Early childhood mathematics is vitally important for young children's present and future educational success. Research demonstrates that virtually all young children have the capability to learn and become competent in mathematics. Furthermore, young children enjoy their early informal experiences with mathematics. Unfortunately, many children's potential in mathematics is not fully realized, especially those children who are economically disadvantaged. This is due, in part, to a lack of opportunities to learn mathematics in early childhood settings or through everyday experiences in the home and in their communities. Improvements in early childhood mathematics education can provide young children with the foundation for school success. Relying on a comprehensive review of the research, Mathematics Learning in Early Childhood lays out the critical areas that should be the focus of young children's early mathematics education, explores the extent to which they are currently being incorporated in early childhood settings, and identifies the changes needed to improve the quality of mathematics experiences for young children. This book serves as a call to action to improve the state of early childhood mathematics. It will be especially useful for policy makers and practitioners-those who work directly with children and their families in shaping the policies that affect the education of young children.
The Everyday Mathematics (EM) program was developed by the University of Chicago School Mathematics Project (UCSMP) and is now used in more than 185,000 classrooms by almost three million students. Its research-based learning delivers the kinds of results that all school districts aspire to. Yet despite that tremendous success, EMoften leaves parents perplexed. Learning is accomplished not through rote memorization, but by actually engaging in real-life math tasks. The curriculum isn’t linear, but rather spirals back and forth, weaving concepts in and out of lessons that build overall understanding and long-term retention. It’s no wonder that many parents have difficulty navigating this innovative mathematical and pedagogic terrain. Now help is here. Inspired by UCSMP’s firsthand experiences with parents and teachers, Everyday Mathematics for Parents will equip parents with an understanding of EM and enable them to help their children with homework—the heart of the great parental adventure of ensuring that children become mathematically proficient. Featuring accessible explanations of the research-based philosophy and design of the program, and insights into the strengths of EM, this little book provides the big-picture information that parents need. Clear descriptions of how and why this approach is different are paired with illustrative tables that underscore the unique attributes of EM. Detailed guidance for assisting students with homework includes explanations of the key EM concepts that underlie each assignment. Resources for helping students practice math more at home also provide an understanding of the long-term utility of EM. Easy to use, yet jam-packed with knowledge and helpful tips, Everyday Mathematics for Parents will become a pocket mentor to parents and teachers new to EM who are ready to step up and help children succeed. With this book in hand, you’ll finally understand that while this may not be the way that you learned math, it’s actually much better.
This 1990 book is aimed at teachers, mathematics educators and general readers who are interested in mathematics education from a psychological point of view.
Adding It Up explores how students in pre-K through 8th grade learn mathematics and recommends how teaching, curricula, and teacher education should change to improve mathematics learning during these critical years. The committee identifies five interdependent components of mathematical proficiency and describes how students develop this proficiency. With examples and illustrations, the book presents a portrait of mathematics learning: Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction. Details on the processes by which students acquire mathematical proficiency with whole numbers, rational numbers, and integers, as well as beginning algebra, geometry, measurement, and probability and statistics. The committee discusses what is known from research about teaching for mathematics proficiency, focusing on the interactions between teachers and students around educational materials and how teachers develop proficiency in teaching mathematics.
The major creations and developments in mathematics from the beginnings in Babylonia and Egypt through the first few decades of the twentieth century are presented with clarity and precision in this comprehensive historical study.
Mathematicians call it the Monty Hall Problem, and it is one of the most interesting mathematical brain teasers of recent times. Imagine that you face three doors, behind one of which is a prize. You choose one but do not open it. The host--call him Monty Hall--opens a different door, always choosing one he knows to be empty. Left with two doors, will you do better by sticking with your first choice, or by switching to the other remaining door? In this light-hearted yet ultimately serious book, Jason Rosenhouse explores the history of this fascinating puzzle. Using a minimum of mathematics (and none at all for much of the book), he shows how the problem has fascinated philosophers, psychologists, and many others, and examines the many variations that have appeared over the years. As Rosenhouse demonstrates, the Monty Hall Problem illuminates fundamental mathematical issues and has abiding philosophical implications. Perhaps most important, he writes, the problem opens a window on our cognitive difficulties in reasoning about uncertainty.
This book includes articles on denotational semanitcs, recursion theoretic aspects of computer science, model theory and algebra, automath and automated reasoning, stability theory, topoi and mathematics, and topoi and logic. It is intended for mathematical logicians and computer scientists.
