**Philosophy of Mathematics Education Journal **

**No. 29 (July 2015)**** **

**25th Anniversary Issue**

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

Editor: Paul Ernest

**Paul Dowling **Social Activity Method: A Fractal Language for Mathematics

**David W. Stinson & Erika C. Bullock **Critical Postmodern Methodology in Mathematics Education Research: Promoting another way of Thinking and Looking

**Florian Schacht & Stephan Hussmann **Between the Social and the Individual: Reconfiguring a Familiar Relation

**Galit Caduri & Einat Heyd-Metzuyanim **Is Collaboration Across Incommensurable Theories in Mathematics Education Possible?

**Heather Mendick **Using Popular Culture to Teach Maths

**Elizabeth Jackson **Student Primary Teachers’ Perceptions of Mathematics

**Paul Ernest **Problem Solving: Its Assimilation to the Teacher's Perspective

**Barbara Pieronkiewicz **Affective Transgression as the Core Objective of Mathematics Education

**Laura Golnabi **The Conditions of Flow and Mathematical Problem Solving

**Inês Hipolito **What is a Mathematical Proof in the Age of Modern Theorem Provers

**Andreas Moutsios-Rentzos **&** Panagiotis Spyrou**** **Fostering internal need for proof: A reading of the genesis of proof in ancient Greece

**Michael DeVilliers **I Have a Dream and Crossed Quadrilaterals

**Sean Chorney **The Practice of Learning Mathematics as Comprising Three Parallel Processes: Mathematics, Tool and Student

**Regina Dorothea Moeller **Teaching the Concept of Velocity in Mathematics Classes** **

**Anna Bellamy **A Critical Analysis of Teaching and Learning Negative Numbers** **

**Jeffrey David Pair **Is God a Mathematician?

**Douglas Henrich **Mathematical Ethics: Values, Valences and Virtue

**Mario A. Natiello and Hernán G. Solari**On the Removal of Infinities from Divergent Series

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**For details of the Aims of the Journal and Editorial policy see earlier issues up to no. 19. **Graduate students are warmly invited to submit coursework assignments and theses for inclusion in this journal, to make available otherwise inaccessible resources for the benefit of the research community in mathematics education and/or the philosophy of mathematics.

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

**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 that the integrity of papers is preserved.

**Acknowledgement** The journal is made possible by the generous support of University of Exeter. Especial thanks are due to Mike Jeffries-Harris for technical assistance.

**Editor**: Professor Paul Ernest, University of Exeter, Graduate School of Education, St Lukes, Exeter EX1 2LU, U.K. P.Ernest @ ex.ac.uk, Web: http://www.people.ex.ac.uk/PErnest/

(Here and elsewhere spaces are inserted around @ to hinder spamming).

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