TY - BOOK AU - National Research Council A2 - Christopher T. Cross A2 - Taniesha A. Woods A2 - Heidi Schweingruber TI - Mathematics Learning in Early Childhood: Paths Toward Excellence and Equity SN - DO - 10.17226/12519 PY - 2009 UR - https://nap.nationalacademies.org/catalog/12519/mathematics-learning-in-early-childhood-paths-toward-excellence-and-equity PB - The National Academies Press CY - Washington, DC LA - English KW - Education AB - 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. ER - TY - BOOK AU - National Research Council A2 - Jeremy Kilpatrick A2 - Jane Swafford A2 - Bradford Findell TI - Adding It Up: Helping Children Learn Mathematics SN - DO - 10.17226/9822 PY - 2001 UR - https://nap.nationalacademies.org/catalog/9822/adding-it-up-helping-children-learn-mathematics PB - The National Academies Press CY - Washington, DC LA - English KW - Education AB - 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. ER - TY - BOOK AU - National Research Council A2 - M. Suzanne Donovan A2 - John D. Bransford TI - How Students Learn: Mathematics in the Classroom SN - DO - 10.17226/11101 PY - 2005 UR - https://nap.nationalacademies.org/catalog/11101/how-students-learn-mathematics-in-the-classroom PB - The National Academies Press CY - Washington, DC LA - English KW - Education AB - How Students Learn: Mathematics in the Classroom builds on the discoveries detailed in the best-selling How People Learn. Now these findings are presented in a way that teachers can use immediately, to revitalize their work in the classroom for even greater effectiveness. This book shows how to overcome the difficulties in teaching math to generate real insight and reasoning in math students. It also features illustrated suggestions for classroom activities. ER - TY - BOOK AU - National Research Council TI - Fueling Innovation and Discovery: The Mathematical Sciences in the 21st Century SN - DO - 10.17226/13373 PY - 2012 UR - https://nap.nationalacademies.org/catalog/13373/fueling-innovation-and-discovery-the-mathematical-sciences-in-the-21st PB - The National Academies Press CY - Washington, DC LA - English KW - Math, Chemistry, and Physics KW - Surveys and Statistics AB - The mathematical sciences are part of everyday life. Modern communication, transportation, science, engineering, technology, medicine, manufacturing, security, and finance all depend on the mathematical sciences. Fueling Innovation and Discovery describes recent advances in the mathematical sciences and advances enabled by mathematical sciences research. It is geared toward general readers who would like to know more about ongoing advances in the mathematical sciences and how these advances are changing our understanding of the world, creating new technologies, and transforming industries. Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence. Prepared as part of the study on the Mathematical Sciences in 2025, a broad assessment of the current state of the mathematical sciences in the United States, Fueling Innovation and Discovery presents mathematical sciences advances in an engaging way. The report describes the contributions that mathematical sciences research has made to advance our understanding of the universe and the human genome. It also explores how the mathematical sciences are contributing to healthcare and national security, and the importance of mathematical knowledge and training to a range of industries, such as information technology and entertainment. Fueling Innovation and Discovery will be of use to policy makers, researchers, business leaders, students, and others interested in learning more about the deep connections between the mathematical sciences and every other aspect of the modern world. To function well in a technologically advanced society, every educated person should be familiar with multiple aspects of the mathematical sciences. ER - TY - BOOK AU - National Research Council A2 - Jeremy Kilpatrick A2 - Jane Swafford TI - Helping Children Learn Mathematics SN - DO - 10.17226/10434 PY - 2002 UR - https://nap.nationalacademies.org/catalog/10434/helping-children-learn-mathematics PB - The National Academies Press CY - Washington, DC LA - English KW - Education AB - 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. ER - TY - BOOK AU - National Research Council TI - Mathematics and 21st Century Biology SN - DO - 10.17226/11315 PY - 2005 UR - https://nap.nationalacademies.org/catalog/11315/mathematics-and-21st-century-biology PB - The National Academies Press CY - Washington, DC LA - English KW - Biology and Life Sciences KW - Math, Chemistry, and Physics KW - Surveys and Statistics AB - The exponentially increasing amounts of biological data along with comparable advances in computing power are making possible the construction of quantitative, predictive biological systems models. This development could revolutionize those biology-based fields of science. To assist this transformation, the U.S. Department of Energy asked the National Research Council