Teaching and Learning Proof Across the Grades

2010-09-23
Teaching and Learning Proof Across the Grades

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  • Author: Despina A. Stylianou
  • Publisher: Routledge
  • ISBN: 1135856745
  • Category : Education
  • Languages : en
  • Pages : 408

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.

Teaching and Learning Proof Across the Grades

2009
Teaching and Learning Proof Across the Grades

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  • Author: Despina A. Stylianou
  • Publisher: Taylor & Francis US
  • ISBN: 9780415989848
  • Category : Education
  • Languages : en
  • Pages : 388

Fra forlagets beskrivelse: 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

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

2017-12-04
Teaching and Learning Algebraic Thinking with 5- to 12-Year-Olds

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  • Author: Carolyn Kieran
  • Publisher: Springer
  • ISBN: 3319683519
  • Category : Education
  • Languages : en
  • Pages : 443

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.

Proving in the Elementary Mathematics Classroom

2016-07-21
Proving in the Elementary Mathematics Classroom

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  • Author: Andreas J. Stylianides
  • Publisher: Oxford University Press
  • ISBN: 019103472X
  • Category : Mathematics
  • Languages : en
  • Pages : 208

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.

Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

2022-03-03
Conceptions and Consequences of Mathematical Argumentation, Justification, and Proof

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  • Author: Kristen N. Bieda
  • Publisher: Springer Nature
  • ISBN: 3030800083
  • Category : Education
  • Languages : en
  • Pages : 331

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.

Proof and Proving in Mathematics Education

2012-06-14
Proof and Proving in Mathematics Education

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  • Author: Gila Hanna
  • Publisher: Springer Science & Business Media
  • ISBN: 9400721293
  • Category : Education
  • Languages : en
  • Pages : 468

*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.

PROFUNEDU 2019

2019-08-06
PROFUNEDU 2019

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  • Author: Naufal Ishartono
  • Publisher: European Alliance for Innovation
  • ISBN: 1631902032
  • Category : Education
  • Languages : en
  • Pages : 306

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.

Advances in Mathematics Education Research on Proof and Proving

2018-01-10
Advances in Mathematics Education Research on Proof and Proving

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  • Author: Andreas J. Stylianides
  • Publisher: Springer
  • ISBN: 3319709968
  • Category : Education
  • Languages : en
  • Pages : 301

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

2012-04-20
Reasoning, Communication And Connections In Mathematics: Yearbook 2012, Association Of Mathematics Educators

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  • Author: Berinderjeet Kaur
  • Publisher: World Scientific
  • ISBN: 9814405442
  • Category : Mathematics
  • Languages : en
  • Pages : 336

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.

International Handbook of Mathematics Teacher Education: Volume 2

2019-12-16
International Handbook of Mathematics Teacher Education: Volume 2

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  • Author:
  • Publisher: BRILL
  • ISBN: 9004418962
  • Category : Education
  • Languages : en
  • Pages : 445

Tools and Processes in Mathematics Teacher Education describes and analyze various promising tools and processes, from different perspectives, aimed at facilitating mathematics teacher learning/development. It provides insights of how mathematics teacher educators think about and approach their work with teachers.