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Awesome Math: Teaching Mathematics with Problem Based Learning
by Titu Andreescu Kathy Cordeiro Alina AndreescuHelp your students to think critically and creatively through team-based problem solving instead of focusing on testing and outcomes. Professionals throughout the education system are recognizing that standardized testing is holding students back. Schools tend to view children as outcomes rather than as individuals who require guidance on thinking critically and creatively. Awesome Math focuses on team-based problem solving to teach discrete mathematics, a subject essential for success in the STEM careers of the future. Built on the increasingly popular growth mindset, this timely book emphasizes a problem-solving approach for developing the skills necessary to think critically, creatively, and collaboratively. In its current form, math education is a series of exercises: straightforward problems with easily-obtained answers. Problem solving, however, involves multiple creative approaches to solving meaningful and interesting problems. The authors, co-founders of the multi-layered educational organization AwesomeMath, have developed an innovative approach to teaching mathematics that will enable educators to: Move their students beyond the calculus trap to study the areas of mathematics most of them will need in the modern world Show students how problem solving will help them achieve their educational and career goals and form lifelong communities of support and collaboration Encourage and reinforce curiosity, critical thinking, and creativity in their students Get students into the growth mindset, coach math teams, and make math fun again Create lesson plans built on problem based learning and identify and develop educational resources in their schools Awesome Math: Teaching Mathematics with Problem Based Learning is a must-have resource for general education teachers and math specialists in grades 6 to 12, and resource specialists, special education teachers, elementary educators, and other primary education professionals.
The Axiom of Choice
by Thomas J. JechComprehensive in its selection of topics and results, this self-contained text examines the relative strengths and consequences of the axiom of choice. Each chapter contains several problems, graded according to difficulty, and concludes with some historical remarks.An introduction to the use of the axiom of choice is followed by explorations of consistency, permutation models, and independence. Subsequent chapters examine embedding theorems, models with finite supports, weaker versions of the axiom, and nontransferable statements. The final sections consider mathematics without choice, cardinal numbers in set theory without choice, and properties that contradict the axiom of choice, including the axiom of determinacy and related topics
An Axiomatic Approach to Geometry: Geometric Trilogy I
by Francis BorceuxFocusing methodologically on those historical aspects that are relevant to supporting intuition in axiomatic approaches to geometry, the book develops systematic and modern approaches to the three core aspects of axiomatic geometry: Euclidean, non-Euclidean and projective. Historically, axiomatic geometry marks the origin of formalized mathematical activity. It is in this discipline that most historically famous problems can be found, the solutions of which have led to various presently very active domains of research, especially in algebra. The recognition of the coherence of two-by-two contradictory axiomatic systems for geometry (like one single parallel, no parallel at all, several parallels) has led to the emergence of mathematical theories based on an arbitrary system of axioms, an essential feature of contemporary mathematics. This is a fascinating book for all those who teach or study axiomatic geometry, and who are interested in the history of geometry or who want to see a complete proof of one of the famous problems encountered, but not solved, during their studies: circle squaring, duplication of the cube, trisection of the angle, construction of regular polygons, construction of models of non-Euclidean geometries, etc. It also provides hundreds of figures that support intuition. Through 35 centuries of the history of geometry, discover the birth and follow the evolution of those innovative ideas that allowed humankind to develop so many aspects of contemporary mathematics. Understand the various levels of rigor which successively established themselves through the centuries. Be amazed, as mathematicians of the 19th century were, when observing that both an axiom and its contradiction can be chosen as a valid basis for developing a mathematical theory. Pass through the door of this incredible world of axiomatic mathematical theories!
