Philosophy of Mathematics Education Journal
No. 39 (September 2022)

Philosophy of Mathematics Education Journal        ISSN 1465-2978 (Online)

Editor: Paul Ernest



Danny Luecke, Sunshine Carlow, Josh Mattes, Warren Christensen, and Hollie Mackey  Circulating Conversations Methodology: Co-Connecting Knowledge to Develop Research Questions at Sitting Bull College
David M. Bowers and Brian R. Lawler   Anarchism as a Methodological Foundation in Mathematics Education:A Portrait of Resistance
Sonia Martins Felix and Sikunder Ali   Capturing Dynamic Shifts in Learning of Mathematics Teachers in a Collaborative Setting: A Positioning Theory Perspective
Munir Fasheh  Watch Out! We have been Invaded by the Euro-American Math for Over a Century!
Amanda Queiroz Moura  Inclusive Practices in Mathematics Classroom: some contributions from Critical Mathematics Education
Brian Greer  Do the Math, Ponder the Words
Greice Keli Silva Lacerda and Stella Maria Peixoto de Azevedo Pedrosa  Ethical and Political Principles Perceived in Remote Mathematics Teaching Interactions
Josh Markle  Tentativeness in the Mathematics Classroom: Two Cases of the Hand as a Landing Site
Marcelo Batarce  Derrida and Mathematics Education: differences
Jürgen Maaß And Stefan Götz  Philosophical Questions and Didactical Considerations on a Reality-Oriented Mathematics Education
Yasmine Abtahi  Rumi, Hope, Ethics and where I see Mathematics
Brian Greer  Roy Wagner on Mathematical Abstraction: Unfiltered Reactions
Maria Hedefalk, Helena Eriksson, Peter Markkanen, and Lovisa Sumpter  Five year Olds in between Sharing and Division
Laurence Delacour  Mathematics in Swedish multilingual preschool: Human and nonhuman actors and the devolution process
Anette Bagger and Juuso Henrik Nieminen  Ethical and Philosophical Dimensions of Mathematics Assessment
Lisa Österling  Mathematics Student Teachers’ Confessional Reflections
Cacey Wells  Perspectives, History, and Countercultures: A Discussion about Reform in Mathematics Education
Kimberly Kirstein  When Acceleration of Math Hinders Opportunity
Glen MacPherson  Description versus Prescription in Mathematics Education
Brian Greer  Learning from history: Jens Høyrup on Mathematics, Education, and Society
Julchen Brieger  “You are thinking too much about reality. Just think about un-reality” – Implementing philosophical debates about infinity in mathematics lessons in primary school
Paul Ernest  Infinity: Notes on the Most Controversial Topic in Mathematics
Mohamed Ababou and Paul Ernest A Dialogue on the Validity of the Concept of Infinity
Zhang Hong  Turing Machine Halting Problem, Russell's Paradox and the View of Dialectical Infinity

This is an Open Access journal

Aim of the Journal is to foster awareness of philosophical aspects of mathematics education and mathematics, understood broadly to include many kinds of theoretical reflection and research; to freely disseminate new thinking and to encourage informal communication, dialogue and international co-operation between teachers, scholars and others engaged in such work. We look for quality of imagination, reasoning, analysis, conceptions, but not for ‘correctness’ or conformity with received views. We do not shy away from controversial issues.

Editorial policy. The editorial hand is used very lightly.  This is an international refereed journal which aims to stimulate the sharing of ideas for no reason other than an interest in these ideas and love of discussion among its contributors and readers. Please send any items for inclusion to the editor as a virus-checked attachment in MS Word or compatible formats (not PDF as we cannot edit this format). Many types of item are welcome including papers, short contributions, letters, discussions, provocations, reactions, or reviews. Graduate students are warmly invited to submit assignments and theses for inclusion in this journal, to make available otherwise inaccessible resources for the benefit of the research community.

Fees. No fees are ever charged for submission, publication or access.

Format of submissions: There are no strict guidelines – authors are requested to make their submissions look like previously published papers – especially the first page headers layout etc.

Refereeing: All papers are submitted to peer-review on which basis the decision is made whether to accept, require revisions or reject. All papers are submitted to peer-review on which basis the decision is made whether to accept, require revisions or reject. We err on the side of acceptance; we do not want to make artificial barriers for our contributors, especially as many do not have English as a first language.

Copyright Notice.  All materials published herein remain copyright of the named authors, or of the editor if unattributed. Permission is given to freely copy the journal contents on a not-for-profit basis, provided full credit is given to the author and the journal, and the integrity of papers is preserved. On the same basis permission is given to cite or quote from the papers provided full credit is given. The journal is committed to open access and free sharing of information.

Acknowledgements The journal is made possible by the generous support of University of Exeter Centre for Research in STEM Education (CRISTEME). Special thanks also to Jane Tanner for maintaining the journal on the web.

Editor:  Paul Ernest, Emeritus Professor, Graduate School of Education, University of Exeter, U.K.  Please direct all submissions and correspondence via email to the editor at P.Ernest @  

Journal URL: