Proving In The Elementary Mathematics Classroom
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| Author | : Andreas J. Stylianides |
| Publisher | : Oxford University Press |
| Total Pages | : 203 |
| Release | : 2016 |
| Genre | : Education |
| ISBN | : 0198723067 |
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.
| Author | : Gila Hanna |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 468 |
| Release | : 2012-06-14 |
| Genre | : Education |
| ISBN | : 9400721293 |
*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.
| Author | : Andreas J. Stylianides |
| Publisher | : Oxford University Press |
| Total Pages | : 203 |
| Release | : 2016-07-21 |
| Genre | : Mathematics |
| ISBN | : 019103472X |
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.
| Author | : Andreas J. Stylianides |
| Publisher | : Springer |
| Total Pages | : 298 |
| Release | : 2018-01-10 |
| Genre | : Education |
| ISBN | : 3319709968 |
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.
| Author | : Erich Christian Wittmann |
| Publisher | : Springer Nature |
| Total Pages | : 332 |
| Release | : 2020-12-09 |
| Genre | : Education |
| ISBN | : 3030615707 |
This open access book features a selection of articles written by Erich Ch. Wittmann between 1984 to 2019, which shows how the “design science conception” has been continuously developed over a number of decades. The articles not only describe this conception in general terms, but also demonstrate various substantial learning environments that serve as typical examples. In terms of teacher education, the book provides clear information on how to combine (well-understood) mathematics and methods courses to benefit of teachers. The role of mathematics in mathematics education is often explicitly and implicitly reduced to the delivery of subject matter that then has to be selected and made palpable for students using methods imported from psychology, sociology, educational research and related disciplines. While these fields have made significant contributions to mathematics education in recent decades, it cannot be ignored that mathematics itself, if well understood, provides essential knowledge for teaching mathematics beyond the pure delivery of subject matter. For this purpose, mathematics has to be conceived of as an organism that is deeply rooted in elementary operations of the human mind, which can be seamlessly developed to higher and higher levels so that the full richness of problems of various degrees of difficulty, and different means of representation, problem-solving strategies, and forms of proof can be used in ways that are appropriate for the respective level. This view of mathematics is essential for designing learning environments and curricula, for conducting empirical studies on truly mathematical processes and also for implementing the findings of mathematics education in teacher education, where it is crucial to take systemic constraints into account.
| Author | : Despina A. Stylianou |
| Publisher | : Routledge |
| Total Pages | : 515 |
| Release | : 2010-09-23 |
| Genre | : Education |
| ISBN | : 1135856745 |
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.
| Author | : Malke Rosenfeld |
| Publisher | : Heinemann Educational Books |
| Total Pages | : 0 |
| Release | : 2016-10-18 |
| Genre | : Education |
| ISBN | : 9780325074702 |
"Kids love to move. But how do we harness all that kinetic energy effectively for math learning? In Math on the Move, Malke Rosenfeld shows how pairing math concepts and whole body movement creates opportunities for students to make sense of math in entirely new ways. Malke shares her experience creating dynamic learning environments by: exploring the use of the body as a thinking tool, highlighting mathematical ideas that are usefully explored with a moving body, providing a range of entry points for learning to facilitate a moving math classroom. ..."--Publisher description.
| Author | : Sung Je Cho |
| Publisher | : Springer |
| Total Pages | : 617 |
| Release | : 2015-02-10 |
| Genre | : Education |
| ISBN | : 3319126881 |
This book comprises the Proceedings of the 12th International Congress on Mathematical Education (ICME-12), which was held at COEX in Seoul, Korea, from July 8th to 15th, 2012. ICME-12 brought together 3500 experts from 92 countries, working to understand all of the intellectual and attitudinal challenges in the subject of mathematics education as a multidisciplinary research and practice. This work aims to serve as a platform for deeper, more sensitive and more collaborative involvement of all major contributors towards educational improvement and in research on the nature of teaching and learning in mathematics education. It introduces the major activities of ICME-12 which have successfully contributed to the sustainable development of mathematics education across the world. The program provides food for thought and inspiration for practice for everyone with an interest in mathematics education and makes an essential reference for teacher educators, curriculum developers and researchers in mathematics education. The work includes the texts of the four plenary lectures and three plenary panels and reports of three survey groups, five National presentations, the abstracts of fifty one Regular lectures, reports of thirty seven Topic Study Groups and seventeen Discussion Groups.
| Author | : David A. Reid |
| Publisher | : BRILL |
| Total Pages | : 265 |
| Release | : 2010-01-01 |
| Genre | : Education |
| ISBN | : 946091246X |
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.
| Author | : Gabriel J. Stylianides |
| Publisher | : Oxford University Press |
| Total Pages | : 197 |
| Release | : 2016-05-05 |
| Genre | : Mathematics |
| ISBN | : 0191066958 |
Curricular resources include the different kinds of materials (digital or physical) that teachers use in or for their teaching (textbooks, lesson plans, etc.) and have a significant influence on students' opportunities to learn. At the same time, teachers play a crucial role as interpreters of such materials, so there is a complex relationship between curricular resources and their classroom use. This book aims to bridge these rather disconnected but highly related programs of research by describing, comparing, and exemplifying new research approaches for studying, in connected ways, both curricular resources and their classroom use, thereby supporting also investigation of the complex interplay between the two. In addition to implications for research, the book has implications for curriculum development and teacher education. Specifically, the book deepens understanding of how curriculum developers can better exploit the potential of curricular resources to support classroom work, and how teacher educators can better support teachers to use curricular resources in the classroom.
