Humans-with-Media and the Reorganization of Mathematical Thinking

Information and Communication Technologies, Modeling, Visualization and Experimentation
Author: Marcelo C. Borba,Monica E. Villarreal
Publisher: Springer Science & Business Media
ISBN: 9780387242637
Category: Education
Page: 229
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This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Borba and Villarreal provide examples from research conducted at the level of basic and university-level education, developed by their research group based in Brazil, and discuss their findings in the light of the relevant literature. Arguing that different media reorganize mathematical thinking in different ways, they discuss how computers, writing and oral discourse transform education at an epistemological as well as a political level. Modeling and experimentation are seen as pedagogical approaches which are in harmony with changes brought about by the presence of information and communication technology in educational settings. Examples of research about on-line mathematics education courses, and Internet used in regular mathematics courses, are presented and discussed at a theoretical level. In this book, mathematical knowledge is seen as developed by collectives of humans-with-media. The authors propose that knowledge is never constructed solely by humans, but by collectives of humans and technologies of intelligence. Theoretical discussion developed in the book, together with new examples, shed new light on discussions regarding visualization, experimentation and multiple representations in mathematics education. Insightful examples from educational practice open up new paths for the reader.

Argumentation and Education

Theoretical Foundations and Practices
Author: Nathalie Muller Mirza,Anne-Nelly Perret-Clermont
Publisher: Springer Science & Business Media
ISBN: 038798125X
Category: Education
Page: 242
View: 6441

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During the last decade, argumentation has attracted growing attention as a means to elicit processes (linguistic, logical, dialogical, psychological, etc.) that can sustain or provoke reasoning and learning. Constituting an important dimension of daily life and of professional activities, argumentation plays a special role in democracies and is at the heart of philosophical reasoning and scientific inquiry. Argumentation, as such, requires specific intellectual and social skills. Hence, argumentation will have an increasing importance in education, both because it is a critical competence that has to be learned, and because argumentation can be used to foster learning in philosophy, history, sciences and in many other domains. Argumentation and Education answers these and other questions by providing both theoretical backgrounds, in psychology, education and theory of argumentation, and concrete examples of experiments and results in school contexts in a range of domains. It reports on existing innovative practices in education settings at various levels.

The History of Mathematical Proof in Ancient Traditions

Author: Karine Chemla
Publisher: Cambridge University Press
ISBN: 1139510584
Category: Philosophy
Page: N.A
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This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

Realism in the Sciences

Proceedings of the Ernan McMullin Symposium, Leuven, 1995
Author: Igor Douven,Leon Horsten
Publisher: Leuven University Press
ISBN: 9789061867630
Category: Philosophy
Page: 216
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Mathematics and Technology

A C.I.E.A.E.M. Sourcebook
Author: Gilles Aldon,Fernando Hitt,Luciana Bazzini,Uwe Gellert
Publisher: Springer
ISBN: 331951380X
Category: Education
Page: 693
View: 1602

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This volume collects most recent work on the role of technology in mathematics education. It offers fresh insight and understanding of the many ways in which technological resources can improve the teaching and learning of mathematics. The first section of the volume focuses on the question how a proposed mathematical task in a technological environment can influence the acquisition of knowledge and what elements are important to retain in the design of mathematical tasks in computing environments. The use of white smart boards, platforms as Moodle, tablets and smartphones have transformed the way we communicate both inside and outside the mathematics classroom. Therefore the second section discussed how to make efficient use of these resources in the classroom and beyond. The third section addresses how technology modifies the way information is transmitted and how mathematical education has to take into account the new ways of learning through connected networks as well as new ways of teaching. The last section is on the training of teachers in the digital era. The editors of this volume have selected papers from the proceedings of the 65th, 66th and 67th CIEAEM conference, and invited the correspondent authors to contribute to this volume by discussing one of the four important topics. The book continues a series of sourcebooks edited by CIEAEM, the Commission Internationale pour l’Étude et l’Amélioration de l’Enseignement des Mathématiques / International Commission for the Study and Improvement of Mathematics Education.