Results from national and international assessments indicate that school children in the United States are not learning mathematics well enough. Many students cannot correctly apply computational algorithms to solve problems. Their understanding and use of decimals and fractions are especially weak. Indeed, helping all children succeed in mathematics is an imperative national goal. However, for our youth to succeed, we need to change how we're teaching this discipline. Helping Children Learn Mathematics provides comprehensive and reliable information that will guide efforts to improve school mathematics from pre-kindergarten through eighth grade. The authors explain the five strands of mathematical proficiency and discuss the major changes that need to be made in mathematics instruction, instructional materials, assessments, teacher education, and the broader educational system and answers some of the frequently asked questions when it comes to mathematics instruction. The book concludes by providing recommended actions for parents and caregivers, teachers, administrators, and policy makers, stressing the importance that everyone work together to ensure a mathematically literate society.
In this collection of essays written over a period of twenty years, Solomon Feferman explains advanced results in modern logic and employs them to cast light on significant problems in the foundations of mathematics. Most troubling among these is the revolutionary way in which Georg Cantor elaborated the nature of the infinite, and in doing so helped transform the face of twentieth-century mathematics. Feferman details the development of Cantorian concepts and the foundational difficulties they engendered. He argues that the freedom provided by Cantorian set theory was purchased at a heavy philosophical price, namely adherence to a form of mathematical platonism that is difficult to support. Beginning with a previously unpublished lecture for a general audience, Deciding the Undecidable, Feferman examines the famous list of twenty-three mathematical problems posed by David Hilbert, concentrating on three problems that have most to do with logic. Other chapters are devoted to the work and thought of Kurt Gödel, whose stunning results in the 1930s on the incompleteness of formal systems and the consistency of Cantors continuum hypothesis have been of utmost importance to all subsequent work in logic. Though Gödel has been identified as the leading defender of set-theoretical platonism, surprisingly even he at one point regarded it as unacceptable. In his concluding chapters, Feferman uses tools from the special part of logic called proof theory to explain how the vast part--if not all--of scientifically applicable mathematics can be justified on the basis of purely arithmetical principles. At least to that extent, the question raised in two of the essays of the volume, Is Cantor Necessary?, is answered with a resounding no. This volume of important and influential work by one of the leading figures in logic and the foundations of mathematics is essential reading for anyone interested in these subjects.
ELEMENTARY ALGEBRA offers a practical approach to the study of beginning algebra concepts, consistent with the needs of today's student. The authors place special emphasis on the worked examples in each section, treating them as the primary means of instruction, since students rely so heavily on examples to complete assignments. Many of the applications (both within the examples and exercises) are also uniquely designed so that students have an experience that is more true to life--students must read information as it appears in headline news sources and extract only the relevant information needed to solve a stated problem. This promotes the text's focus on developing better study habits, problem solving and critical thinking skills along with orienting students to think and reason mathematically. Through Elementary Algebra, students will not only be better prepared for future math courses, they will be better prepared to solve problems and answer questions they encounter in their own lives. Available with InfoTrac Student Collections http://gocengage.com/infotrac. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.
This classic undergraduate text by an eminent educator acquaints students with the fundamental concepts and methods of mathematics. In addition to introducing many noteworthy historical figures from the eighteenth through the mid-twentieth centuries, the book examines the axiomatic method, set theory, infinite sets, the linear continuum and the real number system, and groups. Additional topics include the Frege-Russell thesis, intuitionism, formal systems, mathematical logic, and the cultural setting of mathematics. Students and teachers will find that this elegant treatment covers a vast amount of material in a single reasonably concise and readable volume. Each chapter concludes with a set of problems and a list of suggested readings. An extensive bibliography and helpful indexes conclude the text.
The National Research Council conducted a study to identify a set of incentives that state governments and local school districts can use to attract Ph.D. scientists and mathematicians to secondary school teaching positions. This project investigated the career ambitions of Ph.D.s in the physical and life sciences through focus groups and a national survey to determine the kinds of work conditions and compensation packages that would induce them to take positions teaching physics, chemistry, biology, and various electives in public high schools or positions developing secondary school science and mathematics curricula. The study conducted interviews with Ph.D.s who are already teaching in secondary schools to ascertain information from their experiences, with local school district administrators to assess what they are realistically willing to offer Ph.D. scientists to attract them, and with higher education administrators to explore programmatic changes they would need to institute to provide Ph.D.s with skills tailored to secondary school teaching. These investigations led to this report which describes the incentives local school districts could use in establishing pilot programs in this area.