Axiomatic Method and Category Theory (Synthese Library #364)
by Andrei RodinThis volume explores the many different meanings of the notion of the axiomatic method, offering an insightful historical and philosophical discussion about how these notions changed over the millennia. The author, a well-known philosopher and historian of mathematics, first examines Euclid, who is considered the father of the axiomatic method, before moving onto Hilbert and Lawvere. He then presents a deep textual analysis of each writer and describes how their ideas are different and even how their ideas progressed over time. Next, the book explores category theory and details how it has revolutionized the notion of the axiomatic method. It considers the question of identity/equality in mathematics as well as examines the received theories of mathematical structuralism. In the end, Rodin presents a hypothetical New Axiomatic Method, which establishes closer relationships between mathematics and physics. Lawvere's axiomatization of topos theory and Voevodsky's axiomatization of higher homotopy theory exemplify a new way of axiomatic theory building, which goes beyond the classical Hilbert-style Axiomatic Method. The new notion of Axiomatic Method that emerges in categorical logic opens new possibilities for using this method in physics and other natural sciences. This volume offers readers a coherent look at the past, present and anticipated future of the Axiomatic Method.
Axiomatic Set Theory
by Patrick SuppesOne of the most pressingproblems of mathematics over the last hundred years has been the question: What is a number? One of the most impressive answers has been the axiomatic development of set theory. The question raised is: "Exactly what assumptions, beyond those of elementary logic, are required as a basis for modern mathematics?" Answering this question by means of the Zermelo-Fraenkel system, Professor Suppes' coverage is the best treatment of axiomatic set theory for the mathematics student on the upper undergraduate or graduate level. The opening chapter covers the basic paradoxes and the history of set theory and provides a motivation for the study. The second and third chapters cover the basic definitions and axioms and the theory of relations and functions. Beginning with the fourth chapter, equipollence, finite sets and cardinal numbers are dealt with. Chapter five continues the development with finite ordinals and denumerable sets. Chapter six, on rational numbers and real numbers, has been arranged so that it can be omitted without loss of continuity. In chapter seven, transfinite induction and ordinal arithmetic are introduced and the system of axioms is revised. The final chapter deals with the axiom of choice. Throughout, emphasis is on axioms and theorems; proofs are informal. Exercises supplement the text. Much coverage is given to intuitive ideas as well as to comparative development of other systems of set theory. Although a degree of mathematical sophistication is necessary, especially for the final two chapters, no previous work in mathematical logic or set theory is required. For the student of mathematics, set theory is necessary for the proper understanding of the foundations of mathematics. Professor Suppes in Axiomatic Set Theory provides a very clear and well-developed approach. For those with more than a classroom interest in set theory, the historical references and the coverage of the rationale behind the axioms will provide a strong background to the major developments in the field. 1960 edition.
Axiomatic Thinking I
by Fernando Ferreira Reinhard Kahle Giovanni SommarugaIn this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.Chapter 8 is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com.
Axiomatic Thinking II
by Fernando Ferreira Reinhard Kahle Giovanni SommarugaIn this two-volume compilation of articles, leading researchers reevaluate the success of Hilbert's axiomatic method, which not only laid the foundations for our understanding of modern mathematics, but also found applications in physics, computer science and elsewhere.The title takes its name from David Hilbert's seminal talk Axiomatisches Denken, given at a meeting of the Swiss Mathematical Society in Zurich in 1917. This marked the beginning of Hilbert's return to his foundational studies, which ultimately resulted in the establishment of proof theory as a new branch in the emerging field of mathematical logic. Hilbert also used the opportunity to bring Paul Bernays back to Göttingen as his main collaborator in foundational studies in the years to come.The contributions are addressed to mathematical and philosophical logicians, but also to philosophers of science as well as physicists and computer scientists with an interest in foundations.
Axiomatics: Mathematical Thought and High Modernism
by Alma SteingartThe first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.
Axiomatics: Mathematical Thought and High Modernism
by Alma SteingartThe first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.
