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Uncovering Student Thinking in Mathematics, Grades 6-12: 30 Formative Assessment Probes for the Secondary Classroom
by Cheryl Rose Tobey Carolyn B. ArlineDiscussing standards, research, and more, these 30 probes help secondary teachers assess students' grasp of core mathematics concepts and modify their instruction to improve student achievement.
Uncovering Student Thinking in Mathematics, Grades K-5: 25 Formative Assessment Probes for the Elementary Classroom
by Cheryl Rose Tobey Leslie G. MintonThis book provides 25 easily administered assessments of learners' math knowledge that help teachers monitor learning in real time and improve all students' math skills.
Undecidability, Uncomputability, and Unpredictability (The Frontiers Collection)
by Anthony Aguirre Zeeya Merali David SloanFor a brief time in history, it was possible to imagine that a sufficiently advanced intellect could, given sufficient time and resources, in principle understand how to mathematically prove everything that was true. They could discern what math corresponds to physical laws, and use those laws to predict anything that happens before it happens. That time has passed. Gödel’s undecidability results (the incompleteness theorems), Turing’s proof of non-computable values, the formulation of quantum theory, chaos, and other developments over the past century have shown that there are rigorous arguments limiting what we can prove, compute, and predict. While some connections between these results have come to light, many remain obscure, and the implications are unclear. Are there, for example, real consequences for physics — including quantum mechanics — of undecidability and non-computability? Are there implications for our understanding of the relations between agency, intelligence, mind, and the physical world? This book, based on the winning essays from the annual FQXi competition, contains ten explorations of Undecidability, Uncomputability, and Unpredictability. The contributions abound with connections, implications, and speculations while undertaking rigorous but bold and open-minded investigation of the meaning of these constraints for the physical world, and for us as humans.
Under the Sky We Make: How to Be Human in a Warming World
by Kimberly NicholasIt's warming. It's us. We're sure. It's bad. But we can fix it.After speaking to the international public for close to fifteen years about sustainability, climate scientist Dr. Nicholas realized that concerned people were getting the wrong message about the climate crisis. Yes, companies and governments are hugely responsible for the mess we're in. But individuals CAN effect real, significant, and lasting change to solve this problem. Nicholas explores finding purpose in a warming world, combining her scientific expertise and her lived, personal experience in a way that seems fresh and deeply urgent: Agonizing over the climate costs of visiting loved ones overseas, how to find low-carbon love on Tinder, and even exploring her complicated family legacy involving supermarket turkeys.In her astonishing book Under the Sky We Make, Nicholas does for climate science what Michael Pollan did more than a decade ago for the food on our plate: offering a hopeful, clear-eyed, and somehow also hilarious guide to effecting real change, starting in our own lives. Saving ourselves from climate apocalypse will require radical shifts within each of us, to effect real change in our society and culture. But it can be done. It requires, Dr. Nicholas argues, belief in our own agency and value, alongside a deep understanding that no one will ever hand us power--we're going to have to seize it for ourselves.
The Undercount of Young Children in the U.S. Decennial Census
by William P. O'HareThis book covers several dimensions of the undercount of young children in the U. S. Decennial Census, examines the data from the 2010 U. S. Decennial Census in detail and looks at trends in the undercount of children over time. Other aspects included are the geographic distribution of the net undercount and an exploration for some of the potential explanations for the high net undercount of children. The number of young children in the US is growing, but almost one million young children (under age 5) were missed in the 2010 U. S. Decennial Census. The net undercount of young children has been higher than any other age group for the past several decades and is increasing rapidly, but little attention has been paid to the issue but demographers or the public.
Undergraduate Algebra: A Unified Approach (Springer Undergraduate Mathematics Series)
by Matej BrešarThis textbook offers an innovative approach to abstract algebra, based on a unified treatment of similar concepts across different algebraic structures. This makes it possible to express the main ideas of algebra more clearly and to avoid unnecessary repetition.The book consists of two parts: The Language of Algebra and Algebra in Action. The unified approach to different algebraic structures is a primary feature of the first part, which discusses the basic notions of algebra at an elementary level. The second part is mathematically more complex, covering topics such as the Sylow theorems, modules over principal ideal domains, and Galois theory.Intended for an undergraduate course or for self-study, the book is written in a readable, conversational style, is rich in examples, and contains over 700 carefully selected exercises.
