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Developing Mathematical Reasoning: Avoiding the Trap of Algorithms (Corwin Mathematics Series)
by Pamela Weber HarrisMath is not rote-memorizable. Math is not random-guessable. Math is figure-out-able. Author Pam Harris argues that teaching real math—math that is free of distortions–will reach more students more effectively and result in deeper understanding and longer retention. This book is about teaching undistorted math using the kinds of mental reasoning that mathematicians do. Memorization tricks and algorithms meant to make math "easier" are full of traps that sacrifice long-term student growth for short-lived gains. Students and teachers alike have been led to believe that they’ve learned more and more math, but in reality their brains never get any stronger. Using these tricks may make facts easier to memorize in isolation, but that very disconnect distorts the reality of math. The mountain of trivia piles up until students hit a breaking point. Humanity′s most powerful system of understanding, organizing, and making an impact on the world becomes a soul-draining exercise in confusion, chaos, and lost opportunities. Developing Mathematical Reasoning: Avoiding the Trap of Algorithms emphasizes the importance of teaching students increasingly sophisticated mathematical reasoning and understanding underlying concepts rather than relying on a set rule for solving problems. This book illuminates a hierarchy of mathematical reasoning to help teachers guide students through various domains of math development, from basic counting and adding to more complex proportional and functional reasoning. Everyone is capable of understanding and doing real math. This book: Highlights the important mathematical relationships, strategies, and models for students to develop Offers personal stories, reflection sections, and extensive practical exercises for easy implementation Includes real math—a lot of it—to provide teachers with examples they can put to use in their classrooms immediately This book is a valuable resource for educators looking to reach more students by building a strong foundation of mathematical thinking in their students. By addressing common misconceptions about math and providing practical strategies for teaching real math, this book shows that everyone can use the mathematical relationships they already know to reason about new relationships. In other words, everyone can math.
Developing New National Data on Social Mobility: A Workshop Summary
by Amy Smith"Developing New National Data on Social Mobility" summarizes a workshop convened in June 2013 to consider options for a design for a new national survey on social mobility. The workshop was sponsored by the National Science Foundation and convened by the Committee on Population and the Committee on National Statistics Division of Behavioral and Social Sciences and Education of the National Research Council. Scientific experts from a variety of social and behavioral disciplines met to plan a new national survey on social mobility that will provide the first definitive evidence on recent and long-term trends in social mobility, with the objectives of coming to an understanding of the substantial advances in the methods and statistics for modeling mobility, in survey methodology and population-based survey experiments, in opportunities to merge administrative and survey data, and in the techniques of measuring race, class, education, and income. The workshop also focused on documenting the state of understanding of the mechanisms through which inequality is generated in the past four decades. In the absence of a survey designed and dedicated to the collection of information to assess the status of social mobility, a wide variety of data sources designed for other purposes have been pressed into service in order to illuminate the state of social mobility and its trends. "Developing New National Data on Social Mobility" discusses the key decision points associated with launching a new national level survey of social mobility. This report considers various aspects of a major new national survey, including identifying relevant new theoretical perspectives and technical issues that have implications for modeling, measurement, and data collection.
Developing Number Knowledge: Assessment,Teaching and Intervention with 7-11 year olds (Math Recovery)
by Robert J Wright Pamela D Tabor David Ellemor-CollinsFollowing the great success of the earlier books, this fourth book in the Mathematics Recovery series equips teachers with detailed pedagogical knowledge and resources for teaching number to 7 to 11-year olds. Drawing on extensive programs of research, curriculum development, and teacher development, the book offers a coherent, up-to-date approach emphasising computational fluency and the progressive development of students′ mathematical sophistication. The book is organized in key domains of number instruction, including structuring numbers 1 to 20, knowledge of number words and numerals, conceptual place value, mental computation, written computation methods, fractions, and early algebraic reasoning. Features include: fine-grained progressions of instruction within each domain; detailed descriptions of students′ strategies and difficulties; assessment tasks with notes on students′ responses; classroom-ready instructional activities; This book is designed for classroom and intervention teachers, special education teachers and classroom assistants. The book is an invaluable resource for mathematics advisors and coaches, learning support staff, numeracy consultants, curriculum developers, teacher educators and researchers.