Axiomatics: Mathematical Thought and High Modernism
by Alma SteingartThe first history of postwar mathematics, offering a new interpretation of the rise of abstraction and axiomatics in the twentieth century. Why did abstraction dominate American art, social science, and natural science in the mid-twentieth century? Why, despite opposition, did abstraction and theoretical knowledge flourish across a diverse set of intellectual pursuits during the Cold War? In recovering the centrality of abstraction across a range of modernist projects in the United States, Alma Steingart brings mathematics back into the conversation about midcentury American intellectual thought. The expansion of mathematics in the aftermath of World War II, she demonstrates, was characterized by two opposing tendencies: research in pure mathematics became increasingly abstract and rarified, while research in applied mathematics and mathematical applications grew in prominence as new fields like operations research and game theory brought mathematical knowledge to bear on more domains of knowledge. Both were predicated on the same abstractionist conception of mathematics and were rooted in the same approach: modern axiomatics. For American mathematicians, the humanities and the sciences did not compete with one another, but instead were two complementary sides of the same epistemological commitment. Steingart further reveals how this mathematical epistemology influenced the sciences and humanities, particularly the postwar social sciences. As mathematics changed, so did the meaning of mathematization. Axiomatics focuses on American mathematicians during a transformative time, following a series of controversies among mathematicians about the nature of mathematics as a field of study and as a body of knowledge. The ensuing debates offer a window onto the postwar development of mathematics band Cold War epistemology writ large. As Steingart’s history ably demonstrates, mathematics is the social activity in which styles of truth—here, abstraction—become synonymous with ways of knowing.
Axiomatics of Classical Statistical Mechanics (Dover Books on Physics #Volume 11)
by Rudolf KurthRequiring only familiarity with elements of calculus and analytical geometry, this monograph constructs classical statistical mechanics as a deductive system, based on equations of motion and basic postulates of probability. 1960 edition.
Ay's Neuroanatomy of C. Elegans for Computation (Routledge Revivals)
by Theodore B. Achacoso William S. YamamotoFirst published in 1992, AY's Neuroanatomy of C. elegans for Computation provides the neural circuitry database of the nematode Caenorhabditis elegans, both in printed form and in ASCII files on 5.25-inch diskettes (for use on IBM® and compatible personal computers, Macintosh® computers, and higher level machines). Tables of connections among neuron classes, synapses among individual neurons, gap junctions among neurons, worm cells and their embryonic origin, and synthetically derived neuromuscular connections are presented together with the references from which the data were compiled and edited. Sample data files and source codes of FORTRAN and BASIC programs are provided to illustrate the use of mathematical tools for any researcher or student interested in examining a natural neural network and discovering what makes it tick.
El azaroso arte del engaño: Historias del mundo de la casualidad y la estadística
by Gerardo Herrera CorralEl azar, el error y el engaño están presentes en todos los ámbitos de nuestras vidas: el trabajo, las relaciones personales, la política, la economía. /strong> El error, incluso, es parte esencial del material biológico que nos forma. Los seres vivos llegamos a ser lo que somos por el cambio continuo de la estructura genómica: el código grabado en nuestros genes se equivocó una y otra vez para que, alfin, una de las múltiples configuraciones acabara prevaleciendo. En otras palabras, los seres humanos somos producto del azar y el error. ¿Pero dónde está la frontera entre azar y error? Y más aún: ¿cuál es la diferencia entre error y engaño? Los errores pueden ser una fuente inmejorable de aprendizaje , si sabemos detectarlos. Por otro lado, se puede engañar sin mentir abiertamente, es decir, sin dar información falsa. Esto ocurre con frecuencia, por ejemplo, en la estadística, cuando se oculta información, se dan datos parciales o se ofrecen interpretaciones sesgadas. Por ello, nos dice Gerardo Herrera Corral, el conocimiento estadístico debería formar parte de la educación básica de toda persona. Sí, la estadística puede utilizarse para analizar la realidad, para explicar y comunicar mejor datos complejos, pero también puede emplearse para deformar los hechos, manipular y engañar al público. Este libro reúne historias en las que la estadística es la clave: ¿Es real el cambio climático? ¿Viven más tiempo los fumadores? ¿Hay vida en otros planetas? ¿Se acerca el fin de la cultura del automóvil? Al analizar estos casos, el autor nos ayudará a definir conmayor claridad las barreras entre verdad y mentira, azar y error.