Undergraduate Mathematics Competitions (1995–2016)
by Volodymyr Brayman Alexander KukushVersatile and comprehensive in content, this book of problems will appeal to students in nearly all areas of mathematics. The text offers original and advanced problems proposed from 1995 to 2016 at the Mathematics Olympiads. Essential for undergraduate students, PhD students, and instructors, the problems in this book vary in difficulty and cover most of the obligatory courses given at the undergraduate level, including calculus, algebra, geometry, discrete mathematics, measure theory, complex analysis, differential equations, and probability theory. Detailed solutions to all of the problems from Part I are supplied in Part II, giving students the ability to check their solutions and observe new and unexpected ideas. Most of the problems in this book are not technical and allow for a short and elegant solution. The problems given are unique and non-standard; solving the problems requires a creative approach as well as a deep understanding of the material. Nearly all of the problems are originally authored by lecturers, PhD students, senior undergraduates, and graduate students of the mechanics and mathematics faculty of Taras Shevchenko National University of Kyiv as well as by many others from Belgium, Canada, Great Britain, Hungary, and the United States.
An Undergraduate Primer in Algebraic Geometry (UNITEXT #129)
by Ciro CilibertoThis book consists of two parts. The first is devoted to an introduction to basic concepts in algebraic geometry: affine and projective varieties, some of their main attributes and examples. The second part is devoted to the theory of curves: local properties, affine and projective plane curves, resolution of singularities, linear equivalence of divisors and linear series, Riemann–Roch and Riemann–Hurwitz Theorems.The approach in this book is purely algebraic. The main tool is commutative algebra, from which the needed results are recalled, in most cases with proofs. The prerequisites consist of the knowledge of basics in affine and projective geometry, basic algebraic concepts regarding rings, modules, fields, linear algebra, basic notions in the theory of categories, and some elementary point–set topology.This book can be used as a textbook for an undergraduate course in algebraic geometry. The users of the book are not necessarily intended to become algebraic geometers but may be interested students or researchers who want to have a first smattering in the topic. The book contains several exercises, in which there are more examples and parts of the theory that are not fully developed in the text. Of some exercises, there are solutions at the end of each chapter.
Undernutrition in India: Causes, Consequences and Policy Measures (Sustainable Development Goals Series)
by Aparajita Chattopadhyay Akancha Singh Samriddhi S. GupteThis book deals with issues related to undernutrition and anaemia in India. It establishes its interconnectedness with poverty, tribal living conditions, contraception usage, dietary diversity, and socioeconomic inequality. It addresses SDG 2, namely “end hunger, achieve food security and improved nutrition, and promote sustainable agriculture.” It puts forth the linkages between mother's economic empowerment and children's nutritional status, anaemia of women with particular reference to tribal women, and the issues associated with anaemia in India. It also delves into the relationship between contraceptive usage and anaemia level. It explores the proximate and intermediate determinants of undernutrition disaggregated at the state level in India. It elaborates the importance of ensuring food security and suggests policy measures to improve maternal and child health. The book is an asset for all researchers, academicians, clinicians and policy makers dealing with sociology, economics, public policy, social work, population study, gender issues, biostatistics, health, development, and nutrition.
Understand Statistics: Teach Yourself
by Alan GrahamDo you want to better understand the statistics you hear everyday - and recognise if you're being misled? Here is a straightforward introduction to the principles of this vital field of mathematics. Assuming minimal knowledge and using examples from a wide variety of everyday contexts, this book makes even complex concepts and techniques easy to grasp.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the author's many years of experience.TEST YOURSELFTests in the book and online to keep track of your progress.EXTEND YOUR KNOWLEDGEExtra online articles at www.teachyourself.com to give you a richer understanding of psychology.FIVE THINGS TO REMEMBERQuick refreshers to help you remember the key facts.TRY THISInnovative exercises illustrate what you've learnt and how to use it.
