The Philosophy of Mathematics Education Today

375 Pages·2018·4.55 MB·English

by  Paul Ernest

ICME-13 Monographs
Paul Ernest Editor
The Philosophy
of Mathematics
Education
Today
ICME-13 Monographs
Series editor
Gabriele Kaiser, Faculty of Education, Didactics of Mathematics, Universität
Hamburg, Hamburg, Germany
Each volume in the series presents state-of-the art research on a particular topic in
mathematics education and reflects the international debate as broadly as possible,
while also incorporating insights into lesser-known areas of the discussion. Each
volumeisbasedonthediscussionsandpresentationsduringtheICME-13Congress
and includes the best papers from one of the ICME-13 Topical Study Groups or
Discussion Groups.
More information about this series at http://www.springer.com/series/15585
Paul Ernest
Editor
The Philosophy
of Mathematics Education
Today
123
Editor
PaulErnest
Schoolof Education
University of Exeter
Exeter
UK
ISSN 2520-8322 ISSN 2520-8330 (electronic)
ICME-13 Monographs
ISBN978-3-319-77759-7 ISBN978-3-319-77760-3 (eBook)
https://doi.org/10.1007/978-3-319-77760-3
LibraryofCongressControlNumber:2018934934
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Contents
A Plea for a Critical Transformative Philosophy of Mathematics
Education. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
Luis Radford
Part I Introduction to the Field
The Philosophy of Mathematics Education: An Overview . . . . . . . . . . . 13
Paul Ernest
Part II The Nature of Mathematics
The Who and What of the Philosophy of Mathematical Practices . . . . . 39
Jean Paul Van Bendegem
The Philosophy of Mathematical Education Between Platonism
and the Computer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
Michael Otte
A Dialogical Conception of Explanation in Mathematical Proofs. . . . . . 81
Catarina Dutilh Novaes
The Amalgam of Faith and Reason: Euclid’s Elements
and the Scientific Thinker . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99
Melissa Andrade-Molina, Paola Valero and Ole Ravn
Part III Critical Mathematics Education
Students’ Foregrounds and Politics of Meaning in Mathematics
Education. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115
Ole Skovsmose
The Struggle Is Pedagogical: Learning to Teach Critical
Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131
Eric “Rico” Gutstein
v
vi Contents
Some Thoughts on a Mathematics Education for Environmental
Sustainability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 145
Richard Barwell
Epistemological Questions About School Mathematics. . . . . . . . . . . . . . 161
Margaret Walshaw
The Concept of Culture in Critical Mathematics Education. . . . . . . . . . 173
Brendan Larvor and Karen François
The Ethics of Mathematics: Is Mathematics Harmful? . . . . . . . . . . . . . 187
Paul Ernest
Part IV Philosophical Theory in Mathematics Education Research
On the Need for Theory of Mathematics Learning and the Promise
of ‘Commognition’ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
Anna Sfard
On the Roles of Language in Mathematics Education . . . . . . . . . . . . . . 229
Ladislav Kvasz
The Separation of Mathematics from Reality in Scientific
and Educational Discourse. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Uwe Schürmann
Mathematics Education Actualized in the Cyberspace:
A Philosophical Essay . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253
Maria Aparecida Viggiani Bicudo
PartV Philosophyof/inTeaching,LearningandDoingMathematics
Making Distinctions: A Phenomenological Exploration
in Mathematics Education . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273
John Mason
Using Rules for Elaborating Mathematical Concepts . . . . . . . . . . . . . . . 297
Michael Meyer
Towards a Wider Perspective: Opening a Philosophical Space
in the Mathematics Curriculum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 309
Nadia Stoyanova Kennedy
Creativity Research in Mathematics Education Simplified:
Using the Concept of Bisociation as Ockham’s Razor . . . . . . . . . . . . . . 321
Bronislaw Czarnocha, William Baker and Olen Dias
Teaching of Velocity in Mathematics Classes—Chances
for Philosophical Ideas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
Regina Dorothea Möller
Contents vii
Time for Work: Finding Worth-While-Ness in Making
Mathematics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343
Hilary Povey, Gill Adams and Colin Jackson
Hades—The Invisible Side of Mathematical Thinking . . . . . . . . . . . . . . 353
Walther Paravicini, Jörn Schnieder and Ingrid Scharlau
Developing Rules Due to the Use of Family Resemblances
in Classroom Communication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 365
Jessica Kunsteller
Editor and Contributors
About the Editor
Paul Ernest is emeritus professor at Exeter University, UK where he established
and ran the masters and doctoral programmes in mathematics education including
distance learning modes. His research concerns questions about the nature of
mathematics and how it relates to teaching, learning and society. Inevitably this
raises further questions concerning mathematics and philosophy, including ethics
and social justice, which he continues to address. His publications include The
PhilosophyofMathematicsEducation(Routledge,1991),with2000+citations,and
Social Constructivism as a Philosophy of Mathematics (SUNY Press, 1998). He
founded and edits the Philosophy of Mathematics Education Journal, now in its
28th year of publication, freely accessible via http://socialsciences.exeter.ac.uk/
education/research/centres/stem/publications/pmej/. E-mail: [email protected].
Contributors
Gill Adams Sheffield Institute of Education, Sheffield Hallam University,
Sheffield, UK
Melissa Andrade-Molina Faculty of Engineering and Science, Aalborg
University, Aalborg, Denmark
William Baker Mathematics Department, Hostos Community College, City
University of New York, Bronx, NY, USA
Richard Barwell University of Ottawa, Ottawa, Canada
MariaAparecidaViggianiBicudo SãoPauloStateUniversity,SãoPaulo,Brazil
Bronislaw Czarnocha Mathematics Department, Hostos Community College,
City University of New York, Bronx, NY, USA
ix
x EditorandContributors
OlenDias MathematicsDepartment,HostosCommunityCollege,CityUniversity
of New York, Bronx, NY, USA
Catarina Dutilh Novaes Faculty of Philosophy, University of Groningen,
Groningen, The Netherlands
Paul Ernest Graduate School of Education, University of Exeter, Exeter, UK
Karen François Center for Logic and Philosophy of Science, Vrije Universiteit
Brussel (VUB), Brussels, Belgium
Eric “Rico” Gutstein Department of Curriculum and Instruction, University of
Illinois at Chicago, Chicago, IL, USA
Colin Jackson Sheffield Institute of Education, Sheffield Hallam University,
Sheffield, UK
NadiaStoyanovaKennedy MathematicsDepartment,NewYorkCityCollegeof
Technology, City University of New York, Brooklyn, NY, USA
Jessica Kunsteller Institute of Mathematics Education, University of Cologne,
Cologne, Germany
Ladislav Kvasz Department of Mathematics and Mathematics Education,
Pedagogical Faculty, Charles University, Prague, Czech Republic
Brendan Larvor School of Humanities, University of Hertfordshire, Hatfield,
Herts, UK
John Mason The Open University, Milton Keynes, UK; University of Oxford,
Oxford, UK
Michael Meyer Institute of Mathematics Education, Cologne, Germany
Regina Dorothea Möller University of Erfurt, Erfurt, Germany
Michael Otte Melle, Germany
Walther Paravicini Universität Göttingen, Göttingen, Germany
Hilary Povey Sheffield Institute of Education, Sheffield Hallam University,
Sheffield, UK
Luis Radford Laurentian University, Sudbury, ON, Canada
Ole Ravn Department of Learning and Philosophy, Aalborg University, Aalborg,
Denmark
Ingrid Scharlau Paderborn University, Paderborn, Germany
Jörn Schnieder Lübeck University, Lübeck, Germany
Uwe Schürmann Westfälische Wilhelms-Universität, Münster, Germany
Anna Sfard University of Haifa, Haifa, Israel