Azimuthal Walsh Filters: A Tool to Produce 2D and 3D Light Structures (Progress in Optical Science and Photonics #10)
by Indrani Bhattacharya Lakshminarayan HazraThis book explores the possibility of using azimuthal Walsh filters as an effective tool for manipulating far-field diffraction characteristics near the focal plane of rotationally symmetric imaging systems. It discusses the generation and synthesis of azimuthal Walsh filters, and explores the inherent self-similarity presented in various orders of these filters, classifying them into self-similar groups and sub-groups. Further, it demonstrates that azimuthal Walsh filters possess a unique rotational self-similarity exhibited among adjacent orders. Serving as an atlas of diffraction phenomena with pupil functions represented by azimuthal Walsh filters of different orders, this book describes how orthogonality and self-similarity of these filters could be harnessed to sculpture 2D and 3D light distributions near the focus.
A = B
by null Marko Petkovsek null Herbert S Wilf null Doron ZeilbergerThis book is of interest to mathematicians and computer scientists working in finite mathematics and combinatorics. It presents a breakthrough method for analyzing complex summations. Beautifully written, the book contains practical applications as well as conceptual developments that will have applications in other areas of mathematics.From the ta
B-Model Gromov-Witten Theory (Trends in Mathematics)
by Emily Clader Yongbin RuanThis book collects various perspectives, contributed by both mathematicians and physicists, on the B-model and its role in mirror symmetry. Mirror symmetry is an active topic of research in both the mathematics and physics communities, but among mathematicians, the “A-model” half of the story remains much better-understood than the B-model. This book aims to address that imbalance. It begins with an overview of several methods by which mirrors have been constructed, and from there, gives a thorough account of the “BCOV” B-model theory from a physical perspective; this includes the appearance of such phenomena as the holomorphic anomaly equation and connections to number theory via modularity. Following a mathematical exposition of the subject of quantization, the remainder of the book is devoted to the B-model from a mathematician’s point-of-view, including such topics as polyvector fields and primitive forms, Givental’s ancestor potential, and integrable systems.
Baby 123
by Deborah DonenfeldA companion to BABY ABC, this concept board book features black-and-white photographs of babies interacting with objects that correspond to the featured number, 1 through 10. The object is in color and coordinates with the number featured, making the connection easy and understandable for non-readers. Once again, the diverse cast of babies and easily-countable objects make this book the perfect introduction to numbers.
Back-of-the-Envelope Physics
by Clifford SwartzThe author is the winner of the 2007 Melba Newell Phillips Award given by the American Association of Physics Teachers. Previously, he was awarded their Oersted Medal.Physicists use "back-of-the-envelope" estimates to check whether or not an idea could possibly be right. In many cases, the approximate solution is all that is needed. This compilation of 101 examples of back-of-the-envelope calculations celebrates a quantitative approach to solving physics problems. Drawing on a lifetime of physics research and nearly three decades as the editor of The Physics Teacher, Clifford Swartz provides simple, approximate solutions to physics problems that span a broad range of topics. What note do you get when you blow across the top of a Coke bottle? Could you lose weight on a diet of ice cubes? How can a fakir lie on a bed of nails without getting hurt? Does draining water in the northern hemisphere really swirl in a different direction than its counterpart below the equator? In each case, only a few lines of arithmetic and a few natural constants solve a problem to within a few percent. Covering such subjects as astronomy, magnetism, optics, sound, heat, mechanics, waves, and electricity, the book provides a rich source of material for teachers and anyone interested in the physics of everyday life.
