Teaching And Learning Proof Across The Grades

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Teaching and Learning Proof Across the Grades

Author : Despina A. Stylianou
Publisher : Routledge
ISBN 13 : 1135856745
Total Pages : 515 pages
Book Rating : 4.1/5 (358 download)

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Book Synopsis Teaching and Learning Proof Across the Grades by : Despina A. Stylianou

Download or read book Teaching and Learning Proof Across the Grades written by Despina A. Stylianou and published by Routledge. This book was released on 2010-09-23 with total page 515 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Strengths-Based Teaching and Learning in Mathematics

Author : Beth McCord Kobett
Publisher : Corwin Press
ISBN 13 : 1544374925
Total Pages : 189 pages
Book Rating : 4.5/5 (443 download)

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Book Synopsis Strengths-Based Teaching and Learning in Mathematics by : Beth McCord Kobett

Download or read book Strengths-Based Teaching and Learning in Mathematics written by Beth McCord Kobett and published by Corwin Press. This book was released on 2020-02-27 with total page 189 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book is a game changer! Strengths-Based Teaching and Learning in Mathematics: 5 Teaching Turnarounds for Grades K- 6 goes beyond simply providing information by sharing a pathway for changing practice. . . Focusing on our students’ strengths should be routine and can be lost in the day-to-day teaching demands. A teacher using these approaches can change the trajectory of students’ lives forever. All teachers need this resource! Connie S. Schrock Emporia State University National Council of Supervisors of Mathematics President, 2017-2019 NEW COVID RESOURCES ADDED: A Parent’s Toolkit to Strengths-Based Learning in Math is now available on the book’s companion website to support families engaged in math learning at home. This toolkit provides a variety of home-based activities and games for families to engage in together. Your game plan for unlocking mathematics by focusing on students’ strengths. We often evaluate student thinking and their work from a deficit point of view, particularly in mathematics, where many teachers have been taught that their role is to diagnose and eradicate students’ misconceptions. But what if instead of focusing on what students don’t know or haven’t mastered, we identify their mathematical strengths and build next instructional steps on students’ points of power? Beth McCord Kobett and Karen S. Karp answer this question and others by highlighting five key teaching turnarounds for improving students’ mathematics learning: identify teaching strengths, discover and leverage students’ strengths, design instruction from a strengths-based perspective, help students identify their points of power, and promote strengths in the school community and at home. Each chapter provides opportunities to stop and consider current practice, reflect, and transfer practice while also sharing · Downloadable resources, activities, and tools · Examples of student work within Grades K–6 · Real teachers’ notes and reflections for discussion It’s time to turn around our approach to mathematics instruction, end deficit thinking, and nurture each student’s mathematical strengths by emphasizing what makes them each unique and powerful.

Teaching and Learning Proof Across the Grades

Author : Despina A. Stylianou
Publisher : Taylor & Francis US
ISBN 13 : 9780415887311
Total Pages : 0 pages
Book Rating : 4.8/5 (873 download)

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Book Synopsis Teaching and Learning Proof Across the Grades by : Despina A. Stylianou

Download or read book Teaching and Learning Proof Across the Grades written by Despina A. Stylianou and published by Taylor & Francis US. This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. --from publisher description.

Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12

Author : Amy B. Ellis
Publisher : National
ISBN 13 :
Total Pages : 126 pages
Book Rating : 4.:/5 (31 download)

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Book Synopsis Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 by : Amy B. Ellis

Download or read book Developing Essential Understanding of Proof and Proving for Teaching Mathematics in Grades 9-12 written by Amy B. Ellis and published by National. This book was released on 2012 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focuses on essential knowledge for teachers about proof and the process of proving. It is organised around five big ideas, supported by multiple smaller, interconnected ideas-essential understandings. Taking you beyond a simple introduction to proof and the activities involved in proving, the book will broaden and deepen your mathematical understanding of one of the most challenging topics for students...and teachers.

