Ebook: Perspectives On Mathematical Practices: Bringing Together Philosophy of Mathematics, Sociology of Mathematics, and Mathematics Education

Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.

The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

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Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.

The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

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Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.

The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

Content:
Front Matter....Pages I-XV
Front Matter....Pages -
How and Why Mathematics is Unique as a Social Practice....Pages 3-23
Mathematics As Objective Knowledge And As Human Practice....Pages 25-41
The Comparison Of Mathematics With Narrative....Pages 43-59
Theory of Mind, Social Science, and Mathematical Practice....Pages 61-79
Front Matter....Pages -
Incommensurability In Mathematics....Pages 83-105
Mathematical Progress As Increased Scope....Pages 107-117
Proof in C17 Algebra....Pages 119-133
The Informal Logic Of Mathematical Proof....Pages 135-151
Front Matter....Pages -
Mathematicians’ Narratives About Mathematics....Pages 155-173
Philosophy of Mathematics and Mathematics Education....Pages 175-189
Mathematical Practices In And Across School Contexts....Pages 191-213
The Importance of a Journal for Mathematics Teachers....Pages 215-230
On The Interdisciplinary Study of Mathematical Practice, with a Real Live Case Study....Pages 231-241

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Philosophy of mathematics today has transformed into a very complex network of diverse ideas, viewpoints, and theories. Sometimes the emphasis is on the "classical" foundational work (often connected with the use of formal logical methods), sometimes on the sociological dimension of the mathematical research community and the "products" it produces, then again on the education of future mathematicians and the problem of how knowledge is or should be transmitted from one generation to the next.

The editors of this book felt the urge, first of all, to bring together the widest variety of authors from these different domains and, secondly, to show that this diversity does not exclude a sufficient number of common elements to be present. In the eyes of the editors, this book will be considered a success if it can convince its readers of the following: that it is warranted to dream of a realistic and full-fledged theory of mathematical practices, in the plural. If such a theory is possible, it would mean that a number of presently existing fierce oppositions between philosophers, sociologists, educators, and other parties involved, are in fact illusory.

Content:
Front Matter....Pages I-XV
Front Matter....Pages -
How and Why Mathematics is Unique as a Social Practice....Pages 3-23
Mathematics As Objective Knowledge And As Human Practice....Pages 25-41
The Comparison Of Mathematics With Narrative....Pages 43-59
Theory of Mind, Social Science, and Mathematical Practice....Pages 61-79
Front Matter....Pages -
Incommensurability In Mathematics....Pages 83-105
Mathematical Progress As Increased Scope....Pages 107-117
Proof in C17 Algebra....Pages 119-133
The Informal Logic Of Mathematical Proof....Pages 135-151
Front Matter....Pages -
Mathematicians’ Narratives About Mathematics....Pages 155-173
Philosophy of Mathematics and Mathematics Education....Pages 175-189
Mathematical Practices In And Across School Contexts....Pages 191-213
The Importance of a Journal for Mathematics Teachers....Pages 215-230
On The Interdisciplinary Study of Mathematical Practice, with a Real Live Case Study....Pages 231-241
....