The second edition of this book offers a unique approach to making mathematics education research on the teaching and learning of multiplication and division concepts readily accessible and understandable to pre-service and in-service K-6 mathematics teachers. Revealing students' thought processes with extensive annotated samples of student work and vignettes characteristic of classroom teachers' experience, this book provides teachers a research-based lens to interpret evidence of student thinking, inform instruction and ultimately improve student learning. Based on research gathered in the Ongoing Assessment Project (OGAP), and updated throughout, this engaging and easy-to-use resource also features: New chapters on the OGAP Multiplicative Reasoning Framework and Learning Progressions and Using the OGAP Multiplicative Progression to inform instruction and support student learning In-chapter sections on how Common Core State Standards for Math (CCSSM) are supported by math education research Case Studies are presented, focusing on a core mathematical idea and different types of instructional responses, to illustrate how teachers can elicit evidence of student thinking and use that information to inform instruction Big Ideas frame the chapters and provide a platform for meaningful exploration of the teaching of multiplication and division Looking Back Questions at the end of each chapter allow teachers to analyze student thinking and to consider instructional strategies for their own students Instructional Links help teachers relate concepts from each chapter to their own instructional materials and programs Accompanying online Support Material includes an answer key to Looking Back questions, as well as a copy of the OGAP Fraction Framework and Progression A Focus on Multiplication and Division is part of the popular A Focus on . . . collection, designed to aid the professional development of pre-service and in-service mathematics teachers. As with the other volumes on addition and subtraction, ratios and proportions, and fractions, this updated new edition bridges the gap between what math education researchers know and what teachers need to know to better understand evidence in student work and make effective instructional decisions.

Written by bestselling author Stephen Doyle, this student book will engage and motivate you throughout the course. // Endorsed by WJEC offering high quality support you can trust. // Thorough coverage of all the topics in the A2 Level Applied specification. // Extra support for the problem solving and unstructured questions in the specification. // Plenty of examples with worked answers throughout to enable you to check your understanding as you progress through the course. // Answers to questions are provided in order to check your work.

The French mathematician Rene Thom (Fields medal 1958) died in 2002. In this volume his contributions to biology, semiotics and linguistics are discussed by a group of scholars who have continued his work and have shaped the new paradigm of dynamic semiotics and linguistics. Thom's heritage is full of revolutionary ideas and deep insights which stem from a rich intuition and a sharp awareness of the current state of the sciences, including their potentials and risks. The contributions to this volume are elaborations of papers given at a colloquium at the International Center for Semiotics and Linguistics of the University of Urbino (Italy), in 2005. The central concern of this volume is semiogenesis, i.e. the evolution and differentiation of meaningful ("pregnant") forms in the field of symbolic systems - from bio-communication to language and cultural forms like music, art, architecture or urban forms. The basic questions are: How are meanings created and further differentiated? Where do they come from? What kind of forces drive their unfolding? How can complex cultural forms be understood based on simple morphodynamic principles? Applications concern the perception of forms by animals and humans, the categorization of forms e.g. in a lexicon, and predication or other complex symbolic behaviors which show up in grammar or in cultural artifacts like the unfolding of urban centers.

The book outlines two separate processes for working with groups and discusses their separate applications as well as how they work together for a holistic approach to institutional transformation; it emphasizes group level processes, including academic departments, an area which currently lacks development. The text integrates across a wide range of disciplines and interdisciplinary fields, thus it brings institutional transformation concepts into conversations across many boundaries highlighting how insights from one field can address issues in another. The book is timely in topic, focusing on solutions for institutional racism and sexism and a pathway to collectively address calls for racial justice and equity by blending theory and practice into a praxis for how to implement and sustain socially just institutions; it includes outcomes documenting the positive impacts of the practices described in the text.

This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l'Etude et l'Amelioration de l'Enseignement des Mathematiques / International Commission for the Study and Improvement of Mathematics Education.