Theorem Proving in Higher Order Logics

13th International Conference, TPHOLs 2000 Portland, OR, USA, August 14-18, 2000 Proceedings
Author: Mark Aagaard
Publisher: Springer Science & Business Media
ISBN: 9783540678632
Category: Computers
Page: 533
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This book constitutes the refereed proceedings of the 13th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2000, held in Portland, Oregon, USA in August 2000. The 29 revised full papers presented together with three invited contributions were carefully reviewed and selected from 55 submissions. All current aspects of HOL theorem proving, formal verification of hardware and software systems, and formal verification are covered. Among the HOL theorem provers evaluated are COQ, HOL, Isabelle, HOL/SPIN, PVS, and Isabelle/HOL.

Philosophy of Mathematics

An Introduction to the World of Proofs and Pictures
Author: James Robert Brown
Publisher: Psychology Press
ISBN: 9780415122740
Category: Mathematics
Page: 215
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Philosophy of Mathematics is an excellent introductory text. This student friendly book discusses the great philosophers and the importance of mathematics to their thought. It includes the following topics: * the mathematical image * platonism * picture-proofs * applied mathematics * Hilbert and Godel * knots and nations * definitions * picture-proofs and Wittgenstein * computation, proof and conjecture. The book is ideal for courses on philosophy of mathematics and logic.

Famous Problems and Their Mathematicians

Author: Art Johnson
Publisher: Libraries Unlimited
ISBN: 9781563084461
Category: Education
Page: 179
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Presents brief stories about the life and work of famous mathematicians, including Euler, Fermat, Fibonacci, Fourier, Gauss, Moebius, and Pythagoras, and introduces their theories with puzzles and tasks for students to solve.

Poincare's Prize

The Hundred-Year Quest to Solve One of Math's Greatest Puzzles
Author: George G. Szpiro
Publisher: Penguin
ISBN: 1440634289
Category: Mathematics
Page: 320
View: 8664

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The amazing story of one of the greatest math problems of all time and the reclusive genius who solved it In the tradition of Fermat’s Enigma and Prime Obsession, George Szpiro brings to life the giants of mathematics who struggled to prove a theorem for a century and the mysterious man from St. Petersburg, Grigory Perelman, who fi nally accomplished the impossible. In 1904 Henri Poincaré developed the Poincaré Conjecture, an attempt to understand higher-dimensional space and possibly the shape of the universe. The problem was he couldn’t prove it. A century later it was named a Millennium Prize problem, one of the seven hardest problems we can imagine. Now this holy grail of mathematics has been found. Accessibly interweaving history and math, Szpiro captures the passion, frustration, and excitement of the hunt, and provides a fascinating portrait of a contemporary noble-genius.


proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, Stockholm, Sweden, July 31-August 6, 1999
Author: Thomas L. Dean,International Joint Conferences on Artificial Intelligence
Publisher: Morgan Kaufmann Pub
Category: Computers
Page: 1452
View: 4787

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Informatics and the Teaching of Mathematics

Proceedings of the IFIP TC 3/WG 3.1 Working Conference on Informatics and the Teaching of Mathematics : Sofia, Bulgaria, 16-18 May, 1987
Author: David Carlton Johnson,Frank B. Lovis
Publisher: Elsevier Science Limited
Category: Mathematics
Page: 172
View: 3183

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Proof in mathematics education

research, learning and teaching
Author: David Alexander Reid,Christine Knipping
Publisher: N.A
ISBN: 9789460912443
Category: Education
Page: 251
View: 8475

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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.

Educational Algebra

A Theoretical and Empirical Approach
Author: Eugenio Filloy,Teresa Rojano,Luis Puig
Publisher: Springer Science & Business Media
ISBN: 0387712542
Category: Education
Page: 294
View: 889

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This book takes a theoretical perspective on the study of school algebra, in which both semiotics and history occur. The Methodological design allows for the interpretation of specific phenomena and the inclusion of evidence not addressed in more general treatments. The book gives priority to "meaning in use" over "formal meaning". These approaches and others of similar nature lead to a focus on competence rather than a user’s activity with mathematical language.