@BOOK{NAP author = "National Research Council", editor = "Alix Beatty", title = "Mathematical and Scientific Development in Early Childhood: A Workshop Summary", isbn = "978-0-309-09503-7", abstract = "Expectations for early learning are very different than they were even as recently as a decade ago. With increased recognition of the intellectual capacities of young children, as well as a growing understanding of how these capacities develop and can be fostered, has come a growing recognition that early childhood education, in both formal and informal settings, may not be helping all children maximize their cognitive capacities. Mathematical and Scientific Development in Early Childhood explores the research in cognition and developmental psychology that sheds light on children's capacity to learn mathematical and scientific ideas. This summary report of the discussions and presentations at the workshop is designed to frame the issues relevant to advancing research useful to the development of research-based curricula for mathematics and science for young children.", url = "https://nap.nationalacademies.org/catalog/11178/mathematical-and-scientific-development-in-early-childhood-a-workshop-summary", year = 2005, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP editor = "John Derbyshire", title = "Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics", isbn = "978-0-309-51257-2", abstract = "In August 1859 Bernhard Riemann, a little-known 32-year old mathematician, presented a paper to the Berlin Academy titled: \"On the Number of Prime Numbers Less Than a Given Quantity.\" In the middle of that paper, Riemann made an incidental remark \u2014 a guess, a hypothesis. What he tossed out to the assembled mathematicians that day has proven to be almost cruelly compelling to countless scholars in the ensuing years. Today, after 150 years of careful research and exhaustive study, the question remains. Is the hypothesis true or false?\nRiemann's basic inquiry, the primary topic of his paper, concerned a straightforward but nevertheless important matter of arithmetic \u2014 defining a precise formula to track and identify the occurrence of prime numbers. But it is that incidental remark \u2014 the Riemann Hypothesis \u2014 that is the truly astonishing legacy of his 1859 paper. Because Riemann was able to see beyond the pattern of the primes to discern traces of something mysterious and mathematically elegant shrouded in the shadows \u2014 subtle variations in the distribution of those prime numbers. Brilliant for its clarity, astounding for its potential consequences, the Hypothesis took on enormous importance in mathematics. Indeed, the successful solution to this puzzle would herald a revolution in prime number theory. Proving or disproving it became the greatest challenge of the age.\nIt has become clear that the Riemann Hypothesis, whose resolution seems to hang tantalizingly just beyond our grasp, holds the key to a variety of scientific and mathematical investigations. The making and breaking of modern codes, which depend on the properties of the prime numbers, have roots in the Hypothesis. In a series of extraordinary developments during the 1970s, it emerged that even the physics of the atomic nucleus is connected in ways not yet fully understood to this strange conundrum. Hunting down the solution to the Riemann Hypothesis has become an obsession for many \u2014 the veritable \"great white whale\" of mathematical research. Yet despite determined efforts by generations of mathematicians, the Riemann Hypothesis defies resolution.\nAlternating passages of extraordinarily lucid mathematical exposition with chapters of elegantly composed biography and history, Prime Obsession is a fascinating and fluent account of an epic mathematical mystery that continues to challenge and excite the world. Posited a century and a half ago, the Riemann Hypothesis is an intellectual feast for the cognoscenti and the curious alike. Not just a story of numbers and calculations, Prime Obsession is the engrossing tale of a relentless hunt for an elusive proof \u2014 and those who have been consumed by it.", url = "https://nap.nationalacademies.org/catalog/10532/prime-obsession-bernhard-riemann-and-the-greatest-unsolved-problem-in", year = 2003, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "High School Mathematics at Work: Essays and Examples for the Education of All Students", isbn = "978-0-309-06353-1", abstract = "Traditionally, vocational mathematics and precollege mathematics have been separate in schools. But the technological world in which today's students will work and live calls for increasing connection between mathematics and its applications. Workplace-based mathematics may be good mathematics for everyone.\nHigh School Mathematics at Work illuminates the interplay between technical and academic mathematics. This collection of thought-provoking essays\u2014by mathematicians, educators, and other experts\u2014is enhanced with illustrative tasks from workplace and everyday contexts that suggest ways to strengthen high school mathematical education.