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Teaching and Learning Proof Across the Grades

Teaching and Learning Proof Across the Grades Author Despina A. Stylianou
ISBN-10 9781135856748
Release 2010-09-23
Pages 408
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A Co-Publication of Routledge for the National Council of Teachers of Mathematics (NCTM) In recent years there has been increased interest in the nature and role of proof in mathematics education; with many mathematics educators advocating that proof should be a central part of the mathematics education of students at all grade levels. This important new collection provides that much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. Such a story includes understanding how the forms of proof, including the nature of argumentation and justification as well as what counts as proof, evolve chronologically and cognitively and how curricula and instruction can support the development of students’ understanding of proof. Collectively these essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. By building and extending on existing research and by allowing a variety of voices from the field to be heard, Teaching and Learning Proof Across the Grades not only highlights the main ideas that have recently emerged on proof research, but also defines an agenda for future study.

Scripting Approaches in Mathematics Education

Scripting Approaches in Mathematics Education Author Rina Zazkis
ISBN-10 9783319626925
Release 2017-10-30
Pages 425
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This book shows how the practice of script writing can be used both as a pedagogical approach and as a research tool in mathematics education. It provides an opportunity for script-writers to articulate their mathematical arguments and/or their pedagogical approaches. It further provides researchers with a corpus of narratives that can be analyzed using a variety of theoretical perspectives. Various chapters argue for the use of dialogical method and highlight its benefits and special features. The chapters examine both “low tech” implementations as well as the use of a technological platform, LessonSketch. The chapters present results of and insights from several recent studies, which utilized scripting in mathematics education research and practice.

International Perspectives on the Teaching and Learning of Geometry in Secondary Schools

International Perspectives on the Teaching and Learning of Geometry in Secondary Schools Author Patricio Herbst
ISBN-10 9783319774763
Release 2018-04-27
Pages 386
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This book presents current perspectives on theoretical and empirical issues related to the teaching and learning of geometry at secondary schools. It contains chapters contributing to three main areas. A first set of chapters examines mathematical, epistemological, and curricular perspectives. A second set of chapters presents studies on geometry instruction and teacher knowledge, and a third set of chapters offers studies on geometry thinking and learning. Specific research topics addressed also include teaching practice, learning trajectories, learning difficulties, technological resources, instructional design, assessments, textbook analyses, and teacher education in geometry. Geometry remains an essential and critical topic in school mathematics. As they learn geometry, students develop essential mathematical thinking and visualization skills and learn a language that helps them relate to and interact with the physical world. Geometry has traditionally been included as a subject of study in secondary mathematics curricula, but it has also featured as a resource in out-of-school problem solving, and has been connected to various human activities such as sports, games, and artwork. Furthermore, geometry often plays a role in teacher preparation, undergraduate mathematics, and at the workplace. New technologies, including dynamic geometry software, computer-assisted design software, and geometric positioning systems, have provided more resources for teachers to design environments and tasks in which students can learn and use geometry. In this context, research on the teaching and learning of geometry will continue to be a key element on the research agendas of mathematics educators, as researchers continue to look for ways to enhance student learning and to understand student thinking and teachers’ decision making.

Teaching and Learning Algebraic Thinking with 5 to 12 Year Olds

Teaching and Learning Algebraic Thinking with 5  to 12 Year Olds Author Carolyn Kieran
ISBN-10 9783319683515
Release 2017-12-04
Pages 443
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This book highlights new developments in the teaching and learning of algebraic thinking with 5- to 12-year-olds. Based on empirical findings gathered in several countries on five continents, it provides a wealth of best practices for teaching early algebra. Building on the work of the ICME-13 (International Congress on Mathematical Education) Topic Study Group 10 on Early Algebra, well-known authors such as Luis Radford, John Mason, Maria Blanton, Deborah Schifter, and Max Stephens, as well as younger scholars from Asia, Europe, South Africa, the Americas, Australia and New Zealand, present novel theoretical perspectives and their latest findings. The book is divided into three parts that focus on (i) epistemological/mathematical aspects of algebraic thinking, (ii) learning, and (iii) teaching and teacher development. Some of the main threads running through the book are the various ways in which structures can express themselves in children’s developing algebraic thinking, the roles of generalization and natural language, and the emergence of symbolism. Presenting vital new data from international contexts, the book provides additional support for the position that essential ways of thinking algebraically need to be intentionally fostered in instruction from the earliest grades.

Journal for Research in Mathematics Education

Journal for Research in Mathematics Education Author
ISBN-10 OSU:32435083072264
Release 2012
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Journal for Research in Mathematics Education has been writing in one form or another for most of life. You can find so many inspiration from Journal for Research in Mathematics Education also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Journal for Research in Mathematics Education book for free.

The British National Bibliography

The British National Bibliography Author Arthur James Wells
ISBN-10 STANFORD:36105211722686
Release 2009
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The British National Bibliography has been writing in one form or another for most of life. You can find so many inspiration from The British National Bibliography also informative, and entertaining. Click DOWNLOAD or Read Online button to get full The British National Bibliography book for free.