Posthuman Community Psychology is an exploration of mainstream psychology through a critical posthumanity perspective, examining psychology’s place in the world and its relationship with marginalised people, with a focus on people with disabilities. The book argues that the history of modern psychology is underpinned by reductionism and individualism, which is embedded within the contemporary psychology that we know today despite the challenges from critical and community psychologists who seek a more empowering, inclusive, and activist psychology. The posthuman community psychology ideas that emerge in this book examine and intersect with mainstream psychology, critical and community psychologies, critical posthumanities and disability studies to propose an imaginative, reflective, and relational new psychology that represents a collection of possibilities that do not remain entrenched in older ways of thinking about humans and human connections. Richards proposes that psychology has the potential to evolve and make a powerful and profound difference for marginalised people, but a genuine desire for change from psychologists is essential for this to happen. Illustrating the important considerations needed when examining the relationship between the discipline of psychology and marginalised people, this book is fascinating reading for community psychology students and academics, aspiring professional psychologists, community workers, and policy makers.

Posthuman Community Psychology is an exploration of mainstream psychology through a critical posthumanity perspective, examining psychology’s place in the world and its relationship with marginalised people, with a focus on people with disabilities. The book argues that the history of modern psychology is underpinned by reductionism and individualism, which is embedded within the contemporary psychology that we know today despite the challenges from critical and community psychologists who seek a more empowering, inclusive, and activist psychology. The posthuman community psychology ideas that emerge in this book examine and intersect with mainstream psychology, critical and community psychologies, critical posthumanities and disability studies to propose an imaginative, reflective, and relational new psychology that represents a collection of possibilities that do not remain entrenched in older ways of thinking about humans and human connections. Richards proposes that psychology has the potential to evolve and make a powerful and profound difference for marginalised people, but a genuine desire for change from psychologists is essential for this to happen. Illustrating the important considerations needed when examining the relationship between the discipline of psychology and marginalised people, this book is fascinating reading for community psychology students and academics, aspiring professional psychologists, community workers, and policy makers.

Many people think mathematics is useless. They're wrong. In the UK, the 2.8 million people employed in mathematical science occupations contributed GBP208 billion to the economy in a single year -- that's 10 per cent of the workforce contributing 16 per cent of the economy. What's the Use? asks why there is such a vast gulf between public perceptions of mathematics and reality. It shows how mathematics is vital, often in surprising ways, behind the scenes of daily life. How politicians pick their voters. How an absurd little puzzle solved 300 years ago leads to efficient methods for kidney transplants. How an Irish mathematician's obsession with a new number system improves special effects in movies and computer games. How SatNav relies on at least six mathematical techniques. And how a bizarre, infinitely wiggly curve, helps to optimise deliveries to your door.

This volume analyzes the dominance of STEM fields in various university rankings and the reasons why many governments in the world disproportionately give value to STEM fields. Secondly, although there is general agreement that STEM fields are important, chapter authors also examine the role of interdisciplinary and multidisciplinary approaches for a revised STEM education as well as implications for the future. The book presents examples from the United States, Canada, Japan, Korea, and Taiwan.

This huge CGP Textbook is packed with thousands of questions for both years of A-Level Maths - it's suitable for the Edexcel, AQA, OCR and OCR MEI courses. It's perfect for helping students put their knowledge to the test and build their skills. The book also contains plenty of worked examples, practice exercises on almost every page and review questions at the end of each chapter. Better still, answers to every question are included at the back.

Takes an applied approach to communication ethics emphasizing the development of personal standards for use in personal, professional, and social life Core textbook for communication and media ethics courses 3rd edition features new content focused on digital communication, trauma, partisan political divisions, and the COVID-19 pandemic Online resources for instructors include instructor's manual including section on online teaching, sample assignments, and PowerPoint slides

This book covers all the content needed for AS and Year 1 of the Edexcel Statistics and Mechanics A-Level course and is fully up to date for the latest specifications. It has the clearest notes on all the theory for every topic, including annotated worked examples and explanations; hundreds of challenging questions for every chapter, including problem-solving and modelling; a realistic Practice Paper with a complete mark scheme; and a free Online Edition to read on PC, Mac or tablet (use the unique code printed inside the cover to gain full access). For full A-Level Maths coverage don't miss the Year 1 Pure Maths Student Textbook (9781789088397), and our Year 2 Student Textbooks for Pure Maths (9781789088410) and Statistics and Mechanics (9781789088427).

