also stories about highway confusions occurring when the rules of Cartesian geometry are ignored, small-change errors due to ignorance of ancient paradoxes, and mistakes in calendars arising from poor numerical approximations. This book is about the power and beauty of mathematics. It shows mathematics in action, explained in a way that everybody can understand. It is a book for enticing youngsters and inspiring teachers. Nuno Crato is a leading science writer and mathematician, whose entertaining essays have won a number of international awards.
Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)
by Jennifer M. Bay-Williams John J. SanGiovanni Sherri L. Martinie Jennifer SuhBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation. Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.
Figuring Out Fluency - Addition and Subtraction With Fractions and Decimals: A Classroom Companion (Corwin Mathematics Series)
by Jennifer M. Bay-Williams John J. SanGiovanni Sherri L. Martinie Jennifer SuhBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. It is not about speed or recall. Real fluency is about choosing strategies that are efficient, flexible, lead to accurate solutions, and are appropriate for the given situation. Developing fluency is also a matter of equity and access for all learners. The landmark book Figuring Out Fluency in Mathematics Teaching and Learning offered educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. Now, teachers have the chance to apply that inspiration through explicit instruction and practice every day with the classroom companion Figuring Out Fluency: Addition and Subtraction with Fractions and Decimals. With this book, teachers can: Dive deeper into the Significant Strategies for fluency explained in the anchor book Learn how these strategies grow from and relate to the basic fact strategies children learn Access over 100 strategy-aligned and classroom-ready activities for fluency instruction and practice in adding and subtracting fractions and decimals, including worked examples, routines, games, and centers Find activities for assessing all components of addition and subtraction fluency for fractions and decimals, plus support for engaging families Download all of the needed support tools, game boards, and other resources from the companion website for immediate implementation. Give each and every student the knowledge and power to become skilled and confident mathematical thinkers and doers.
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)
by null Jennifer M. Bay-Williams null John J. SanGiovanniBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.
Figuring Out Fluency in Mathematics Teaching and Learning, Grades K-8: Moving Beyond Basic Facts and Memorization (Corwin Mathematics Series)
by null Jennifer M. Bay-Williams null John J. SanGiovanniBecause fluency practice is not a worksheet. Fluency in mathematics is more than adeptly using basic facts or implementing algorithms. Real fluency involves reasoning and creativity, and it varies by the situation at hand. Figuring Out Fluency in Mathematics Teaching and Learning offers educators the inspiration to develop a deeper understanding of procedural fluency, along with a plethora of pragmatic tools for shifting classrooms toward a fluency approach. In a friendly and accessible style, this hands-on guide empowers educators to support students in acquiring the repertoire of reasoning strategies necessary to becoming versatile and nimble mathematical thinkers. It includes: "Seven Significant Strategies" to teach to students as they work toward procedural fluency. Activities, fluency routines, and games that encourage learning the efficiency, flexibility, and accuracy essential to real fluency. Reflection questions, connections to mathematical standards, and techniques for assessing all components of fluency. Suggestions for engaging families in understanding and supporting fluency. Fluency is more than a toolbox of strategies to choose from; it’s also a matter of equity and access for all learners. Give your students the knowledge and power to become confident mathematical thinkers.