Proof in mathematics education

Proof in mathematics education Author David Alexander Reid
ISBN-10 9460912443
Release 2010-07
Pages 251
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Research on teaching and learning proof and proving has expanded in recent decades. This reflects the growth of mathematics education research in general, but also an increased emphasis on proof in mathematics education. This development is a welcome one for those interested in the topic, but also poses a challenge, especially to teachers and new scholars. It has become more and more difficult to get an overview of the field and to identify the key concepts used in research on proof and proving. This book is intended to help teachers, researchers and graduate students to overcome the difficulty of getting an overview of research on proof and proving. It reviews the key findings and concepts in research on proof and proving, and embeds them in a contextual frame that allows the reader to make sense of the sometimes contradictory statements found in the literature. It also provides examples from current research that explore how larger patterns in reasoning and argumentation provide insight into teaching and learning.

The Adolescent Brain

The Adolescent Brain Author Valerie F. Reyna
ISBN-10 UCSD:31822039410113
Release 2012
Pages 457
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"This book brings together the work of scientists with basic or foundational research expertise (e.g., cognitive, developmental, and social psychologists; neuroscientists) and those with an applied emphasis (e.g., on education; public health; applied economics and decision research; and science, technology, engineering, and mathematics, the so-called STEM fields) to address a critically understudied area in life-course learning: higher order cognition in adolescence and young adulthood. The purpose of integrating these scientific communities is twofold: (a) to advance the basic science of the developing brain by focusing scientists on key problems that are ripe for groundbreaking discoveries and (b) to apply cutting-edge theory and high-quality research methods to real-world problems of learning, cognition, and development, thereby enhancing the effectiveness of research and its immediate relevance to pressing societal needs"--Preface. (PsycINFO Database Record (c) 2012 APA, all rights reserved).

Children s Reasoning While Building Fraction Ideas

Children   s Reasoning While Building Fraction Ideas Author Carolyn A. Maher
ISBN-10 9789463510080
Release 2017-06-10
Pages 16
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This book may be used for research, graduate and undergraduate teacher education, and teacher development. It presents an integrated set of studies of a heterogeneously grouped class of twenty-one nine-year olds, engaged in exploring fraction ideas prior to classroom instruction under conditions that supported investigation, collaboration and argumentation. It demonstrates with text and video narrative how young children can reason about mathematics in surprisingly sophisticated ways when provided the opportunity to do so in the proper classroom environment. In this volume, fourth grade students’ reasoning about fraction concepts is described through careful analysis and accompanying video excerpts showcasing the variety and originality of their thinking. These children will serve as an inspiration for educators to encourage the development of reasoning and argumentation in their students as part of a mathematics curriculum designed to produce critical thinkers.

Mathematics Teaching in the Middle School

Mathematics Teaching in the Middle School Author
ISBN-10 PSU:000061876484
Release 2009-08
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Mathematics Teaching in the Middle School has been writing in one form or another for most of life. You can find so many inspiration from Mathematics Teaching in the Middle School also informative, and entertaining. Click DOWNLOAD or Read Online button to get full Mathematics Teaching in the Middle School book for free.

Algebra in the Early Grades

Algebra in the Early Grades Author James J. Kaput
ISBN-10 9781351577083
Release 2017-09-25
Pages 552
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This volume is the first to offer a comprehensive, research-based, multi-faceted look at issues in early algebra. In recent years, the National Council for Teachers of Mathematics has recommended that algebra become a strand flowing throughout the K-12 curriculum, and the 2003 RAND Mathematics Study Panel has recommended that algebra be “the initial topical choice for focused and coordinated research and development [in K-12 mathematics].” This book provides a rationale for a stronger and more sustained approach to algebra in school, as well as concrete examples of how algebraic reasoning may be developed in the early grades. It is organized around three themes: The Nature of Early Algebra Students’ Capacity for Algebraic Thinking Issues of Implementation: Taking Early Algebra to the Classrooms. The contributors to this landmark volume have been at the forefront of an effort to integrate algebra into the existing early grades mathematics curriculum. They include scholars who have been developing the conceptual foundations for such changes as well as researchers and developers who have led empirical investigations in school settings. Algebra in the Early Grades aims to bridge the worlds of research, practice, design, and theory for educators, researchers, students, policy makers, and curriculum developers in mathematics education.

Mathematical Proficiency for All Students Toward a Strategic Research and Development Program in Mathematics Education

Mathematical Proficiency for All Students  Toward a Strategic Research and Development Program in Mathematics Education Author Deborah Loewenberg
ISBN-10 9780833034113
Release 2003-04-15
Pages 122
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A clear need exists for substantial improvement in mathematics proficiency in U.S. schools. The RAND Mathematics Study Panel was convened to inform the U.S. Department of Education's Office of Educational Research and Improvement on ways to improve the quality and usability of education research and development (R&D). The panel identified three areas for focused R&D: development of teachers' mathematical knowledge used in teaching; teaching and learning of skills needed for mathematical thinking and problem-solving; and teaching and learning of algebra from kindergarten through the 12th grade.