Developing Numeracy in the Secondary School: A Practical Guide for Students and Teachers
by Howard Tanner Sonia Jones Alyson DaviesAs the National Numeracy Strategy (NNS) extends into secondary schools this book for trainee and practicing mathematics teachers provides practical guidance on developing effective strategies for the teaching of numeracy at KS3 and 4 based on the DfEE requirements. The teaching and learning approaches suggested in the NNS are analyzed and explained using case-study examples from secondary schools. Many of these ideas were developed by teacher inquiry groups in the Raising Standards in Numeracy project. The book includes examples of pupils' work; lesson plans and pupil activities; ideas for using ICT to enhance mathematics; teacher guidance on both teaching and assessment; and ideas for developing numeracy across the curriculum. This book offers an introduction to the subject of numeracy accompanied by lesson ideas and practical guidance. It will prove a valuable resource for all trainee and new mathematics teachers.
Developing Primary Mathematics Teaching: Reflecting on Practice with the Knowledge Quartet
by Fay Turner Tim Rowland E Anne Thwaites Peter HuckstepHow can KS1/2 teachers improve their mathematics teaching? This book helps readers to become better, more confident teachers of mathematics by enabling them to focus critically on what they know and what they do in the classroom. Building on their close observation of primary mathematics classrooms, the authors provide those starting out in the teaching profession with a four-stage framework which acts as a tool of support for developing their teaching: - making sense of foundation knowledge - focusing on what teachers know about mathematics - transforming knowledge - representing mathematics to learners through examples, analogies, illustrations and demonstrations - connection - helping learners to make sense of mathematics through understanding how ideas and concepts are linked to each other - contingency - what to do when the unexpected happens Each chapter includes practical activities, lesson descriptions and extracts of classroom transcripts to help teachers reflect on effective practice.
Developing Spatial Data Infrastructures: From Concept to Reality
by Ian Williamson Abbas Rajabifard Mary-Ellen F.FeeneyExpert perspectives on SDI theory and practiceThe spatial data infrastructure (SDI) concept continues to evolve and become an increasingly important element of the infrastructure that supports economic development, environmental management, and social stability. Because of its dynamic and complex nature, however, it remains a fuzzy concept
Developing Students’ Reasoning in Precalculus: Covariational Explorations Enriched by Rates of Change and Limits (Springer Texts in Education)
by Andrzej SokolowskiThis book aims to develop high school and undergraduate students’ covariational reasoning and algebraic skills to succeed in calculus and STEM subjects. The book reflects on contemporary research in math education where students explore algebraic tools and reason mathematically to construct new knowledge. The volume is made up of six chapters covering polynomial, rational, and transcendental functions. An early introduction of limits to support the analyses of linear functions progresses to other book chapters ensuring consistency, parallelism, and a scaffold knowledge delivery. A gradual introduction to function rates of change along with function monotonicity and concavity intertwines with modeling techniques that merge students’ mathematical reasoning with scientific contexts. A forthcoming online component of the book consists of ready-to-download exploratory modeling activities and worksheets that further solidify students’ fluency in understanding how to apply abstract math concepts to gain a deeper understanding of natural and social sciences.
Developing Young Children’s Mathematical Learning Outdoors: Linking Pedagogy and Practice
by Lynda KeithDeveloping Young Children’s Mathematical Learning Outdoors provides detailed guidance and practical advice on planning mathematical experiences for young children outdoors. By examining the key features of a mathematically rich outdoor environment, it illustrates how this can motivate children in leading their own learning and mathematical thinking.Drawing upon the author’s wealth of experience, the book provides support for students and early years' practitioners in developing a deeper understanding of how to plan quality experiences, which combine pedagogy with effective practice. Covering all aspects of mathematics, it identifies meaningful contexts and shows how adults can use open-ended questions and prompts to promote children’s mathematical play outside.With rich case studies and reflective questions included throughout, as well as suggestions for useful resources to put the ideas in the book into practice, it is essential reading for all those that want to develop curious and creative mathematical thinkers in the early years.