\nThis important book addresses how to make mathematical education of all students meaningful\u2014how to meet the practical needs of students entering the work force after high school as well as the needs of students going on to postsecondary education.\nThe short readable essays frame basic issues, provide background, and suggest alternatives to the traditional separation between technical and academic mathematics. They are accompanied by intriguing multipart problems that illustrate how deep mathematics functions in everyday settings\u2014from analysis of ambulance response times to energy utilization, from buying a used car to \"rounding off\" to simplify problems.\nThe book addresses the role of standards in mathematics education, discussing issues such as finding common ground between science and mathematics education standards, improving the articulation from school to work, and comparing SAT results across settings.\nExperts discuss how to develop curricula so that students learn to solve problems they are likely to encounter in life\u2014while also providing them with approaches to unfamiliar problems. The book also addresses how teachers can help prepare students for postsecondary education.\nFor teacher education the book explores the changing nature of pedagogy and new approaches to teacher development. What kind of teaching will allow mathematics to be a guide rather than a gatekeeper to many career paths? Essays discuss pedagogical implication in problem-centered teaching, the role of complex mathematical tasks in teacher education, and the idea of making open-ended tasks\u2014and the student work they elicit\u2014central to professional discourse.\nHigh School Mathematics at Work presents thoughtful views from experts. It identifies rich possibilities for teaching mathematics and preparing students for the technological challenges of the future. This book will inform and inspire teachers, teacher educators, curriculum developers, and others involved in improving mathematics education and the capabilities of tomorrow's work force.", url = "https://nap.nationalacademies.org/catalog/5777/high-school-mathematics-at-work-essays-and-examples-for-the", year = 1998, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Knowing and Learning Mathematics for Teaching: Proceedings of a Workshop", isbn = "978-0-309-07252-6", abstract = "There are many questions about the mathematical preparation teachers need. Recent recommendations from a variety of sources state that reforming teacher preparation in postsecondary institutions is central in providing quality mathematics education to all students. The Mathematics Teacher Preparation Content Workshop examined this problem by considering two central questions:\n\n What is the mathematical knowledge teachers need to know in order to teach well?\n How can teachers develop the mathematical knowledge they need to teach well?\n\nThe Workshop activities focused on using actual acts of teaching such as examining student work, designing tasks, or posing questions, as a medium for teacher learning. The Workshop proceedings, Knowing and Learning Mathematics for Teaching, is a collection of the papers presented, the activities, and plenary sessions that took place.", url = "https://nap.nationalacademies.org/catalog/10050/knowing-and-learning-mathematics-for-teaching-proceedings-of-a-workshop", year = 2001, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Jeremy Kilpatrick and Jane Swafford", title = "Helping Children Learn Mathematics", isbn = "978-0-309-08431-4", abstract = "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\u2019re 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.", url = "https://nap.nationalacademies.org/catalog/10434/helping-children-learn-mathematics", year = 2002, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Everybody Counts: A Report to the Nation on the Future of Mathematics Education", isbn = "978-0-309-03977-2", abstract = "Mathematics is the key to opportunity. No longer only the language of science, mathematics is now essential to business, finance, health, and defense. Yet because of the lack of mathematical literacy, many students are not prepared for tomorrow's jobs. Everybody Counts suggests solutions. Written for everyone concerned about our children's education, this book discusses why students in this country do not perform well in mathematics and outlines a comprehensive plan for revitalizing mathematics education in America, from kindergarten through college.