Understand Statistics: Teach Yourself
by Alan GrahamDo you want to better understand the statistics you hear everyday - and recognise if you're being misled? Here is a straightforward introduction to the principles of this vital field of mathematics. Assuming minimal knowledge and using examples from a wide variety of everyday contexts, this book makes even complex concepts and techniques easy to grasp.NOT GOT MUCH TIME?One, five and ten-minute introductions to key principles to get you started.AUTHOR INSIGHTSLots of instant help with common problems and quick tips for success, based on the author's many years of experience.TEST YOURSELFTests in the book and online to keep track of your progress.EXTEND YOUR KNOWLEDGEExtra online articles at www.teachyourself.com to give you a richer understanding of psychology.FIVE THINGS TO REMEMBERQuick refreshers to help you remember the key facts.TRY THISInnovative exercises illustrate what you've learnt and how to use it.
Understandable Statistics: Concepts and Methods, Advanced Placement High School Edition (7th Edition)
by Charles Henry Brase Corrinne Pellillo BraseThe seventh edition of Understandable Statistics: Concepts and Methods continues to emphasize concepts of statistics. Statistical methods are carefully presented with a focus on understanding both the suitability of the method and the meaning of the result. Statistical methods and measurements are developed in the context of applications.
Understandable Statistics: Concepts and Methods
by Charles Henry Brase Corrinne Pellillo BraseUnderstandable Statistics is a thorough, yet approachable statistics text. Designed to help students overcome their apprehension about statistics, the text provides guidance and informal advice showing students the links between statistics and their everyday lives. To reinforce this approach, the book integrates real-life data selected from a variety of sources including journals, periodicals, newspapers and the Internet. The use of graphing calculators, Excel, Minitab and SPSS is covered, but not required. A set of technology resources accompanying the Eighth Edition, designed to provide reinforcement for struggling students, includes a market-leading video and DVD series, interactive lessons, and simulations.
Understandable Statistics: Concepts and Methods (Tenth Edition)
by Charles Henry Brase Corrinne Pellillo BraseUnderstandable Statistics: Concepts and Methods, Tenth Edition is a thorough, yet accessible program designed to help readers overcome their apprehensions about statistics. The authors provide clear guidance and informal advice while showing the links between statistics and the world.
Understanding Analysis
by Stephen AbbottThis lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one. Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler's computation of ζ(2), the Weierstrass Approximation Theorem, and the gamma function are now among the book's cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis. Review of the first edition: "This is a dangerous book. Understanding Analysis is so well-written and the development of the theory so w ell-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. . . . Understanding Analysis is perfectly titled; if your students read it, that's what's going to happen. . . . This terrific book will become the text of choice for the single-variable introductory analysis course . . . " -- Steve Kennedy, MAA Reviews
Understanding Analysis and its Connections to Secondary Mathematics Teaching (Springer Texts in Education)
by Nicholas H. Wasserman Timothy Fukawa-Connelly Keith Weber Juan Pablo Mejía Ramos Stephen AbbottGetting certified to teach high school mathematics typically requires completing a course in real analysis. Yet most teachers point out real analysis content bears little resemblance to secondary mathematics and report it does not influence their teaching in any significant way. This textbook is our attempt to change the narrative. It is our belief that analysis can be a meaningful part of a teacher's mathematical education and preparation for teaching. This book is a companion text. It is intended to be a supplemental resource, used in conjunction with a more traditional real analysis book.The textbook is based on our efforts to identify ways that studying real analysis can provide future teachers with genuine opportunities to think about teaching secondary mathematics. It focuses on how mathematical ideas are connected to the practice of teaching secondary mathematics–and not just the content of secondary mathematics itself. Discussions around pedagogy are premised on the belief that the way mathematicians do mathematics can be useful for how we think about teaching mathematics. The book uses particular situations in teaching to make explicit ways that the content of real analysis might be important for teaching secondary mathematics, and how mathematical practices prevalent in the study of real analysis can be incorporated as practices for teaching.This textbook will be of particular interest to mathematics instructors–and mathematics teacher educators–thinking about how the mathematics of real analysis might be applicable to secondary teaching, as well as to any prospective (or current) teacher who has wondered about what the purpose of taking such courses could be.
