Conceptions And Consequences Of Mathematical Argumentation Justification And Proof
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Conceptions And Consequences Of Mathematical Argumentation Justification And Proof
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Author : Kristen N. Bieda
language : en
Publisher: Springer Nature
Release Date : 2022-03-03
Conceptions And Consequences Of Mathematical Argumentation Justification And Proof written by Kristen N. Bieda and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-03-03 with Education categories.
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.
Understanding The Generality Of Mathematical Statements
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Author : Milena Damrau
language : en
Publisher: Springer Nature
Release Date : 2024-02-02
Understanding The Generality Of Mathematical Statements written by Milena Damrau and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-02 with Mathematics categories.
In this open access book Milena Damrau investigates the understanding of generality of mathematical statements in first-year university students and its relation to other proof-related activities. Through an experimental study, she particularly analyses the effect of different types of arguments (empirical, generic, and ordinary proofs) and statements (familiar and unfamiliar, as well as true and false ones) on several proof-related activities. The results reveal students' struggles with the concept of generality, how their understanding of generality is related to proof reading and construction and how different types of arguments and statements impact students’ performance in other proof-related activities. The findings offer valuable insights for improving mathematics courses at the transition from school to university and highlight the need for more experimental studies in mathematics education.
Mathematics Education In The Information Age
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Author : Stacy A. Costa
language : en
Publisher: Springer Nature
Release Date : 2020-12-10
Mathematics Education In The Information Age written by Stacy A. Costa and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-12-10 with Mathematics categories.
This book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.
Pisa Learning For Tomorrow S World First Results From Pisa 2003
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Author : OECD
language : en
Publisher: OECD Publishing
Release Date : 2004-12-07
Pisa Learning For Tomorrow S World First Results From Pisa 2003 written by OECD and has been published by OECD Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-07 with categories.
This report presents the first internationally comparable results to OECD's 2003 Programme for International Student Assessment (PISA) Survey of the educational performance of 15-year-olds in reading, mathematics, and science in 25 OECD countries.
Investigaci N Para La Mejora De Las Pr Cticas Educativas Desde Una Perspectiva Hol Stica
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Author : Blanca Berral Ortiz
language : es
Publisher: Dykinson
Release Date : 2024-07-23
Investigaci N Para La Mejora De Las Pr Cticas Educativas Desde Una Perspectiva Hol Stica written by Blanca Berral Ortiz and has been published by Dykinson this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-07-23 with Education categories.
Proof In Mathematics Education
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Author : David A. Reid
language : en
Publisher: BRILL
Release Date : 2010-01-01
Proof In Mathematics Education written by David A. Reid and has been published by BRILL this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-01-01 with Education categories.
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.
Second Handbook Of Research On Mathematics Teaching And Learning
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Author : Frank K. Lester
language : en
Publisher: IAP
Release Date : 2007-02-01
Second Handbook Of Research On Mathematics Teaching And Learning written by Frank K. Lester and has been published by IAP this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-02-01 with Education categories.
The audience remains much the same as for the 1992 Handbook, namely, mathematics education researchers and other scholars conducting work in mathematics education. This group includes college and university faculty, graduate students, investigators in research and development centers, and staff members at federal, state, and local agencies that conduct and use research within the discipline of mathematics. The intent of the authors of this volume is to provide useful perspectives as well as pertinent information for conducting investigations that are informed by previous work. The Handbook should also be a useful textbook for graduate research seminars. In addition to the audience mentioned above, the present Handbook contains chapters that should be relevant to four other groups: teacher educators, curriculum developers, state and national policy makers, and test developers and others involved with assessment. Taken as a whole, the chapters reflects the mathematics education research community's willingness to accept the challenge of helping the public understand what mathematics education research is all about and what the relevance of their research fi ndings might be for those outside their immediate community.
The Argument Of Mathematics
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Author : Andrew Aberdein
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-07-01
The Argument Of Mathematics written by Andrew Aberdein and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-01 with Philosophy categories.
Written by experts in the field, this volume presents a comprehensive investigation into the relationship between argumentation theory and the philosophy of mathematical practice. Argumentation theory studies reasoning and argument, and especially those aspects not addressed, or not addressed well, by formal deduction. The philosophy of mathematical practice diverges from mainstream philosophy of mathematics in the emphasis it places on what the majority of working mathematicians actually do, rather than on mathematical foundations. The book begins by first challenging the assumption that there is no role for informal logic in mathematics. Next, it details the usefulness of argumentation theory in the understanding of mathematical practice, offering an impressively diverse set of examples, covering the history of mathematics, mathematics education and, perhaps surprisingly, formal proof verification. From there, the book demonstrates that mathematics also offers a valuable testbed for argumentation theory. Coverage concludes by defending attention to mathematical argumentation as the basis for new perspectives on the philosophy of mathematics.
Curricular Resources And Classroom Use
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Author : Gabriel J. Stylianides
language : en
Publisher: Oxford University Press
Release Date : 2016
Curricular Resources And Classroom Use written by Gabriel J. Stylianides and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Education categories.
Curricular resources have a significant influence on students' opportunities to learn. At the same time, teachers play a crucial role as interpreters of such materials. This book examines how to make the most of the potential of curricular resources to support classroom work.
Concepts Of Proof In Mathematics Philosophy And Computer Science
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Author : Dieter Probst
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-07-25
Concepts Of Proof In Mathematics Philosophy And Computer Science written by Dieter Probst and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-07-25 with Philosophy categories.
A proof is a successful demonstration that a conclusion necessarily follows by logical reasoning from axioms which are considered evident for the given context and agreed upon by the community. It is this concept that sets mathematics apart from other disciplines and distinguishes it as the prototype of a deductive science. Proofs thus are utterly relevant for research, teaching and communication in mathematics and of particular interest for the philosophy of mathematics. In computer science, moreover, proofs have proved to be a rich source for already certified algorithms. This book provides the reader with a collection of articles covering relevant current research topics circled around the concept 'proof'. It tries to give due consideration to the depth and breadth of the subject by discussing its philosophical and methodological aspects, addressing foundational issues induced by Hilbert's Programme and the benefits of the arising formal notions of proof, without neglecting reasoning in natural language proofs and applications in computer science such as program extraction.