\nsingle copy, $8.95; 2-9 copies, $7.50 each; 10 or more copies, $6.95 each (no other discounts apply)", url = "https://nap.nationalacademies.org/catalog/1199/everybody-counts-a-report-to-the-nation-on-the-future", year = 1989, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Steve Leinwand and Gail Burrill", title = "Improving Mathematics Education: Resources for Decision Making", isbn = "978-0-309-08300-3", abstract = "Improving Mathematics Education has been designed to help inform stakeholders about the decisions they face, to point to recent research findings, and to provide access to the most recent thinking of experts on issues of national concern in mathematics education. The essence of the report is that information is available to help those charged with improving student achievement in mathematics. The documents cited above can guide those who make decisions about content, learning, teaching, and assessment. The report is organized around five key questions:\n\n What should we teach, given what we know and value about mathematics and its roles?\n How should we teach so children learn, given what we know about students, mathematics, and how people learn mathematics?\n What preparation and support do teachers need?\n How do we know whether what we are doing is working?\n What must change?\n\nEach of the five main chapters in this report considers a key area of mathematics education and describes the core messages of current publication(s) in that area. To maintain the integrity of each report's recommendations, we used direct quotes and the terminology defined and used in that report. If the wording or terminology seems to need clarification, the committee refers the reader directly to the original document. Because these areas are interdependent, the documents often offer recommendations related to several different areas. While the individual documents are discussed under only one of the components in Improving Mathematics Education, the reader should recognize that each document may have a broader scope. In general, the references in this report should serve as a starting point for the interested reader, who can refer to the original documents for fuller discussions of the recommendations and, in some cases, suggestions for implementation. Improving Mathematics Education is designed to help educators build a critical knowledge base about mathematics education, recognizing that the future of the nation's students is integrally intertwined with the decisions we make (or fail to make) about the mathematics education they receive.", url = "https://nap.nationalacademies.org/catalog/10268/improving-mathematics-education-resources-for-decision-making", year = 2001, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Ann Shannon", title = "Keeping Score", isbn = "978-0-309-06535-1", abstract = "Curriculum reform, performance assessment, standards, portfolios, and high stakes testing-what's next? What does this all mean for me in my classroom? Many teachers have asked such questions since mathematics led the way in setting standards with the publication of the Curriculum and Evaluation Standards for School Mathematics (National Council of Teachers of Mathematics [NCTM], 1989). This seminal document and others that followed served as catalysts for mathematics education reform, giving rise to new initiatives related to curriculum, instruction, and assessment over the past decade. In particular, approaches to classroom, school, and district-wide assessment have undergone a variety of changes as educators have sought to link classroom teaching to appropriate assessment opportunities.\nSince the publication of Everybody Counts (National Research Council [NRC], 1989), the Mathematical Sciences Education Board (MSEB) has dedicated its efforts to the improvement of mathematics education. A national summit on assessment led to the publication of For Good Measure (NRC, 1991). This statement of goals and objectives for assessment in mathematics was followed by Measuring Up (NRC, 1993a), which provided prototypical fourth-grade performance assessment tasks linked to the goals of the NCTM's Curriculum and Evaluation Standards. Measuring What Counts (NRC, 1993b) demonstrated the importance of mathematics content, learning, and equity as they relate to assessment. The MSEB is now prepared to present perspectives on issues in mathematics education assessment for those most directly engaged in implementing the reform initiatives on a daily basis-classroom teachers, school principals, supervisors, and others in school-based settings.", url = "https://nap.nationalacademies.org/catalog/9635/keeping-score", year = 1999, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Jeremy Kilpatrick and Jane Swafford and Bradford Findell", title = "Adding It Up: Helping Children Learn Mathematics", isbn = "978-0-309-21895-5", abstract = "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. \nThe 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:\n\n Research findings on what children know about numbers by the time they arrive in pre-K and the implications for mathematics instruction.\n 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.