Developing a 21st Century Global Library for Mathematics Research
by Committee on Planning a Global Library of the Mathematical SciencesLike most areas of scholarship, mathematics is a cumulative discipline: new research is reliant on well-organized and well-curated literature. Because of the precise definitions and structures within mathematics, today's information technologies and machine learning tools provide an opportunity to further organize and enhance discoverability of the mathematics literature in new ways, with the potential to significantly facilitate mathematics research and learning. Opportunities exist to enhance discoverability directly via new technologies and also by using technology to capture important interactions between mathematicians and the literature for later sharing and reuse. "Developing a 21st Century Global Library for Mathematics Research" discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to make this information system a reality will require much more than indexing and will instead depend on community input paired with machine learning, where mathematicians' expertise can fill the gaps of automatization. This report proposes the establishment of an organization; the development of a set of platforms, tools, and services; the deployment of an ongoing applied research program to complement the development work; and the mobilization and coordination of the mathematical community to take the first steps toward these capabilities. The report recommends building on the extensive work done by many dedicated individuals under the rubric of the World Digital Mathematical Library, as well as many other community initiatives. "Developing a 21st Century Global Library for Mathematics" envisions a combination of machine learning methods and community-based editorial effort that makes a significantly greater portion of the information and knowledge in the global mathematical corpus available to researchers as linked open data through a central organizational entity-referred to in the report as the Digital Mathematics Library. This report describes how such a library might operate - discussing development and research needs, role in facilitating discover and interaction, and establishing partnerships with publishers.
Developing, Validating and Using Internal Ratings
by Giacomo De Laurentis Renato Maino Luca MolteniThis book provides a thorough analysis of internal rating systems. Two case studies are devoted to building and validating statistical-based models for borrowers' ratings, using SPSS-PASW and SAS statistical packages. Mainstream approaches to building and validating models for assigning counterpart ratings to small and medium enterprises are discussed, together with their implications on lending strategy.Key Features:* Presents an accessible framework for bank managers, students and quantitative analysts, combining strategic issues, management needs, regulatory requirements and statistical bases.* Discusses available methodologies to build, validate and use internal rate models.* Demonstrates how to use statistical packages for building statistical-based credit rating systems.* Evaluates sources of model risks and strategic risks when using statistical-based rating systems in lending.This book will prove to be of great value to bank managers, credit and loan officers, quantitative analysts and advanced students on credit risk management courses.
Development Methodologies for Big Data Analytics Systems: Plan-driven, Agile, Hybrid, Lightweight Approaches (Transactions on Computational Science and Computational Intelligence)
by Manuel Mora Jorge Marx Gomez Fen Wang Hector Duran-LimonThis book presents research in big data analytics (BDA) for business of all sizes. The authors analyze problems presented in the application of BDA in some businesses through the study of development methodologies based on the three approaches – 1) plan-driven, 2) agile and 3) hybrid lightweight. The authors first describe BDA systems and how they emerged with the convergence of Statistics, Computer Science, and Business Intelligent Analytics with the practical aim to provide concepts, models, methods and tools required for exploiting the wide variety, volume, and velocity of available business internal and external data - i.e. Big Data – and provide decision-making value to decision-makers. The book presents high-quality conceptual and empirical research-oriented chapters on plan-driven, agile, and hybrid lightweight development methodologies and relevant supporting topics for BDA systems suitable to be used for large-, medium-, and small-sized business organizations.
Development and Planning: Essays in Honour of Paul Rosenstein-Rodan (Routledge Library Editions: Development)
by Paul Rosenstein RodanFirst published in 1972, this is a book of essays offered in honour of Paul Rosenstein-Rodan, the distinguished economist whose career started in mid-1920s Vienna and subsequently spanned Europe, Britain, the USA and many of the less developed countries of the world.The book includes reviews of past developments, chapters on development trade and value theory, an assessment of contemporary emerging economic patterns, development and trade policy, and investment policy. Further essays cover the intellectual history of development economics, general aspects of growth and economic policy in underdeveloped countries and the problems of income distribution and sectoral and regional development.