to recommend mathematical research activities to enable more effective use of the large amounts of existing genomic information and the structural and functional genomic information being created. The resulting study is a broad, scientifically based view of the opportunities lying at the mathematical science and biology interface. The book provides a review of past successes, an examination of opportunities at the various levels of biological systems— from molecules to ecosystems—an analysis of cross-cutting themes, and a set of recommendations to advance the mathematics-biology connection that are applicable to all agencies funding research in this area. ER - TY - BOOK AU - National Research Council TI - Assessing the Reliability of Complex Models: Mathematical and Statistical Foundations of Verification, Validation, and Uncertainty Quantification SN - DO - 10.17226/13395 PY - 2012 UR - https://nap.nationalacademies.org/catalog/13395/assessing-the-reliability-of-complex-models-mathematical-and-statistical-foundations PB - The National Academies Press CY - Washington, DC LA - English KW - Math, Chemistry, and Physics KW - Surveys and Statistics AB - Advances in computing hardware and algorithms have dramatically improved the ability to simulate complex processes computationally. Today's simulation capabilities offer the prospect of addressing questions that in the past could be addressed only by resource-intensive experimentation, if at all. Assessing the Reliability of Complex Models recognizes the ubiquity of uncertainty in computational estimates of reality and the necessity for its quantification. As computational science and engineering have matured, the process of quantifying or bounding uncertainties in a computational estimate of a physical quality of interest has evolved into a small set of interdependent tasks: verification, validation, and uncertainty of quantification (VVUQ). In recognition of the increasing importance of computational simulation and the increasing need to assess uncertainties in computational results, the National Research Council was asked to study the mathematical foundations of VVUQ and to recommend steps that will ultimately lead to improved processes. Assessing the Reliability of Complex Models discusses changes in education of professionals and dissemination of information that should enhance the ability of future VVUQ practitioners to improve and properly apply VVUQ methodologies to difficult problems, enhance the ability of VVUQ customers to understand VVUQ results and use them to make informed decisions, and enhance the ability of all VVUQ stakeholders to communicate with each other. This report is an essential resource for all decision and policy makers in the field, students, stakeholders, UQ experts, and VVUQ educators and practitioners. ER - TY - BOOK A2 - John Derbyshire TI - Unknown Quantity: A Real and Imaginary History of Algebra SN - DO - 10.17226/11540 PY - 2006 UR - https://nap.nationalacademies.org/catalog/11540/unknown-quantity-a-real-and-imaginary-history-of-algebra PB - The National Academies Press CY - Washington, DC LA - English KW - Explore Science KW - Math, Chemistry, and Physics KW - Surveys and Statistics AB - Prime Obsession taught us not to be afraid to put the math in a math book. Unknown Quantity heeds the lesson well. So grab your graphing calculators, slip out the slide rules, and buckle up! John Derbyshire is introducing us to algebra through the ages -- and it promises to be just what his die-hard fans have been waiting for. "Here is the story of algebra." With this deceptively simple introduction, we begin our journey. Flanked by formulae, shadowed by roots and radicals, escorted by an expert who navigates unerringly on our behalf, we are guaranteed safe passage through even the most treacherous mathematical terrain. Our first encounter with algebraic arithmetic takes us back 38 centuries to the time of Abraham and Isaac, Jacob and Joseph, Ur and Haran, Sodom and Gomorrah. Moving deftly from Abel's proof to the higher levels of abstraction developed by Galois, we are eventually introduced to what algebraists have been focusing on during the last century. As we travel through the ages, it becomes apparent that the invention of algebra was more than the start of a specific discipline of mathematics -- it was also the birth of a new way of thinking that clarified both basic numeric concepts as well as our perception of the world around us. Algebraists broke new ground when they discarded the simple search for solutions to equations and concentrated instead on abstract groups. This dramatic shift in thinking revolutionized mathematics. Written for those among us who are unencumbered by a fear of formulae, Unknown Quantity delivers on its promise to present a history of algebra. Astonishing in its bold presentation of the math and graced with narrative authority, our journey through the world of algebra is at once intellectually satisfying and pleasantly challenging. ER -