• Utilizes case studies from different disciplines and sectors within engineering and other related technical areas to demonstrate how to go from data, to insight, and to decision making • Introduces various approaches to build models that exploits different algorithms • Discusses predictive models that can be built through machine learning and used to mine patterns from large datasets • Explores the augmentation of technical and mathematical materials with explanatory worked examples • Includes a glossary, lecture notes, self-assessments, and worked-out practice exercises

As data is an important asset for any organization, it is essential to apply semantic technologies in data science to fulfill the need of any organization. This volume of a two-volume handbook set provides a roadmap for new trends and future developments of data science with semantic technologies. Data Science with Semantic Technologies: New Trends and Future Developments highlights how data science enables the user to create intelligence through these technologies. In addition, this book offers the answers to various questions such as can semantic technologies be able to facilitate data science? Which type of data science problems can be tackled by semantic technologies? How can data scientists get benefited from these technologies? What is the role of semantic technologies in data science? What is the current progress and future of data science with semantic technologies? Which types of problems require the immediate attention of the researchers? What should be the vision 2030 for data science? This volume can serve as an important guide towards applications of data science with semantic technologies for the upcoming generation and thus becomes a unique resource for scholars, researchers, professionals, and practitioners in this field.

Gone are the days when data was interlinked with related data by humans and to find insights coherently, human interpretation was required. Data is no more just data. It is now considered a Thing or Entity or Concept- to bring the meaning to it, so that a machine not only understands the concept but also extrapolates the way humans do. Data Science with Semantic Technologies: Deployment and Exploration volume of a two-volume handbook set provides a roadmap for the deployment of semantic technologies in the field of data science and enables the user to create intelligence through these technologies by exploring the opportunities and eradicating the challenges in the current and future time frame. In addition, this book offers the answer to various questions like What makes a technology semantic as opposed to other approaches to data science? What is knowledge data science? How does knowledge data science relate to other fields? This book explores the optimal use of these technologies to provide the highest benefit to the user under one comprehensive source and title. As there is no dedicated book available in the market on this topic at this time, this proposed new book becomes a unique and only resource for scholars, researchers, data scientists, professionals, and practitioners. This volume can serve as an important guide towards applications of data science with semantic technologies for the upcoming generation and thus becomes a unique resource for scholars, researchers, professionals, and practitioners in this field.

For Finance and Treasury professionals to effectively pitch, sell, and comprehend the true appeal and relevance of a particular security, there is nothing more important than knowing how the value of said security has been determined. While punching numbers into a computer may provide the information needed, it is nevertheless essential to have a firm grasp of the valuation concepts in order to make the best, most informed decisions. Offering a straightforward, accessible approach not found anywhere else, this comprehensive new book provides a clear-cut road map through the mathematical concepts associated with the investments sector of Treasury management.
Written by an expert in the field, Investment Mathematics for Finance and Treasury Professionals explains the principles and formulae used in the fixedincome cash markets. It presents an in-depth, yet practical look at the applications associated with these money and capital markets instruments. The book also covers calculations and applications in the foreign exchange and equities markets. The same in-depth coverage is applied to the various fixed-income and foreign exchange derivatives markets used as both speculative and hedging tools. Spanning the spectrum from price/yield changes to risk/return, and packed with numerous examples that illustrate key concepts, this exhaustive resource includes:
* Yield spread analysis--methods of price/yield quotation, yield spreads by maturity, off-the-run vs. on-the-run
* Price/yield sensitivity--hedge ratios, basis point value, dollar duration, convexity
* Term structure of interest rates different yield curve structures, zero coupon yield curve, Treasury trading STRIPS
* Foreign exchange--crossrates, spot rates, forward points, covered interest arbitrage
* Options--plain vanilla vs. exotic options, over-the-counter vs. exchange-traded options, understanding option valuation models, and option hedging and trading strategies
* Interest rate swaps, swaptions, caps, floors, collars, inverse floaters
* Risk/return--valuation theory, capital asset pricing model, value at risk