\n\nThe 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.", url = "https://nap.nationalacademies.org/catalog/9822/adding-it-up-helping-children-learn-mathematics", year = 2001, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "U.S. Research Institutes in the Mathematical Sciences: Assessment and Perspectives", isbn = "978-0-309-06492-7", abstract = "This report is the result of a fast-track study of U.S. mathematical sciences research institutes done in response to a request from the National Science Foundation (NSF). The task of the Committee on U.S. Mathematical Sciences Research Institutes was to address the following three questions:\n\n What are the characteristic features of effective mathematical sciences research institutes in the ways that they further mathematical research in the United States, and are there ways that the current configuration can be improved?\n What kinds of institutes should there be in the United States, and how many does the nation need?\n How should U.S. mathematical sciences research institutes be configured (with regard to, for example, diversity of operating formats, distribution of mathematical fields, and interinstitute cooperation or coordination) in order to have the nation's mathematical research enterprise continue to be most productive and successful?\n", url = "https://nap.nationalacademies.org/catalog/9449/us-research-institutes-in-the-mathematical-sciences-assessment-and-perspectives", year = 1999, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Mathematics Education in the Middle Grades: Teaching to Meet the Needs of Middle Grades Learners and to Maintain High Expectations: Proceedings of a National Convocation and Action Conferences", isbn = "978-0-309-06797-3", abstract = "In September 1998, the Math Science Education Board National held a Convocation on Middle Grades Mathematics that was co-sponsored by the National Council of Teachers of Mathematics, the National Middle School Association, and the American Educational Research Association. The Convocation was structured to present the teaching of middle school mathematics from two points of view: teaching mathematics with a focus on the subject matter content or teaching mathematics with a focus on the whole child and whole curriculum. This book discusses the challenges before the nation's mathematical sciences community to focus its energy on the improvement of middle grades mathematics education and to begin an ongoing national dialogue on middle grades mathematics education.", url = "https://nap.nationalacademies.org/catalog/9764/mathematics-education-in-the-middle-grades-teaching-to-meet-the", year = 2000, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Gail E. Pritchard", title = "Improving Learning with Information Technology: Report of a Workshop", isbn = "978-0-309-08413-0", abstract = "In spring 2000, representatives from the U.S. Department of Education (DOEd) and senior staff at the National Research Council (NRC) recognized a common frustration: that the potential of information technology to transform K-12 education remains unrealized. In fall 2000 the U.S. DOEd formally requested that the National Academies undertake an interdisciplinary project called Improving Learning with Information Technology (ILIT). The project was launched with a symposium on January 24-25, 2001. This report summarizes the proceedings of the symposium and is intended for people interested in considering better strategies for using information technology in the educational arena. While it offers insights from the presenters on both the challenges to and the opportunities for forging a better dialogue among learning scientists, technologists, and educators, it does not contain conclusions or recommendations. Rather, it highlights issues to consider, constituents to engage, and strategies to employ in the effort to build a coalition to harness the power of information technologies for the improvement of American education. Every effort has been made to convey the speakers' content and viewpoints accurately. Recognizing the speculative nature of many of the speaker contributions, most attributions identify a speaker by area of expertise rather than by name. The report reflects the proceedings of the workshop and is not intended to be a comprehensive review of all the issues involved in the project to improve learning with information technology.", url = "https://nap.nationalacademies.org/catalog/10352/improving-learning-with-information-technology-report-of-a-workshop", year = 2002, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Reshaping School Mathematics: A Philosophy and Framework for Curriculum", isbn = "978-0-309-04187-4", abstract = "The United States must restructure mathematics education\u2014both what is learned and the way it is taught\u2014if children are to develop the mathematical knowledge and skills they will need to be personally and professionally competent in the twenty-first century. Joining the recent reports that have opened a national dialogue on these issues, Reshaping School Mathematics focuses discussion on essential ideas that transcend details of current curricula or assessment results. It examines changing perspectives on the role of mathematics in society and changing practice in the use of technology\u2014particularly calculators and computers\u2014in mathematics education.", url = "https://nap.nationalacademies.org/catalog/1498/reshaping-school-mathematics-a-philosophy-and-framework-for-curriculum", year = 1990, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Christopher T. Cross and Taniesha A. Woods and Heidi Schweingruber", title = "Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity", isbn = "978-0-309-12806-3", abstract = "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.