ELEMENTARY ALGEBRA, International Edition offers a practical approach to the study of beginning algebra concepts, consistent with the needs of today’s student. The authors place special emphasis on the worked examples in each section, treating them as the primary means of instruction, since students rely so heavily on examples to complete assignments. Many of the applications (both within the examples and exercises) are also uniquely designed so that students have an experience that is more true to life—students must read information as it appears in headline news sources and extract only the relevant information needed to solve a stated problem. This promotes the text’s focus on developing better study habits, problem solving and critical thinking skills along with orienting students to think and reason mathematically. Through ELEMENTARY ALGEBRA, International Edition, students will not only be better prepared for future math courses, they will be better prepared to solve problems and answer questions they encounter in their own lives.
This book takes a novel look at the topics of school mathematics--arithmetic, geometry, algebra, and calculus. In this stroll on the mathematical seashore we hope to find, quoting Newton, "...a smoother pebble or a prettier shell than ordinary..." This book assembles a collection of mathematical pebbles that are important as well as beautiful.
This book contains a key component of the NII 2000 project of the Computer Science and Telecommunications Board, a set of white papers that contributed to and complements the project's final report, The Unpredictable Certainty: Information Infrastructure Through 2000, which was published in the spring of 1996. That report was disseminated widely and was well received by its sponsors and a variety of audiences in government, industry, and academia. Constraints on staff time and availability delayed the publication of these white papers, which offer details on a number of issues and positions relating to the deployment of information infrastructure.
This book takes a fresh look at programs for advanced studies for high school students in the United States, with a particular focus on the Advanced Placement and the International Baccalaureate programs, and asks how advanced studies can be significantly improved in general. It also examines two of the core issues surrounding these programs: they can have a profound impact on other components of the education system and participation in the programs has become key to admission at selective institutions of higher education. By looking at what could enhance the quality of high school advanced study programs as well as what precedes and comes after these programs, this report provides teachers, parents, curriculum developers, administrators, college science and mathematics faculty, and the educational research community with a detailed assessment that can be used to guide change within advanced study programs.
Animal life, now and over the past half billion years, is incredibly diverse. Describing and understanding the evolution of this diversity of body plans - from vertebrates such as humans and fish to the numerous invertebrate groups including sponges, insects, molluscs, and the many groups of worms - is a major goal of evolutionary biology. In this book, a group of leading researchers adopt a modern, integrated approach to describe how current molecular genetic techniques and disciplines as diverse as palaeontology, embryology, and genomics have been combined, resulting in a dramatic renaissance in the study of animal evolution. The last decade has seen growing interest in evolutionary biology fuelled by a wealth of data from molecular biology. Modern phylogenies integrating evidence from molecules, embryological data, and morphology of living and fossil taxa provide a wide consensus of the major branching patterns of the tree of life; moreover, the links between phenotype and genotype are increasingly well understood. This has resulted in a reliable tree of relationships that has been widely accepted and has spawned numerous new and exciting questions that require a reassessment of the origins and radiation of animal life. The focus of this volume is at the level of major animal groups, the morphological innovations that define them, and the mechanisms of change to their embryology that have resulted in their evolution. Current research themes and future prospects are highlighted including phylogeny reconstruction, comparative developmental biology, the value of different sources of data and the importance of fossils, homology assessment, character evolution, phylogeny of major groups of animals, and genome evolution. These topics are integrated in the light of a 'new animal phylogeny', to provide fresh insights into the patterns and processes of animal evolution. Animal Evolution provides a timely and comprehensive statement of progress in the field for academic researchers requiring an authoritative, balanced and up-to-date overview of the topic. It is also intended for both upper level undergraduate and graduate students taking courses in animal evolution, molecular phylogenetics, evo-devo, comparative genomics and associated disciplines.
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
Optical science and engineering affect almost every aspect of our lives. Millions of miles of optical fiber carry voice and data signals around the world. Lasers are used in surgery of the retina, kidneys, and heart. New high-efficiency light sources promise dramatic reductions in electricity consumption. Night-vision equipment and satellite surveillance are changing how wars are fought. Industry uses optical methods in everything from the production of computer chips to the construction of tunnels. Harnessing Light surveys this multitude of applications, as well as the status of the optics industry and of research and education in optics, and identifies actions that could enhance the field's contributions to society and facilitate its continued technical development.