Backdoor Attacks against Learning-Based Algorithms (Wireless Networks)
by Haojin Zhu Shaofeng Li Xuemin (Sherman) Shen Wen WuThis book introduces a new type of data poisoning attack, dubbed, backdoor attack. In backdoor attacks, an attacker can train the model with poisoned data to obtain a model that performs well on a normal input but behaves wrongly with crafted triggers. Backdoor attacks can occur in many scenarios where the training process is not entirely controlled, such as using third-party datasets, third-party platforms for training, or directly calling models provided by third parties. Due to the enormous threat that backdoor attacks pose to model supply chain security, they have received widespread attention from academia and industry. This book focuses on exploiting backdoor attacks in the three types of DNN applications, which are image classification, natural language processing, and federated learning.Based on the observation that DNN models are vulnerable to small perturbations, this book demonstrates that steganography and regularization can be adopted to enhance the invisibility of backdoor triggers. Based on image similarity measurement, this book presents two metrics to quantitatively measure the invisibility of backdoor triggers. The invisible trigger design scheme introduced in this book achieves a balance between the invisibility and the effectiveness of backdoor attacks. In the natural language processing domain, it is difficult to design and insert a general backdoor in a manner imperceptible to humans. Any corruption to the textual data (e.g., misspelled words or randomly inserted trigger words/sentences) must retain context-awareness and readability to human inspectors. This book introduces two novel hidden backdoor attacks, targeting three major natural language processing tasks, including toxic comment detection, neural machine translation, and question answering, depending on whether the targeted NLP platform accepts raw Unicode characters.The emerged distributed training framework, i.e., federated learning, has advantages in preserving users' privacy. It has been widely used in electronic medical applications, however, it also faced threats derived from backdoor attacks. This book presents a novel backdoor detection framework in FL-based e-Health systems. We hope this book can provide insightful lights on understanding the backdoor attacks in different types of learning-based algorithms, including computer vision, natural language processing, and federated learning. The systematic principle in this book also offers valuable guidance on the defense of backdoor attacks against future learning-based algorithms.
Background Modeling and Foreground Detection for Video Surveillance
by Thierry Bouwmans Fatih Porikli Benjamin Höferlin Antoine V AcavantBackground modeling and foreground detection are important steps in video processing used to detect robustly moving objects in challenging environments. This requires effective methods for dealing with dynamic backgrounds and illumination changes as well as algorithms that must meet real-time and low memory requirements.Incorporating both establish
Backseat Driver: The Role of Data in Great Car Safety Debates (ASA-CRC Series on Statistical Reasoning in Science and Society)
by Norma Faris HubeleBuying the safest car for your family shouldn’t be up for debate. Yet for decades, car safety advocates, manufacturers, and lawmakers in the United States have clashed over whether to make automobiles safer. All sides armed themselves with data in the hopes of winning the great car safety debates. In this way, crash statistics and the analysts who studied them made history. But data were always in the backseat, merely supporting different points of view. That is, until now. With car safety, it’s the value we place on every human life that counts. Automobile safety expert Dr. Norma Faris Hubele delivers a lively discussion of the role data play in protecting you and your family on the road. You’ll gain a greater appreciation for how: A World War I pilot’s near-death experience birthed the U.S. car safety movement Data from real car crashes helped create the first vehicle safety standards A shift toward fuel-efficient cars affected fatality risk in the 1970s–1980s versus now Vehicle size has changed, and the problems that creates for you and others sharing the road Car safety rating systems, even when limited, empower consumers and motivate manufacturers Federal regulators decide whether to issue a safety recall on your vehicle Data’s role is evolving with the advent of driver-assist and self-driving technologies
Backward Stochastic Differential Equations: From Linear to Fully Nonlinear Theory (Probability Theory and Stochastic Modelling #86)
by Jianfeng ZhangThis book provides a systematic and accessible approach to stochastic differential equations, backward stochastic differential equations, and their connection with partial differential equations, as well as the recent development of the fully nonlinear theory, including nonlinear expectation, second order backward stochastic differential equations, and path dependent partial differential equations. Their main applications and numerical algorithms, as well as many exercises, are included. The book focuses on ideas and clarity, with most results having been solved from scratch and most theories being motivated from applications. It can be considered a starting point for junior researchers in the field, and can serve as a textbook for a two-semester graduate course in probability theory and stochastic analysis. It is also accessible for graduate students majoring in financial engineering.