Understanding and Applying Basic Statistical Methods Using R
by Rand R. WilcoxFeatures a straightforward and concise resource for introductory statistical concepts, methods, and techniques using R Understanding and Applying Basic Statistical Methods Using R uniquely bridges the gap between advances in the statistical literature and methods routinely used by non-statisticians. Providing a conceptual basis for understanding the relative merits and applications of these methods, the book features modern insights and advances relevant to basic techniques in terms of dealing with non-normality, outliers, heteroscedasticity (unequal variances), and curvature. Featuring a guide to R, the book uses R programming to explore introductory statistical concepts and standard methods for dealing with known problems associated with classic techniques. Thoroughly class-room tested, the book includes sections that focus on either R programming or computational details to help the reader become acquainted with basic concepts and principles essential in terms of understanding and applying the many methods currently available. Covering relevant material from a wide range of disciplines, Understanding and Applying Basic Statistical Methods Using R also includes: Numerous illustrations and exercises that use data to demonstrate the practical importance of multiple perspectives Discussions on common mistakes such as eliminating outliers and applying standard methods based on means using the remaining data Detailed coverage on R programming with descriptions on how to apply both classic and more modern methods using R A companion website with the data and solutions to all of the exercises Understanding and Applying Basic Statistical Methods Using R is an ideal textbook for an undergraduate and graduate-level statistics courses in the science and/or social science departments. The book can also serve as a reference for professional statisticians and other practitioners looking to better understand modern statistical methods as well as R programming.
Understanding and Applying Research Design
by Martin Lee Abbott Jennifer MckinneyA fresh approach to bridging research design with statistical analysis While good social science requires both research design and statistical analysis, most books treat these two areas separately. Understanding and Applying Research Design introduces an accessible approach to integrating design and statistics, focusing on the processes of posing, testing, and interpreting research questions in the social sciences.The authors analyze real-world data using SPSS software, guiding readers on the overall process of science, focusing on premises, procedures, and designs of social scientific research. Three clearly organized sections move seamlessly from theoretical topics to statistical techniques at the heart of research procedures, and finally, to practical application of research design:Premises of Research introduces the research process and the capabilities of SPSS, with coverage of ethics, Empirical Generalization, and Chi Square and Contingency Table AnalysisProcedures of Research explores key quantitative methods in research design including measurement, correlation, regression, and causationDesigns of Research outlines various design frameworks, with discussion of survey research, aggregate research, and experimentsThroughout the book, SPSS software is used to showcase the discussed techniques, and detailed appendices provide guidance on key statistical procedures and tips for data management. Numerous exercises allow readers to test their comprehension of the presented material, and a related website features additional data sets and SPSS code.Understanding and Applying Research Design is an excellent book for social sciences and education courses on research methods at the upper-undergraduate level. The book is also an insightful reference for professionals who would like to learn how to pose, test, and interpret research questions with confidence.