Development and Protection of Mineral Resources: The Application of Geotechnical Engineering and Geological Exploration in the Development and Protection of Mineral Resources (Springer Series in Geomechanics and Geoengineering)
by Mohamed Abdelkader Ismail Leiming WangThis book comprises papers that showcase recent advancements and applications of innovative technologies in mining, offering theoretical insights and practical references for industry professionals. The 8th International Conference on Mineral Resources, Geotechnology and Geological Exploration (MRGGE 2024) was successfully held on June 14-16, 2024, in Shijiazhuang, China. This conference aims to address the dual challenge of providing essential mineral resources while ensuring environmental protection and sustainability in the mining industry. The proceedings encompass a wide range of topics, including ecological restoration of mines, geotechnical engineering, cleaning materials, geological exploration, and energy storage. The intended readership includes engineers, consultants, managers, academics, scientists, and government officials actively engaged in the mineral industry, serving as a valuable resource for promoting sustainable practices and advancing the field.
Development of Gene Therapies: Strategic, Scientific, Regulatory, and Access Considerations (Chapman & Hall/CRC Biostatistics Series)
by Oleksandr Sverdlov Avery McIntoshCell and gene therapies have become the third major drug modality in pharmaceutical medicine of the 21st century after low molecular weight and antibody drugs. The gene therapy (GTx) field is rapidly advancing, and yet there are still fundamental scientific questions that remain to be answered. Development of GTx products poses unique challenges and opportunities for drug developers. However, there is lack of a systematic exposition of the GTx product development and the pivotal role of the biostatistician in this process. Development of Gene Therapies: Strategic, Scientific, and Regulatory, and Access Considerations attempts to summarize the current state-of-the-art strategic, scientific, statistical, and regulatory aspects of GTx development. Intended to provide an exposition to the GTx new product development through peer-reviewed papers written by subject matter experts in this emerging field, this book will be useful for researchers in gene therapy drug development, biostatisticians, regulators, patient advocates, graduate students, and the finance and business development community . Key Features: A collection of papers covering a wide spectrum of topics in gene therapies (GTx), written by leading subject matter experts. An exposition of the core principles of GTx product development, emerging business models, industry standards, best practices, and regulatory pathways. An exposition of statistical and innovative modeling tools for design and analysis of clinical trials of GTx. Insights into commercial models, access hurdles, and health economics of gene therapies. Case studies of successful GTx approvals from core team members that developed the first two FDA-approved AAV gene therapies: Luxturna and Zolgensma. A discussion of potential benefits and hurdles to be overcome for GTx in coming years from a multi-stakeholder perspective.
Development of Innovative Drugs via Modeling with MATLAB
by Ronald Gieschke Daniel SerafinThe development of innovative drugs is becoming more difficult while relying on empirical approaches. This inspired all major pharmaceutical companies to pursue alternative model-based paradigms. The key question is: How to find innovative compounds and, subsequently, appropriate dosage regimens? Written from the industry perspective and based on many years of experience, this book offers: - Concepts for creation of drug-disease models, introduced and supplemented with extensive MATLAB programs - Guidance for exploration and modification of these programs to enhance the understanding of key principles - Usage of differential equations to pharmacokinetic, pharmacodynamic and (patho-) physiologic problems thereby acknowledging their dynamic nature - A range of topics from single exponential decay to adaptive dosing, from single subject exploration to clinical trial simulation, and from empirical to mechanistic disease modeling. Students with an undergraduate mathematical background or equivalent education, interest in life sciences and skills in a high-level programming language such as MATLAB, are encouraged to engage in model-based pharmaceutical research and development.
Development of a Methodology for the Evaluation of Active Safety using the Example of Preventive Pedestrian Protection
by Thomas HelmerThe book reports on a new methodology for optimization and evaluation of traffic safety, which simulates the processes involved in traffic conflicts on the basis of detailed dynamical, human, and technical models. The models incorporate the whole spectrum of human cognitive functions and responses, the responses of an active safety system and the interactions between the human and the system as they occur in a sample of relevant traffic contexts. Using the developed method, the author was able to assess the reduction in accidents and injuries as well as the possible side effects resulting from a preventive pedestrian-protection system. The book provides practical solutions in the area of active safety systems. It represents an interesting source of information for researchers and professionals as well as all stakeholders, including policy makers and consumer advocates, with the common goal of promoting the implementation and adoption of highly efficient systems for preventing accidents and injuries.
