teaching and learning proof across the grades a k 16 perspective studies in mathematical thinking and learning series

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Teaching And Learning Proof Across The Grades

Author : Despina A. Stylianou
ISBN : 9781135856748
Genre : Education
File Size : 90. 68 MB
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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

Author : Rina Zazkis
ISBN : 9783319626925
Genre : Education
File Size : 51. 98 MB
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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

Author : Patricio Herbst
ISBN : 9783319774763
Genre : Education
File Size : 55. 56 MB
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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

Author : Carolyn Kieran
ISBN : 9783319683515
Genre : Education
File Size : 29. 78 MB
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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.

Mathematical Argumentation In Middle School The What Why And How

Author : Jennifer Knudsen
ISBN : 9781506394237
Genre : Education
File Size : 21. 6 MB
Format : PDF
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Get them talking: Your formula for bringing math concepts to life! Want your middle schoolers to intelligently engage with mathematical ideas? Look no further. This research-based gem brings tough Standards for Mathematical Practice 3 standards for mathematical argumentation and critical reasoning alive—all within a thoroughly explained four-part model that covers generating cases, conjecturing, justifying, and concluding. Immediately engage students in fun, classroom-ready argumentation activities Help students explore—and take ownership of—mathematical ideas and concepts Promote precise use of mathematical language Includes games, vignettes, a rich companion website, sample tasks, and links to online tools. Bring well-planned, well-constructed mathematical discourse to life in your classroom today!

Mathematics Teaching Learning And Liberation In The Lives Of Black Children

Author : Danny Bernard Martin
ISBN : 9781135590963
Genre : Education
File Size : 68. 81 MB
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With issues of equity at the forefront of mathematics education research and policy, Mathematics Teaching, Learning, and Liberation in the Lives of Black Children fills the need for authoritative, rigorous scholarship that sheds light on the ways that young black learners experience mathematics in schools and their communities. This timely collection significantly extends the knowledge base on mathematics teaching, learning, participation, and policy for black children and it provides new framings of relevant issues that researchers can use in future work. More importantly, this book helps move the field beyond analyses that continue to focus on and normalize failure by giving primacy to the stories that black learners tell about themselves and to the voices of mathematics educators whose work has demonstrated a commitment to the success of these children.

Proving In The Elementary Mathematics Classroom

Author : Andreas J. Stylianides
ISBN : 9780191034725
Genre : Mathematics
File Size : 53. 23 MB
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Although proving is core to mathematics as a sense-making activity, it currently has a marginal place in elementary classrooms internationally. Blending research with practical perspectives, this book addresses what it would take to elevate the place of proving at elementary school. The book uses classroom episodes from two countries to examine different kinds of proving tasks and the proving activity they can generate in the elementary classroom. It examines further the role of teachers in mediating the relationship between proving tasks and proving activity, including major mathematical and pedagogical issues that arise for teachers as they implement each kind of proving task. In addition to its contribution to research knowledge, the book has important implications for teaching, curricular resources, and teacher education.

Handbook Of Research On Teaching

Author : Drew Gitomer
ISBN : 9780935302554
Genre : Education
File Size : 29. 87 MB
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The Fifth Edition of the Handbook of Research on Teachingis an essential resource for students and scholars dedicated to the study of teaching and learning. This volume offers a vast array of topics ranging from the history of teaching to technological and literacy issues. In each authoritative chapter, the authors summarize the state of the field while providing conceptual overviews of critical topics related to research on teaching. Each of the volume's 23 chapters is a canonical piece that will serve as a reference tool for the field. The Handbook provides readers with an unaparalleled view of the current state of research on teaching across its multiple facets and related fields.

Proof In Mathematics Education

Author : David Alexander Reid
ISBN : 9460912443
Genre : Education
File Size : 84. 76 MB
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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.

Children S Reasoning While Building Fraction Ideas

Author : Carolyn A. Maher
ISBN : 9789463510080
Genre : Education
File Size : 25. 49 MB
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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.

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