Complete with supporting appendixes that contain statistical information on such essentials as historical interest rate patterns, conversion factors for Treasury bond futures, the standard normal distribution, and day count basis for different bonds, Investment Mathematics for Finance and Treasury Professionals is an indispensable reference for anyone involved with corporate and municipal treasury functions.
Providing Finance and Treasury professionals the fundamental information necessary to understand the mathematical concepts and applications used in investment decisions, this in-depth and accessible resource explains and clarifies the concepts behind investment mathematics. With numerous examples and comprehensive appendixes containing important statistical data, Investment Mathematics for Finance and Treasury Professionals covers everything from price/yield changes and yield spread analysis to term structure of interest rates, derivatives, and risk/return.

This book engages with contemporary, and often polarizing, debates surrounding the risks of adolescent use of digital media and internet technologies. By drawing on multiple research studies, the text synthesizes current understandings of the impacts of social network use, online gaming, pornography, and phenomena, including cyberbullying, cyberstalking, and internet addiction, to develop recommendations for the effective identification of at-risk youth, as well as strategies for informed communication about online risks and opportunities. It shows how media discussion of risks to children and teenagers from new technology is highly emotive and often exaggerated, rooted in the “moral panic” surrounding new cultural practices that young people engage in, but which adults do not understand. Online risks are thus conceptualized as centering on three areas, specific to adolescence, which have undergone radical changes due to new internet technology. These include young people’s identity, the types of content that are accessed, and social relationships. The author shows how these matters stem from the potential of new technology to establish new interpersonal connections, emphasizing how it brings opportunities, as much as risks. As such, he provides a uniquely balanced discussion of potential dangers, while also emphasizing the opportunities for social, academic, and personal growth which new technologies afford young people. It will be indispensable for researchers and clinicians interested in assessing levels of online risk, as well as scholars and educators with interests in cyberpsychology, social psychology, cyber culture, social aspects of computing and media, and adolescent development.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

-Explores the development of elementary students’ understanding of the mathematics of measure, demonstrating how measurement can serve as an anchor for supporting a deeper understanding of future mathematics learning, as well as learning in other STEM disciplines. -Describes a learning progression built on benchmarks of student learning about measure in length, angle, area, volume, and rational number, exploring related concepts, classroom experiences, and instructional practices at each stage—an approach relevant for scholars, teacher educators, and specialists in math education. -Written by two leading researchers in math and science education, who draw from decades of experience in K-5 classroom research. -Accompanied by online resources developed for practitioners, including instructional guides, examples of student thinking, and other teacher-focused materials, helping clarify how to bring concepts of measure and rational number to life in classrooms.

This monograph gives the reader an up-to-date account of the fine properties of real-valued functions and measures. The unifying theme of the book is the notion of nonmeasurability, from which one gets a full understanding of the structure of the subsets of the real line and the maps between them. The material covered in this book will be of interest to a wide audience of mathematicians, particularly to those working in the realm of real analysis, general topology, and probability theory. Set theorists interested in the foundations of real analysis will find a detailed discussion about the relationship between certain properties of the real numbers and the ZFC axioms, Martin's axiom, and the continuum hypothesis.

This book serves as a valuable resource for mathematics and science teachers at secondary school level, teenagers and parents. It contains written versions of Royal Institution masterclasses on a wide selection of topics in pure and applied mathematics. The masterclasses are a popular program of advanced study conducted each year for mathematically talented university-bound British youth. They serve as a unique introduction to the kinds of topics found at the undergraduate level, yet presented in a manner that is meant to stimulate interest and challenge young minds. Topics include chaos theory, meteorology, storage limitations of computers, population growth and decay, as well as the mechanics of dinosaurs. The book is well-illustrated, easy to read, and contains worksheets with interesting problems (and solutions). The emphasis throughout is on enjoying the challenge of mathematics.