Understanding Mathematics and Science Matters


Book Description

The research reported in this book provides reliable evidence on and knowledge about mathematics and science instruction that emphasizes student understanding--instruction consistent with the needs of students who will be citizens in an increasingly demanding technological world. The National Center for Improving Student Learning in Mathematics and Science--established in 1996 as a research center and funded by the U.S. Department of Education--was instrumental in developing instructional practices supportive of high student achievement in and understanding of mathematics and science concepts. NCISLA researchers worked with teachers, students, and administrators to construct learning environments that exemplify current research and theory about effective learning of mathematics and science. The careful programs of research conducted examined how instructional content and design, assessment, professional development, and organizational support can be designed, implemented, and orchestrated to support the learning of all students. This book presents a summary of the concepts, findings, and conclusions of the Center's research from 1996-2001. In the Introduction, the chapters in Understanding Mathematics and Science Matters are situated in terms of the reform movement in school mathematics and school science. Three thematically structured sections focus on, respectively, research directed toward what is involved when students learn mathematics and science with understanding; research on the role of teachers and the problems they face when attempting to teach their students mathematics and science with understanding; and a collaboration among some of the contributors to this volume to gather information about classroom assessment practices and organizational support for reform. The goal of this book is to help educational practitioners, policymakers, and the general public to see the validity of the reform recommendations, understand the recommended guidelines, and to use these to transform teaching and learning of mathematics and science in U.S. classrooms.




Science Matters


Book Description

A science book for the general reader that is informative enough to be a popular textbook and yet well-written enough to appeal to general readers. “Hazen and Trefil [are] unpretentious—good, down-to-earth, we-can-explain-anything science teachers, the kind you wish you had but never did.”—The New York Times Book Review Knowledge of the basic ideas and principles of science is fundamental to cultural literacy. But most books on science are often too obscure or too specialized to do the general reader much good. Science Matters is a rare exception—a science book that is informative enough for introductory courses in high school and college, and yet lucid enough for readers uncomfortable with scientific jargon and complicated mathematics. And now, revised and expanded, it is up-to-date, so that readers can enjoy Hazen and Trefil's refreshingly accessible explanations of the most recent developments in science, from particle physics to biotechnology.




Science Matters


Book Description

All earnest and honest human quests for knowledge are efforts to understand Nature, which includes both human and nonhuman systems, the objects of study in science. Thus, broadly speaking, all these quests are in the science domain. The methods and tools used may be different; for example, the literary people use mainly their bodily sensors and their brain as the information processor, while natural scientists may use, in addition, measuring instruments and computers. Yet, all these activities could be viewed in a unified perspective ? they are scientific developments at varying stages of maturity and have a lot to learn from each other.That ?everything in Nature is part of science? was well recognized by Aristotle, da Vinci and many others. Yet, it is only recently, with the advent of modern science and experiences gathered in the study of statistical physics, complex systems and other disciplines, that we know how the human-related disciplines can be studied scientifically.Science Matters is about all human-dependent knowledge, wherein humans (the material system of Homo sapiens) are studied scientifically from the perspective of complex systems. It includes all the topics covered in the humanities and social sciences. Containing contributions from knowledgeable humanists, social scientists and physicists, the book is intended for those ? from artists to scientists ? who are curious about the world and are interested in understanding it with a unified perspective.




Philosophy of Science Matters


Book Description

Nineteen distinguished philosophers, including four Lakatos award winners, address various aspects of Peter Achinstein's influential views on the nature of scientific evidence, explanation, and realism -- with replies from Achinstein himself.




Science Matters


Book Description

Explains the basic scientific principles that govern our world, and shows how they manifest themselves in our everyday lives




How Not to Be Wrong


Book Description

A brilliant tour of mathematical thought and a guide to becoming a better thinker, How Not to Be Wrong shows that math is not just a long list of rules to be learned and carried out by rote. Math touches everything we do; It's what makes the world make sense. Using the mathematician's methods and hard-won insights-minus the jargon-professor and popular columnist Jordan Ellenberg guides general readers through his ideas with rigor and lively irreverence, infusing everything from election results to baseball to the existence of God and the psychology of slime molds with a heightened sense of clarity and wonder. Armed with the tools of mathematics, we can see the hidden structures beneath the messy and chaotic surface of our daily lives. How Not to Be Wrong shows us how--Publisher's description.