Proof in Mathematics Education

Author : David A. Reid
Publisher : BRILL
ISBN 13 : 946091246X
Total Pages : 265 pages
Book Rating : 4.4/5 (69 download)

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Book Synopsis Proof in Mathematics Education by : David A. Reid

Download or read book Proof in Mathematics Education written by David A. Reid and published by BRILL. This book was released on 2010-01-01 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Reasoning and Proof

Author : Karren Schultz-Ferrell
Publisher : Math Process Standards
ISBN 13 : 9780325010335
Total Pages : 0 pages
Book Rating : 4.0/5 (13 download)

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Book Synopsis Introduction to Reasoning and Proof by : Karren Schultz-Ferrell

Download or read book Introduction to Reasoning and Proof written by Karren Schultz-Ferrell and published by Math Process Standards. This book was released on 2007 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: NCTM's Process Standards were designed to support teaching that helps children develop independent, effective mathematical thinking. The books in the Heinemann Math Process Standards Series give every elementary teacher the opportunity to explore each one of the standards in depth. And with language and examples that don't require prior math training to understand, the series offers friendly, reassuring advice to any teacher preparing to embrace the Process Standards. In Introduction to Reasoning and Proof, Karren Shultz-Ferrell, Brenda Hammond, and Josepha Roblesfamiliarize you with ways to help students explore their reasoning and support their mathematical thinking. They offer an array of entry points for understanding, planning, and teaching, including strategies that help students develop strong mathematical reasoning and construct solid justifications for their thinking. Full of activities that are modifiable for immediate use with students of all levels and written by veteran teachers for teachers of every level of experience, Introduction to Reasoning and Proof highlights the importance of encouraging children to describe their reasoning about mathematical activities, while also recommending ways to question students about their conclusions and their thought processes in ways that help support classroom-wide learning. Best of all, like all the titles in the Math Process Standards Series, Introduction to Reasoning and Proof comes with two powerful tools to help you get started and plan well: a CD-ROM with activities customizable to match your lessons and a correlation guide that helps you match mathematical content with the processes it utilizes. If your students could benefit from more opportunities to explain their reasoning about math concepts. Or if you're simply looking for new ways to work the reasoning and proof standards into your curriculum, read, dog-ear, and teach with Introduction to Reasoning and Proof. And if you'd like to learn about any of NCTM's process standards, or if you're looking for new, classroom-tested ways to address them in your math teaching, look no further than Heinemann's Math Process Standards Series. You'll find them explained in the most understandable and practical way: from one teacher to another.

Teacher Proof

Author : Tom Bennett
Publisher : Routledge
ISBN 13 : 1135040273
Total Pages : 177 pages
Book Rating : 4.1/5 (35 download)

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Book Synopsis Teacher Proof by : Tom Bennett

Download or read book Teacher Proof written by Tom Bennett and published by Routledge. This book was released on 2013-07-04 with total page 177 pages. Available in PDF, EPUB and Kindle. Book excerpt: ‘Tom Bennett is the voice of the modern teacher.’ - Stephen Drew, Senior Vice-Principal, Passmores Academy, UK, featured on Channel 4’s Educating Essex Do the findings from educational science ever really improve the day-to-day practice of classroom teachers? Education is awash with theories about how pupils best learn and teachers best teach, most often propped up with the inevitable research that ‘proves’ the case in point. But what can teachers do to find the proof within the pudding, and how can this actually help them on wet Wednesday afternoon?. Drawing from a wide range of recent and popular education theories and strategies, Tom Bennett highlights how much of what we think we know in schools hasn’t been ‘proven’ in any meaningful sense at all. He inspires teachers to decide for themselves what good and bad education really is, empowering them as professionals and raising their confidence in the classroom and the staffroom alike. Readers are encouraged to question and reflect on issues such as: the most common ideas in modern education and where these ideas were born the crisis in research right now how research is commissioned and used by the people who make policy in the UK and beyond the provenance of education research: who instigates it, who writes it, and how to spot when a claim is based on evidence and when it isn’t the different way that data can be analysed what happens to the research conclusions once they escape the laboratory. Controversial, erudite and yet unremittingly entertaining, Tom includes practical suggestions for the classroom throughout. This book will be an ally to every teacher who’s been handed an instruction on a platter and been told, ‘the research proves it.’