\nRelying 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.\n ", url = "https://nap.nationalacademies.org/catalog/12519/mathematics-learning-in-early-childhood-paths-toward-excellence-and-equity", year = 2009, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP title = "Mathematical Foundations of High-Performance Computing and Communications", url = "https://nap.nationalacademies.org/catalog/9277/mathematical-foundations-of-high-performance-computing-and-communications", year = 1991, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "The Assessment of Science Meets the Science of Assessment: Summary of a Workshop", isbn = "978-0-309-06546-7", abstract = "To explore the connections between new approaches to science education and new developments in assessment, the Board on Testing and Assessment (BOTA) of the National Research Council (NRC) sponsored a two-day conference on February 22 and 23, 1997. Participants included BOTA members, other measurement experts, and educators and policymakers concerned with science education reform. The conference encouraged the exchange of ideas between those with measurement expertise and those with creative approaches to instruction and assessment.", url = "https://nap.nationalacademies.org/catalog/9588/the-assessment-of-science-meets-the-science-of-assessment-summary", year = 1999, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Measuring What Counts: A Conceptual Guide for Mathematics Assessment", isbn = "978-0-309-04981-8", abstract = "To achieve national goals for education, we must measure the things that really count. Measuring What Counts establishes crucial research- based connections between standards and assessment.\nArguing for a better balance between educational and measurement concerns in the development and use of mathematics assessment, this book sets forth three principles\u2014related to content, learning, and equity\u2014that can form the basis for new assessments that support emerging national standards in mathematics education.", url = "https://nap.nationalacademies.org/catalog/2235/measuring-what-counts-a-conceptual-guide-for-mathematics-assessment", year = 1993, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", title = "Measuring What Counts: A Policy Brief", isbn = "978-0-309-04986-3", abstract = "Measuring What Counts: A Policy Brief provides highlights of the main volume in the context of implications for educational policy.", url = "https://nap.nationalacademies.org/catalog/2250/measuring-what-counts-a-policy-brief", year = 1993, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Dianne P. O'Leary and Scott T. Weidman", title = "The Interface of Three Areas of Computer Science with the Mathematical Sciences: Summary of a Workshop", url = "https://nap.nationalacademies.org/catalog/9951/the-interface-of-three-areas-of-computer-science-with-the-mathematical-sciences", year = 2000, publisher = "The National Academies Press", address = "Washington, DC" } @BOOK{NAP author = "National Research Council", editor = "Jere Confrey and Vicki Stohl", title = "On Evaluating Curricular Effectiveness: Judging the Quality of K-12 Mathematics Evaluations", isbn = "978-0-309-09242-5", abstract = "This book reviews the evaluation research literature that has accumulated around 19 K-12 mathematics curricula and breaks new ground in framing an ambitious and rigorous approach to curriculum evaluation that has relevance beyond mathematics. The committee that produced this book consisted of mathematicians, mathematics educators, and methodologists who began with the following charge:\n\n Evaluate the quality of the evaluations of the thirteen National Science Foundation (NSF)-supported and six commercially generated mathematics curriculum materials;\n Determine whether the available data are sufficient for evaluating the efficacy of these materials, and if not;\n Develop recommendations about the design of a project that could result in the generation of more reliable and valid data for evaluating such materials.\n\n The committee collected, reviewed, and classified almost 700 studies, solicited expert testimony during two workshops, developed an evaluation framework, established dimensions\/criteria for three methodologies (content analyses, comparative studies, and case studies), drew conclusions on the corpus of studies, and made recommendations for future research.", url = "https://nap.nationalacademies.org/catalog/11025/on-evaluating-curricular-effectiveness-judging-the-quality-of-k-12", year = 2004, publisher = "The National Academies Press", address = "Washington, DC" }