High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice


Book Description

Empower students to be the change—join the teaching mathematics for social justice movement! We live in an era in which students have —through various media and their lived experiences— a more visceral experience of social, economic, and environmental injustices. However, when people think of social justice, mathematics is rarely the first thing that comes to mind. Through model lessons developed by over 30 diverse contributors, this book brings seemingly abstract high school mathematics content to life by connecting it to the issues students see and want to change in the world. Along with expert guidance from the lead authors, the lessons in this book explain how to teach mathematics for self- and community-empowerment. It walks teachers step-by-step through the process of using mathematics—across all high school content domains—as a tool to explore, understand, and respond to issues of social injustice including: environmental injustice; wealth inequality; food insecurity; and gender, LGBTQ, and racial discrimination. This book features: Content cross-referenced by mathematical concept and social issues Downloadable instructional materials for student use User-friendly and logical interior design for daily use Guidance for designing and implementing social justice lessons driven by your own students’ unique passions and challenges Timelier than ever, teaching mathematics through the lens of social justice will connect content to students’ daily lives, fortify their mathematical understanding, and expose them to issues that will make them responsive citizens and leaders in the future.




Mathematics and Scientific Representation


Book Description

Mathematics plays a central role in much of contemporary science, but philosophers have struggled to understand what this role is or how significant it might be for mathematics and science. In this book Christopher Pincock tackles this perennial question in a new way by asking how mathematics contributes to the success of our best scientific representations. In the first part of the book this question is posed and sharpened using a proposal for how we can determine the content of a scientific representation. Several different sorts of contributions from mathematics are then articulated. Pincock argues that each contribution can be understood as broadly epistemic, so that what mathematics ultimately contributes to science is best connected with our scientific knowledge. In the second part of the book, Pincock critically evaluates alternative approaches to the role of mathematics in science. These include the potential benefits for scientific discovery and scientific explanation. A major focus of this part of the book is the indispensability argument for mathematical platonism. Using the results of part one, Pincock argues that this argument can at best support a weak form of realism about the truth-value of the statements of mathematics. The book concludes with a chapter on pure mathematics and the remaining options for making sense of its interpretation and epistemology. Thoroughly grounded in case studies drawn from scientific practice, this book aims to bring together current debates in both the philosophy of mathematics and the philosophy of science and to demonstrate the philosophical importance of applications of mathematics.




Handbook of Child Psychology and Developmental Science, Cognitive Processes


Book Description

The essential reference for human development theory, updated and reconceptualized The Handbook of Child Psychology and Developmental Science, a four-volume reference, is the field-defining work to which all others are compared. First published in 1946, and now in its Seventh Edition, the Handbook has long been considered the definitive guide to the field of developmental science. Volume 2: Cognitive Processes describes cognitive development as a relational phenomenon that can be studied only as part of a larger whole of the person and context relational system that sustains it. In this volume, specific domains of cognitive development are contextualized with respect to biological processes and sociocultural contexts. Furthermore, key themes and issues (e.g., the importance of symbolic systems and social understanding) are threaded across multiple chapters, although every each chapter is focused on a different domain within cognitive development. Thus, both within and across chapters, the complexity and interconnectivity of cognitive development are well illuminated. Learn about the inextricable intertwining of perceptual development, motor development, emotional development, and brain development Understand the complexity of cognitive development without misleading simplification, reducing cognitive development to its biological substrates, or viewing it as a passive socialization process Discover how each portion of the developmental process contributes to subsequent cognitive development Examine the multiple processes – such as categorizing, reasoning, thinking, decision making and judgment – that comprise cognition The scholarship within this volume and, as well, across the four volumes of this edition, illustrate that developmental science is in the midst of a very exciting period. There is a paradigm shift that involves increasingly greater understanding of how to describe, explain, and optimize the course of human life for diverse individuals living within diverse contexts. This Handbook is the definitive reference for educators, policy-makers, researchers, students, and practitioners in human development, psychology, sociology, anthropology, and neuroscience.




International Handbook of Research in History, Philosophy and Science Teaching


Book Description

This inaugural handbook documents the distinctive research field that utilizes history and philosophy in investigation of theoretical, curricular and pedagogical issues in the teaching of science and mathematics. It is contributed to by 130 researchers from 30 countries; it provides a logically structured, fully referenced guide to the ways in which science and mathematics education is, informed by the history and philosophy of these disciplines, as well as by the philosophy of education more generally. The first handbook to cover the field, it lays down a much-needed marker of progress to date and provides a platform for informed and coherent future analysis and research of the subject. The publication comes at a time of heightened worldwide concern over the standard of science and mathematics education, attended by fierce debate over how best to reform curricula and enliven student engagement in the subjects. There is a growing recognition among educators and policy makers that the learning of science must dovetail with learning about science; this handbook is uniquely positioned as a locus for the discussion. The handbook features sections on pedagogical, theoretical, national, and biographical research, setting the literature of each tradition in its historical context. It reminds readers at a crucial juncture that there has been a long and rich tradition of historical and philosophical engagements with science and mathematics teaching, and that lessons can be learnt from these engagements for the resolution of current theoretical, curricular and pedagogical questions that face teachers and administrators. Science educators will be grateful for this unique, encyclopaedic handbook, Gerald Holton, Physics Department, Harvard University This handbook gathers the fruits of over thirty years’ research by a growing international and cosmopolitan community Fabio Bevilacqua, Physics Department, University of Pavia




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