Proof and Proving in Mathematics Education

Author : Gila Hanna
Publisher : Springer Science & Business Media
ISBN 13 : 9400721293
Total Pages : 468 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Proof and Proving in Mathematics Education by : Gila Hanna

Download or read book Proof and Proving in Mathematics Education written by Gila Hanna and published by Springer Science & Business Media. This book was released on 2012-06-14 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: *THIS BOOK IS AVAILABLE AS OPEN ACCESS BOOK ON SPRINGERLINK* One of the most significant tasks facing mathematics educators is to understand the role of mathematical reasoning and proving in mathematics teaching, so that its presence in instruction can be enhanced. This challenge has been given even greater importance by the assignment to proof of a more prominent place in the mathematics curriculum at all levels. Along with this renewed emphasis, there has been an upsurge in research on the teaching and learning of proof at all grade levels, leading to a re-examination of the role of proof in the curriculum and of its relation to other forms of explanation, illustration and justification. This book, resulting from the 19th ICMI Study, brings together a variety of viewpoints on issues such as: The potential role of reasoning and proof in deepening mathematical understanding in the classroom as it does in mathematical practice. The developmental nature of mathematical reasoning and proof in teaching and learning from the earliest grades. The development of suitable curriculum materials and teacher education programs to support the teaching of proof and proving. The book considers proof and proving as complex but foundational in mathematics. Through the systematic examination of recent research this volume offers new ideas aimed at enhancing the place of proof and proving in our classrooms.

Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

Author : Carolyn Kieran
Publisher : Springer
ISBN 13 : 3319683519
Total Pages : 443 pages
Book Rating : 4.3/5 (196 download)

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Book Synopsis Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds by : Carolyn Kieran

Download or read book Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds written by Carolyn Kieran and published by Springer. This book was released on 2017-12-04 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

Author : Kristen N. Bieda
Publisher : Springer Nature
ISBN 13 : 3030800083
Total Pages : 331 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof by : Kristen N. Bieda

Download or read book Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof written by Kristen N. Bieda and published by Springer Nature. This book was released on 2022-03-03 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book aims to advance ongoing debates in the field of mathematics and mathematics education regarding conceptions of argumentation, justification, and proof and the consequences for research and practice when applying particular conceptions of each construct. Through analyses of classroom practice across grade levels using different lenses - particular conceptions of argumentation, justification, and proof - researchers consider the implications of how each conception shapes empirical outcomes. In each section, organized by grade band, authors adopt particular conceptions of argumentation, justification, and proof, and they analyse one data set from each perspective. In addition, each section includes a synthesis chapter from an expert in the field to bring to the fore potential implications, as well as new questions, raised by the analyses. Finally, a culminating section considers the use of each conception across grade bands and data sets.

Proving in the Elementary Mathematics Classroom

Author : Andreas J. Stylianides
Publisher : Oxford University Press
ISBN 13 : 019103472X
Total Pages : 203 pages
Book Rating : 4.1/5 (91 download)

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Book Synopsis Proving in the Elementary Mathematics Classroom by : Andreas J. Stylianides

Download or read book Proving in the Elementary Mathematics Classroom written by Andreas J. Stylianides and published by Oxford University Press. This book was released on 2016-07-21 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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

Author : Patricio Herbst
Publisher : Springer
ISBN 13 : 331977476X
Total Pages : 383 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis International Perspectives on the Teaching and Learning of Geometry in Secondary Schools by : Patricio Herbst

Download or read book International Perspectives on the Teaching and Learning of Geometry in Secondary Schools written by Patricio Herbst and published by Springer. This book was released on 2018-04-27 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

PROFUNEDU 2019

Author : Naufal Ishartono
Publisher : European Alliance for Innovation
ISBN 13 : 1631902032
Total Pages : 306 pages
Book Rating : 4.6/5 (319 download)

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Book Synopsis PROFUNEDU 2019 by : Naufal Ishartono

Download or read book PROFUNEDU 2019 written by Naufal Ishartono and published by European Alliance for Innovation. This book was released on 2019-08-06 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 4th Progressive and Fun Education (The 4th Profunedu) International Conference is a forum for researchers and lecturers within the ALPTK Muhammadiyah College to disseminate their best research results. This conference aims to provide a platform for researchers and academics to share their research findings with others and meet lecturers and researchers from other institutions and to strengthen the collaboration and networking amongs the participants. The 4th Profunedu was held on 6-8 August 2019 in Makassar, Indonesia. It is hoped that this proceeding can help improve the quality of education, especially the quality of education in Indonesia.