Understanding and Changing the World: From Information to Knowledge and Intelligence
by Joseph SifakisThis book discusses the importance of knowledge as an intangible asset, separate from physical entities, that can enable us to understand and/or change the world. It provides a thorough treatment of knowledge, one that is free of ideological and philosophical preconceptions, and which relies exclusively on concepts and principles from the theory of computing and logic. It starts with an introduction to knowledge as truthful and useful information, and its development and management by computers and humans. It analyses the relationship between computational processes and physical phenomena, as well as the processes of knowledge production and application by humans and computers. In turn, the book presents autonomous systems that are called upon to replace humans in complex operations as a step toward strong AI, and discusses the risks – real or hypothetical – of the careless use of these systems. It compares human and machine intelligence, attempting to answer the question of whether and to what extent computers, as they stand today, can approach human-level situation awareness and decision-making. Lastly, the book explains the functioning of individual consciousness as an autonomous system that manages short- and long-term objectives on the basis of value criteria and accumulated knowledge. It discusses how individual values are shaped in society and the role of institutions in fostering and maintaining a common set of values for strengthening social cohesion. The book differs from books on the philosophy of science in many respects, e.g. by considering knowledge in its multiple facets and degrees of validity and truthfulness. It follows the dualist tradition of logicians, emphasizing the importance of logic and language and considering an abstract concept of information very different from the one used in the physical sciences. From this perspective, it levels some hopefully well-founded criticism at approaches that consider information and knowledge as nothing more than the emergent properties of physical phenomena. The book strikes a balance between popular books that sidestep fundamental issues and focus on sensationalism, and scientific or philosophical books that are not accessible to non-experts. As such, it is intended for a broad audience interested in the role of knowledge as a driver for change and development, and as a common good whose production and application could shape the future of humanity.
Understanding and Conducting Research in the Health Sciences
by Christopher J. Cunningham Bart L. Weathington David J. PittengerA comprehensive introduction to behavioral and social science research methods in the health sciencesUnderstanding and Conducting Research in the Health Sciences is designed to develop and facilitate the ability to conduct research and understand the practical value of designing, conducting, interpreting, and reporting behavioral and social science research findings in the health science and medical fields. The book provides complete coverage of the process behind these research methods, including information-gathering, decision formation, and results presentation.Examining the application of behavioral and social science research methodologies within the health sciences, the book focuses on implementing and developing relevant research questions, collecting and managing data, and communicating various research perspectives. An essential book for readers looking to possess an understanding of all aspects of conducting research in the health science field, Understanding and Conducting Research in the Health Sciences features:Various research designs that are appropriate for use in the health sciences, including single-participant, multi-group, longitudinal, correlational, and experimental designsStep-by-step coverage of single-factor and multifactor studies as well as single-subject and nonexperimental methodsAccessible chapter explanations, real-world examples, and numerous illustrations throughoutGuidance regarding how to write about research within the formatting styles of the American Medical Association and the American Psychological AssociationThe book is an excellent educational resource for healthcare and health service practitioners and researchers who are interested in conducting and understanding behavioral and social science research done within the health sciences arena. The book is also a useful resource for students taking courses in the fields of medicine, public health, epidemiology, biostatistics, and the health sciences.
Understanding and Interpreting Machine Learning in Medical Image Computing Applications: First International Workshops, Mlcn 2018, Dlf 2018, And Imimic 2018, Held In Conjunction With Miccai 2018, Granada, Spain, September 16-20, 2018, Proceedings (Lecture Notes in Computer Science #11038)
by Danail Stoyanov Zeike Taylor Seyed Mostafa Kia Ipek Oguz Mauricio Reyes Anne Martel Lena Maier-Hein Andre F. Marquand Edouard Duchesnay Tommy Löfstedt Bennett Landman M. Jorge Cardoso Carlos A. Silva Sergio Pereira Raphael MeierThis book constitutes the refereed joint proceedings of the First International Workshop on Machine Learning in Clinical Neuroimaging, MLCN 2018, the First International Workshop on Deep Learning Fails, DLF 2018, and the First International Workshop on Interpretability of Machine Intelligence in Medical Image Computing, iMIMIC 2018, held in conjunction with the 21st International Conference on Medical Imaging and Computer-Assisted Intervention, MICCAI 2018, in Granada, Spain, in September 2018. The 4 full MLCN papers, the 6 full DLF papers, and the 6 full iMIMIC papers included in this volume were carefully reviewed and selected. The MLCN contributions develop state-of-the-art machine learning methods such as spatio-temporal Gaussian process analysis, stochastic variational inference, and deep learning for applications in Alzheimer's disease diagnosis and multi-site neuroimaging data analysis; the DLF papers evaluate the strengths and weaknesses of DL and identify the main challenges in the current state of the art and future directions; the iMIMIC papers cover a large range of topics in the field of interpretability of machine learning in the context of medical image analysis.
