Mathematical Conversations Within the Practice of Mathematics [microform] PDF Download

Author: Lynn Melanie Gordon Calvert
Publisher: National Library of Canada = Bibliothèque nationale du Canada
ISBN: 9780612395329
Category : Communication in education
Languages : en
Pages : 264

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Author: Lynn M. Gordon Calvert
Publisher: Peter Lang Incorporated, International Academic Publishers
ISBN:
Category : Education
Languages : en
Pages : 196

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Mathematical Conversations within the Practice of Mathematics questions underlying assumptions and broadens current perceptions of mathematical practice and discourse. Rather than simply a verbal exchange, a conversational discourse is viewed as a way to maintain our relationships with others as we seek meaning and coherence in our lived experiences. This book explores the nature of mathematical conversations and their place in the practice of mathematics. The necessary incompleteness of expression, explanation, and understanding within mathematical conversations is revealed and explored in this book resulting in alternative images of intelligent action, acceptable explanations, and the nature of mathematics and reality.

Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :

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Author: Lynn Gordon Calvert
Publisher:
ISBN:
Category : Communication in education
Languages : en
Pages : 264

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Book Description

Author: Lynn Gordon Calvert
Publisher:
ISBN:
Category : Communication in education
Languages : en
Pages : 0

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Author: John de Pillis
Publisher: Cambridge University Press
ISBN: 9780883855409
Category : Mathematics
Languages : en
Pages : 364

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Illustrated book showing that there are few degrees of separation between mathematics and topics that provoke interesting conversations.

Author: Nathan Sidoli
Publisher: Library and Archives Canada = Bibliothèque et Archives Canada
ISBN: 9780612943766
Category :
Languages : en
Pages : 562

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The study is an examination of the mathematical methods of Ptolemy and his predecessors. It attempts, so far as possible, to situate this work in the context of what we know about the rest of Greek mathematics and the exact sciences, with little or no reference to current scientific and mathematical knowledge. Each of these chapters describes a domain of Greek mathematical practice that is not witnessed in the theoretical texts and is generally left out of discussions of Greek mathematics. Moreover, in each case, I help the reader develop a sense for the methods and practices of the ancients instead of focusing simply on their results. The third chapter is an examination of all of the evidence we have for the so-called Menelaus Theorem, the fundamental theorem of ancient spherical trigonometry. It studies the texts of Ptolemy, his predecessors and his commentators and shows that the line of transmission cannot have been as straightforward as has previously been assumed. This is followed by an investigation of Ptolemy's practices in applying the fundamental theorem. This study of Ptolemy's spherical astronomy acts as a case study which gives us insight into the deductive structure of Ptolemy's exact science. This investigation allows us to develop a sense for how the ancient mathematical astronomer used these methods to produce new results. The final chapter is an exegesis of ancient methods of projecting the sphere onto the plane. It explores the texts of Ptolemy and his predecessors which are concerned with projecting the sphere either for the purpose of drawing maps or in order to model the sphere and solve for arc lengths. This leads to discussions of two important ancient methods of doing spherical geometry. The second chapter is a study of the first and most crucial application of these methods: the development of the chord table and its application to trigonometric problems. It also examines the trigonometric methods of the Hellenistic mathematical astronomers and shows how these fundamentally differed from Ptolemy's practice. It develops a general picture of the mathematical practices used in the trigonometry by means of chord tables. After a brief discussion of Ptolemy's philosophy of mathematics, the first chapter gives a classification of types of mathematical text found in Ptolemy and the Greek applied mathematical tradition in general. This is followed by sections that deal with the use of ratio and tables in Ptolemy's work. In order to apply metrical methods to geometrical problems, Ptolemy uses proportions as equations and develops tables to model continuous functions. Both of these practices, although natural to us, are unusual in the context of Greek mathematics. I examine the implicit assumptions and explain how these methods serve the applied mathematician.

Author: Alexandre Borovik
Publisher: American Mathematical Soc.
ISBN: 0821847619
Category : Mathematics
Languages : en
Pages : 345

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Discusses, from a working mathematician's point of view, the mystery of mathematical intuition: Why are certain mathematical concepts more intuitive than others? And to what extent does the 'small scale' structure of mathematical concepts and algorithms reflect the workings of the human brain?

Author: Swapna Mukhopadhyay
Publisher: Brill / Sense
ISBN: 9789460919206
Category : Education
Languages : en
Pages : 323

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Book Description
This book grew out of a public lecture series, Alternative forms of knowledge construction in mathematics, conceived and organized by the first editor, and held annually at Portland State University from 2006. Starting from the position that mathematics is a human construction, implying that it cannot be separated from its historical, cultural, social, and political contexts, the purpose of these lectures was to provide a public intellectual space to interrogate conceptions of mathematics and mathematics education, particularly by looking at mathematical practices that are not considered relevant to mainstream mathematics education. One of the main thrusts was to contemplate the fundamental question of whose mathematics is to be valorized in a multicultural world, a world in which, as Paolo Freire said, "The intellectual activity of those without power is always characterized as non-intellectual". To date, nineteen scholars (including the second editor) have participated in the series. All of the lectures have been streamed for global dissemination at: http: //www. media. pdx. edu/dlcmedia/events/AFK/Most of the speakers contributed a chapter to this book, based either on their original talk or on a related topic.

Author: Mathilde Gerbelli-Gauthier
Publisher:
ISBN: 9781470467807
Category : Communication in mathematics
Languages : en
Pages : 139

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The articles in this volume grew out of a 2019 workshop, held at Johns Hopkins University, that was inspired by a belief that when mathematicians take time to reflect on the social forces involved in the production of mathematics, actionable insights result. Topics range from mechanisms that lead to an inclusion-exclusion dichotomy within mathematics to common pitfalls and better alternatives to how mathematicians approach teaching, mentoring and communicating mathematical ideas.