This is your first point of reference in understanding the future direction of sustainable technology. It introduces the very latest in practical sustainability techniques and illustrates the diverse technologies being developed to create optimum eco-efficiency in our built environment. Peter F. Smith takes you through the current research and prototypes which will affect every feature of the evolution of building design. As sustainable building becomes increasingly essential - with the advent of climate change, government legislation and international treaties - this is valuable knowledge for every architect, engineer and designer who wishes their designs to be both responsive and cutting edge. With information from the leaders in their fields, this book is a comprehensive reference to the emerging technologies for this innovative approach to design.
The economic and social challenges confronting the nation today demand that all citizens acquire and learn to use complex reasoning and thinking skills. Education and Learning to Think confronts the issues facing our schools as they take on this mission. This volume reviews previous research, highlights successful learning strategies, and makes specific recommendations about problems and directions requiring further study. Among the topics covered are the nature of thinking and learning, the possibilities of teaching general reasoning, the attempts to improve intelligence, thinking skills in academic disciplines, methods of cultivating the disposition toward higher order thinking and learning, and the integral role motivation plays in these activities.
With the 1989 release of Everybody Counts by the Mathematical Sciences Education Board (MSEB) of the National Research Council and the Curriculum and Evaluation Standards for School Mathematics by the National Council of Teachers of Mathematics (NCTM), the "standards movement" in K-12 education was launched. Since that time, the MSEB and the NCTM have remained committed to deepening the public debate, discourse, and understanding of the principles and implications of standards-based reform. One of the main tenets in the NCTM Standards is commitment to providing high-quality mathematical experiences to all students. Another feature of the Standards is emphasis on development of specific mathematical topics across the grades. In particular, the Standards emphasize the importance of algebraic thinking as an essential strand in the elementary school curriculum. Issues related to school algebra are pivotal in many ways. Traditionally, algebra in high school or earlier has been considered a gatekeeper, critical to participation in postsecondary education, especially for minority students. Yet, as traditionally taught, first-year algebra courses have been characterized as an unmitigated disaster for most students. There have been many shifts in the algebra curriculum in schools within recent years. Some of these have been successful first steps in increasing enrollment in algebra and in broadening the scope of the algebra curriculum. Others have compounded existing problems. Algebra is not yet conceived of as a K-14 subject. Issues of opportunity and equity persist. Because there is no one answer to the dilemma of how to deal with algebra, making progress requires sustained dialogue, experimentation, reflection, and communication of ideas and practices at both the local and national levels. As an initial step in moving from national-level dialogue and speculations to concerted local and state level work on the role of algebra in the curriculum, the MSEB and the NCTM co-sponsored a national symposium, "The Nature and Role of Algebra in the K-14 Curriculum," on May 27 and 28, 1997, at the National Academy of Sciences in Washington, D.C.
Whether or not you use a computer, you probably use a telephone, electric power, and a bank. Although you may not be aware of their presence, networked computer systems are increasingly becoming an integral part of your daily life. Yet, if such systems perform poorly or don't work at all, then they can put life, liberty, and property at tremendous risk. Is the trust that we--as individuals and as a society--are placing in networked computer systems justified? And if it isn't, what can we do to make such systems more trustworthy? This book provides an assessment of the current state of the art procedures for building trustworthy networked information systems. It proposes directions for research in computer and network security, software technology, and system architecture. In addition, the book assesses current technical and market trends in order to better inform public policy as to where progress is likely and where incentives could help. Trust in Cyberspace offers insights into: --The strengths and vulnerabilities of the telephone network and Internet, the two likely building blocks of any networked information system. --The interplay between various dimensions of trustworthiness: environmental disruption, operator error, "buggy" software, and hostile attack. --The implications for trustworthiness of anticipated developments in hardware and software technology, including the consequences of mobile code. --The shifts in security technology and research resulting from replacing centralized mainframes with networks of computers. --The heightened concern for integrity and availability where once only secrecy mattered. --The way in which federal research funding levels and practices have affected the evolution and current state of the science and technology base in this area. You will want to read this book if your life is touched in any way by computers or telecommunications. But then, whose life isn't?
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