Understanding and Managing Socioeconomic Systems Behaviour: Applications of Qualitative and Quantitative System Dynamics and Agent-Based Modelling in Healthcare and Pharmaceuticals, Finance, Arts and Culture, Sociology and Education Systems (Contributions to Management Science)
by Rossen Kazakov Penka Petrova Yavora KazakovaThis book illustrates effective decision-making in complex socio-economic systems utilising system dynamics and agent-based simulation modelling approaches. It provides practical guidance on the application of conceptual and numerical modelling and simulation for analysing economic, strategic, regulatory, sociological and ethical questions from a complex systems perspective. Its theoretical, methodological and practical illustrations will enhance readers’ understanding of the application of simulation modelling for effective systems management. By virtually experimenting with alternative management scenarios, it will help them improve decision-making and control mechanisms. The book explores practical examples from the fields of pharmaceuticals, healthcare, finance, sociology, education and culture from a strategic, regulatory and ethics perspective. As such, it offers a valuable resource for managers, both at for-profit corporations and non-profit organisations, public policymakers and regulators alike.
Understanding and Teaching Primary Mathematics
by Tony CottonWritten by an education consultant with widespread experience of teaching mathematics in the UK and internationally, Understanding and Teaching Primary Mathematics seamlessly combines pedagogy and subject knowledge to build confidence and equip you with all the skills and know-how you need to successfully teach mathematics to children of any age. This 3rd edition has been fully updated to reflect the latest research developments and initiatives in the field, as well as key changes to both the UK National Curriculum and International Baccalaureate, including a brand new chapter on 'Algebra' and a reworked focus on the early years. Extra features also include helpful call-outs to the book's revised and updated companion website, which offers a shared site with a range of resources relevant to both this book and its new companion volume, Teaching for Mathematical Understanding. Stimulating, accessible and well-illustrated, with comprehensive coverage of subject knowledge and pedagogy, Understanding and Teaching Primary Mathematics is an essential purchase for trainee and practising teachers alike. Companion website features new to this edition include: video clips in which the author demonstrates the concepts covered in the book through teaching to a real class PowerPoint presentations which provide support for those using the book as a part of a teacher training course updated weblinks to external sites with useful teaching information and resources
Understanding and Teaching Primary Mathematics
by Tony CottonWritten by an experienced teacher and teacher educator with widespread experience of teaching mathematics in the UK and internationally, the bestselling Understanding and Teaching Primary Mathematics combines pedagogy and subject knowledge to build confidence and equip you with all the skills and know-how you need to successfully teach mathematics to children of any age.This fifth edition has been completely updated to include the latest developments in learning and teaching mathematics, including mastery approaches, a Singapore approach and the use of manipulatives in the primary classroom. There are new activities for you to use in your teaching and links to the dedicated website, which contains materials to develop a personal portfolio, more activities to use in your classroom and presentations and podcasts to support your further professional development to reflect the latest research developments. It covers all areas of the mathematics curriculum and will allow you to become a confident teacher of mathematics through developing your own subject knowledge.Tony draws on his many years of experience teaching mathematics and working with early career teachers to share classroom activities which will support you in learning mathematics through engaging in mathematical activity with your learners.
Understanding and Teaching Primary Mathematics in Australia
by Tony Cotton Jess Greenbaum Michael MinasWritten by experienced teacher educator and author, Tony Cotton, and two Australian primary teachers, Jess Greenbaum and Michael Minas, Understanding and Teaching Primary Mathematics in Australia combines pedagogy and mathematics subject knowledge to build teachers’ confidence both in their mathematical subject knowledge and in their ability to teach mathematics effectively. The book covers all the key areas of the Australian Curriculum for mathematics from teaching number and calculation strategies to exploring geometry and statistics. There are also chapters that deal with the teaching of mathematics in the Early Years, inclusive approaches to mathematics teaching and teaching mathematics using ICT. Stimulating, accessible and containing a wealth of practical ideas for use in the classroom, Understanding and Teaching Primary Mathematics in Australia is an essential text for graduate and practicing teachers alike.