Development of a Numerical Simulation Method for Rocky Body Impacts and Theoretical Analysis of Asteroidal Shapes (Springer Theses)
by Keisuke SugiuraThis book describes numerical simulations of collisions between asteroids, based on a unique numerical code developed by the author. The code accurately solves the elastic dynamic equations and describes the effects of fracture and friction, which makes it possible to investigate the shapes of impact outcomes produced by asteroid collisions and subsequent gravitational accumulation of fragments.The author parallelizes the code with high parallelization efficiency; accordingly, it can be used to conduct high-resolution simulations with the aid of supercomputers and clarify the shapes of small remnants produced through the catastrophic destruction of asteroids. The author demonstrates that flat asteroids can only be produced by impacts involving objects with similar mass and low velocity, which suggests that the flat asteroids in our solar system were created in the planet formation era and have kept their shapes until today. The author also shows that asteroid collisions under certain conditions can produce the extremely elongated shape of an interstellar minor body, 1I/‘Oumuamua. In brief, the book offers a comprehensive investigation of asteroid impacts and shapes, making it a uniquely valuable resource.
Development of the Settlement Network in the Central European Countries
by András Balogh Tamás CsapóThis volume intends to summarize the most important changes in the Central European countries and their settlement network emphasizing the last 20 years since the collapse of the Iron Curtain.
Development, Globalization, Global Values, and Security: Essays in Honor of Arno Tausch
by Glen SegellThis book, written in honor of Arno Tausch, presents cutting-edge research on globalization, development, and global values. Internationally renowned authors cover topics such as global economic and political cycles, global values, and support for terrorism. Over the last five decades, the Austrian political scientist Arno Tausch was a pioneer in studies on globalization, development and global values. This collection of essays takes up the issues dealt with by Tausch and presents perspectives for the 21st Century. Throughout his work, Tausch applied quantitative methods to study the fundamental issues of the global political economy and the global political system, like dependency, economic and political cycles, and global values, based on a rigorous study of available social scientific data, like the World Values Survey and the Arab Barometer.
Developmental Mathematics
by C. L. Johnston Alden T. Willis Gale M. HughesThis traditional, straight-forward, extremely popular book is noted for its one-step, one-concept-at-a-time approach. In the new edition, the authors have brought in new coverage to meet NCTM standards where appropriate.
Developmental Mathematics
by Elayn Martin-GayElayn Martin-Gay's developmental math program is motivated by her firm belief that every student can succeed. Martin-Gay's focus on the student shapes her clear, accessible writing, inspires her constant pedagogical innovations, and contributes to the popularity and effectiveness of her video resources. This revision of Martin-Gay's algebra series continues her focus on students and what they need to be successful. This program provides a better teaching and learning experience, for you and your students. Here's how: The new Martin-Gay Student Success Program provides an integrated teaching and learning system--combining the textbook, MyMathLab®, student and video organizers, and the video program--which is designed to help students gain the math and study skills they need for success in developmental math and beyond.
Developmental Mathematics
by K. Elayn Martin-GayDevelopmental Mathematics is a new addition to the Martin-Gay work text series and is intended for a 2-3 semester sequence of Basic Math,Introductory Algebra and Intermediate Algebra. The text provides complete coverage for basic mathematics and introductory algebra courses and with the appendices ("further topics in algebra") it provides the necessary intermediate algebra topics. The Whole Numbers; Multiplying and Dividing Fractions; Adding and Subtracting Fractions; Decimals; Per¢ Geometry; Statistics and Probability; Real Numbers and Introduction to Algebra; Equations, Inequalities, and Problem Solving; Graphing Equations and Inequalities; Systems of Linear Equations; Exponents and Polynomials; Factoring Polynomials; Rational Expressions; Roots and Radicals; Quadratic Equations and Nonlinear Graphs; Further Algebraic Topics; Tables; The Bigger Picture; Further Geometric Topics; Inductive and Deductive Reasoning; Sample THEA Test For all readers interested in developmental mathematics.
Developmental Mathematics (Second Edition)
by Elayn Martin-GayElayn Martin-Gay firmly believes that every student can succeed, and her developmental math textbooks and video resources are motivated by this belief. Developmental Mathematics, Second Edition was written to help readers effectively make the transition from arithmetic to algebra. The new edition offers new resources like the Student Organizer and now includes Student Resources in the back of the book to help students on their quest for success.
Developmental Mathematics 2e Textbook And Software Bundle
by Hawkes LearningDevelopmental Mathematics 2e Textbook