Advanced Mathematical Thinking

Advanced Mathematical Thinking Author David Tall
ISBN-10 9780306472039
Release 2006-04-11
Pages 292
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This book is the first major study of advanced mathematical thinking as performed by mathematicians and taught to students in senior high school and university. Topics covered include the psychology of advanced mathematical thinking, the processes involved, mathematical creativity, proof, the role of definitions, symbols, and reflective abstraction. It is highly appropriate for the college professor in mathematics or the general mathematics educator.

A Handbook for Teaching and Learning in Higher Education

A Handbook for Teaching and Learning in Higher Education Author Heather Fry
ISBN-10 9781317650225
Release 2014-08-21
Pages 452
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This entirely new edition of a very successful book focuses on developing professional academic skills for supporting and supervising student learning and effective teaching. It is built on the premise that the roles of those who teach in higher education are complex and multi-faceted. A Handbook for Teaching and Learning in Higher Education is sensitive to the competing demands of teaching, research, scholarship, and academic management. The new edition reflects and responds to the rapidly changing context of higher education and to current understanding of how to best support student learning. Drawing together a large number of expert authors, it continues to feature extensive use of case studies that show how successful teachers have implemented these ideas. It includes key topics such as student engagement and motivation, internationalisation, employability, inclusive strategies for teaching, effective use of technology and issues relating to postgraduate students and student retention. Part 1 explores a number of aspects of the context of UK higher education that affect the education of students, looking at the drivers of institutional behaviours and how to achieve success as a university teacher. Part 2 examines learning, teaching and supervising in higher education and includes chapters on working with diversity, encouraging independent learning and learning gain. Part 3 considers approaches to teaching and learning in different disciplines, covering a full range including arts and humanities, social sciences, experimental sciences through to medicine and dentistry. Written to support the excellence in teaching and learning design required to bring about student learning of the highest quality, this will be essential reading for all new lecturers, particularly anyone taking an accredited course in teaching and learning in higher education, as well as those experienced lecturers who wish to improve their teaching practice. Those working in adult learning and educational development will also find the book to be a particularly useful resource. In addition it will appeal to staff who support learning and teaching in various other roles.

Education for Life and Work

Education for Life and Work Author Committee on Defining Deeper Learning and 21st Century Skills
ISBN-10 9780309256506
Release 2013-01-01
Pages 229
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Americans have long recognized that investments in public education contribute to the common good, enhancing national prosperity and supporting stable families, neighborhoods, and communities. Education is even more critical today, in the face of economic, environmental, and social challenges. Today's children can meet future challenges if their schooling and informal learning activities prepare them for adult roles as citizens, employees, managers, parents, volunteers, and entrepreneurs. To achieve their full potential as adults, young people need to develop a range of skills and knowledge that facilitate mastery and application of English, mathematics, and other school subjects. At the same time, business and political leaders are increasingly asking schools to develop skills such as problem solving, critical thinking, communication, collaboration, and self-management - often referred to as "21st century skills." Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century describes this important set of key skills that increase deeper learning, college and career readiness, student-centered learning, and higher order thinking. These labels include both cognitive and non-cognitive skills- such as critical thinking, problem solving, collaboration, effective communication, motivation, persistence, and learning to learn. 21st century skills also include creativity, innovation, and ethics that are important to later success and may be developed in formal or informal learning environments. This report also describes how these skills relate to each other and to more traditional academic skills and content in the key disciplines of reading, mathematics, and science. Education for Life and Work: Developing Transferable Knowledge and Skills in the 21st Century summarizes the findings of the research that investigates the importance of such skills to success in education, work, and other areas of adult responsibility and that demonstrates the importance of developing these skills in K-16 education. In this report, features related to learning these skills are identified, which include teacher professional development, curriculum, assessment, after-school and out-of-school programs, and informal learning centers such as exhibits and museums.

Mathematics Learning in Early Childhood

Mathematics Learning in Early Childhood Author National Research Council
ISBN-10 0309147433
Release 2009-11-13
Pages 398
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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.

Proofs without Words II

Proofs without Words II Author Roger B. Nelsen
ISBN-10 0883857219
Release 2000-12-07
Pages 142
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Like its predecessor, Proofs without Words, this book is a collection of pictures or diagrams that help the reader see why a particular mathematical statement may be true, and how one could begin to go about proving it. While in some proofs without words an equation or two may appear to help guide that process, the emphasis is clearly on providing visual clues to stimulate mathematical thought. The proofs in this collection are arranged by topic into five chapters: geometry and algebra; trigonometry, calculus and analytic geometry; inequalities; integer sums; and sequences and series. Teachers will find that many of the proofs in this collection are well suited for classroom discussion and for helping students to think visually in mathematics.