The Learning and Teaching of Geometry in Secondary Schools

Author : Pat Herbst
Publisher : Routledge
ISBN 13 : 1351973525
Total Pages : 405 pages
Book Rating : 4.3/5 (519 download)

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Book Synopsis The Learning and Teaching of Geometry in Secondary Schools by : Pat Herbst

Download or read book The Learning and Teaching of Geometry in Secondary Schools written by Pat Herbst and published by Routledge. This book was released on 2017-03-16 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: IMPACT (Interweaving Mathematics Pedagogy and Content for Teaching) is an exciting new series of texts for teacher education which aims to advance the learning and teaching of mathematics by integrating mathematics content with the broader research and theoretical base of mathematics education. The Learning and Teaching of Geometry in Secondary Schools reviews past and present research on the teaching and learning of geometry in secondary schools and proposes an approach for design research on secondary geometry instruction. Areas covered include: teaching and learning secondary geometry through history; the representations of geometric figures; students’ cognition in geometry; teacher knowledge, practice and, beliefs; teaching strategies, instructional improvement, and classroom interventions; research designs and problems for secondary geometry. Drawing on a team of international authors, this new text will be essential reading for experienced teachers of mathematics, graduate students, curriculum developers, researchers, and all those interested in exploring students’ study of geometry in secondary schools.

Advances in Mathematics Education Research on Proof and Proving

Author : Andreas J. Stylianides
Publisher : Springer
ISBN 13 : 3319709968
Total Pages : 298 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Advances in Mathematics Education Research on Proof and Proving by : Andreas J. Stylianides

Download or read book Advances in Mathematics Education Research on Proof and Proving written by Andreas J. Stylianides and published by Springer. This book was released on 2018-01-10 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores new trends and developments in mathematics education research related to proof and proving, the implications of these trends and developments for theory and practice, and directions for future research. With contributions from researchers working in twelve different countries, the book brings also an international perspective to the discussion and debate of the state of the art in this important area. The book is organized around the following four themes, which reflect the breadth of issues addressed in the book: • Theme 1: Epistemological issues related to proof and proving; • Theme 2: Classroom-based issues related to proof and proving; • Theme 3: Cognitive and curricular issues related to proof and proving; and • Theme 4: Issues related to the use of examples in proof and proving. Under each theme there are four main chapters and a concluding chapter offering a commentary on the theme overall.

Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators

Author : Berinderjeet Kaur
Publisher : World Scientific
ISBN 13 : 9814405442
Total Pages : 335 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators by : Berinderjeet Kaur

Download or read book Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators written by Berinderjeet Kaur and published by World Scientific. This book was released on 2012-04-20 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: This fourth volume in the series of yearbooks by the Association of Mathematics Educators in Singapore entitled Reasoning, Communication and Connections in Mathematics is unique in that it focuses on a single theme in mathematics education. The objective is to encourage teachers and researchers to advance reasoning, communication and connections in mathematics classrooms.Several renowned international researchers in the field have published their work in this volume. The fifteen chapters of the book illustrate evidence-based practices that school teachers and researchers can experiment with in their own classrooms to bring about meaningful learning outcomes. Three major themes: mathematical tasks, classroom discourse, and connectivity within and beyond mathematics, shape the ideas underpinning reasoning, communication and connections in these chapters. The book makes a significant contribution towards mathematical processes essential for learners of mathematics. It is a good resource for mathematics educators and research students.

Mathematics & Mathematics Education: Searching for Common Ground

Author : Michael N. Fried
Publisher : Springer Science & Business Media
ISBN 13 : 9400774737
Total Pages : 385 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Mathematics & Mathematics Education: Searching for Common Ground by : Michael N. Fried

Download or read book Mathematics & Mathematics Education: Searching for Common Ground written by Michael N. Fried and published by Springer Science & Business Media. This book was released on 2013-11-29 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the fruit of a symposium in honor of Ted Eisenberg concerning the growing divide between the mathematics community and the mathematics education community, a divide that is clearly unhealthy for both. The work confronts this disturbing gap by considering the nature of the relationship between mathematics education and mathematics, and by examining areas of commonality as well as disagreement. It seeks to provide insight into the mutual benefit both stand to gain by building bridges based on the natural bonds between them.