Backward Stochastic Differential Equations with Jumps and Their Actuarial and Financial Applications: BSDEs with Jumps (EAA Series)
by Łukasz DelongBackward stochastic differential equations with jumps can be used to solve problems in both finance and insurance. Part I of this book presents the theory of BSDEs with Lipschitz generators driven by a Brownian motion and a compensated random measure, with an emphasis on those generated by step processes and Lévy processes. It discusses key results and techniques (including numerical algorithms) for BSDEs with jumps and studies filtration-consistent nonlinear expectations and g-expectations. Part I also focuses on the mathematical tools and proofs which are crucial for understanding the theory. Part II investigates actuarial and financial applications of BSDEs with jumps. It considers a general financial and insurance model and deals with pricing and hedging of insurance equity-linked claims and asset-liability management problems. It additionally investigates perfect hedging, superhedging, quadratic optimization, utility maximization, indifference pricing, ambiguity risk minimization, no-good-deal pricing and dynamic risk measures. Part III presents some other useful classes of BSDEs and their applications. This book will make BSDEs more accessible to those who are interested in applying these equations to actuarial and financial problems. It will be beneficial to students and researchers in mathematical finance, risk measures, portfolio optimization as well as actuarial practitioners.
Bad at Math?: Dismantling Harmful Beliefs That Hinder Equitable Mathematics Education (Corwin Mathematics Series)
by Lidia GonzalezMath really is for everyone—so let’s prove it. You’ve heard it from kids, from friends, and from celebrities: "I’m bad at math." It’s a line that society tends to accept without examination—after all, some people just aren’t "math people," right? Wrong. As we do with other essential skills, we need to expose the stereotypes, challenge the negative mindsets, and finally confront the systemic opportunity gaps in math education, and replace them with a new vision for what math is, who it’s for, and who can excel at it. In this book you’ll find Research on teacher and student mindsets and their effect on student achievement Audience-specific and differentiated tools, reflection questions, and suggested actions for educators at all levels of the system Examples from popular media, as well as personal stories and anecdotes Quotes, data-driven figures, and suggestions for deeper learning on all aspects of a positive and equitable vision of math education Both social commentary and a toolkit of solutions, this bold new book directly challenges the constructs that have historically dictated our perceptions of what makes someone a "math person". Only by dismantling those misplaced assumptions can we reform math education so it works for everyone. Because in truth, we are all math people.
Bad at Math?: Dismantling Harmful Beliefs That Hinder Equitable Mathematics Education (Corwin Mathematics Series)
by Lidia GonzalezMath really is for everyone—so let’s prove it. You’ve heard it from kids, from friends, and from celebrities: "I’m bad at math." It’s a line that society tends to accept without examination—after all, some people just aren’t "math people," right? Wrong. As we do with other essential skills, we need to expose the stereotypes, challenge the negative mindsets, and finally confront the systemic opportunity gaps in math education, and replace them with a new vision for what math is, who it’s for, and who can excel at it. In this book you’ll find Research on teacher and student mindsets and their effect on student achievement Audience-specific and differentiated tools, reflection questions, and suggested actions for educators at all levels of the system Examples from popular media, as well as personal stories and anecdotes Quotes, data-driven figures, and suggestions for deeper learning on all aspects of a positive and equitable vision of math education Both social commentary and a toolkit of solutions, this bold new book directly challenges the constructs that have historically dictated our perceptions of what makes someone a "math person". Only by dismantling those misplaced assumptions can we reform math education so it works for everyone. Because in truth, we are all math people.