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## Publications

Publications (101)

Inštrumentálny realizmus sme predstavili ako epistemologickú koncepciu zameranú na analýzu zmien jazyka matematiky. Podľa tejto koncepcie je možné odlíšiť zmeny jazyka štyroch rozličných druhov. Z pohľadu inštrumentálneho realizmu je úlohou vyučovania matematiky v kognitívnom systéme žiaka navodzovať zmeny všetkých štyroch druhov. Rôzne prístupy k...

The aim of this paper is to connect Wittgenstein’s picture theory of meaning with the Hegelian idea of the development of the self. Combining Wittgenstein with Hegel is perhaps not so original (see Mácha/Berg 2019); nevertheless, the context by means of which they will be connected, namely the history of painting, is perhaps new. I will argue that...

Instrumental realism is a type of scientific realism which emphasizes the importance of scientific instruments for the acquisition of scientific knowledge. According to instrumental realism, we have epistemic access to reality but this access is often indirect, mediated by means of instruments. The development of science is accompanied by the intro...

The aim of the paper is to analyze how language affects scientific research, from planning experiments and interpreting their results, through constructing models and the testing their predictions, to building theories and justifying their principles. I try to give an overview of the potentialities of language of science. I propose to distinguish s...

This article is based on the panel on inquiry based mathematics education and the development of learning trajectories held at the VARGA 100 Conference. After an introduction presenting the theme and organization of the panel, this article focuses on the diversity of conceptualizations of inquiry based education existing today in mathematics educat...

The aim of the paper is to present an epistemological position called instrumental realism and to show how this position can be used as a tool for the analysis of different approaches to mathematics education. Instrumental realism is based on the conviction that any successful study of a particular segment of reality must on the one hand take into...

The aim of the paper is to argue for the cognitive unity of the mathematical results ascribed by ancient authors to Thales. These results are late ascriptions and so it is difficult to say anything certain about them on philological grounds. I will seek characteristic features of the cognitive unity of the mathematical results ascribed to Thales by...

Scientific realism plays a central role in the philosophico-methodological discussions on research. Two are the main directions in the contributions made to scientific realism: the “internal” line and the “external” path. Following the first line, there are new visions of realism focused on central aspects of science: semantic, logic, epistemologic...

Structural realism is an answer to the challenge posed for realism by the argument from the pessimistic meta-induction (Laudan 1981). It attempts to combine scientific realism with the existence of scientific revolutions in arguing that the mathematical structure of a scientific theory is preserved in the course of a scientific revolution. Structur...

The aim of the paper is to answer some arguments raised against mathematical structuralism developed by Michael Resnik. These arguments stress the abstractness of mathematical objects, especially their causal inertness, and conclude that mathematical objects, the structures posited by Resnik included, are inaccessible to human cognition. In the pap...

The language of mathematics attracted recently the attention of philosophers, historians of mathematics, and researchers in mathematics education (see Dutilh Novaes in Formal languages in logic. A philosophical and cognitive analysis. Cambridge University, Cambridge, UK, 2012, Hoyrup in The development of algebraic symbolism. College Publications,...

In connection with the vigorous growth of the cognitive sciences in the course of the last twenty years, several works in the philosophy of mathematics have been issued that attempt to exploit the findings of cognitive sciences in interpreting visual thought in mathematics. The aim of this article is to complement the cognitive interpretation of vi...

V 48. čísle časopisu Reflexe vyšla recenze mé knihy Zrod vedy ako lingvistická udalosť od Štěpána Holuba. Recenze je napsána s porozuměním a její výhrady jsou ve většině případů oprávněné. Celkově jsem v recenzi našel dvacet čtyři kritických připomínek, které se dotýkají jak zásadních koncepčních otázek, tak drobných terminologických nejasností. Ve...

This paper is the second part in a series of articles aimed at reconstructing the emergence of mathematics as a deductive discipline in ancient Greece in the period between Thales and Euclid. We understand the emergence of mathematics as the birth of a language which enables the undertaking of deductive proofs. While in the preceding part we focuse...

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant moder...

This survey provides a brief and selective overview of research in the philosophy of mathematics education. It asks what makes up the philosophy of mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical mathematics education, and the most relevant moder...

Probleme Studierender mit mathematischen Inhalten zu Beginn ihres Studiums werden häufig nur im Hinblick auf das Vorhandensein oder Fehlen erwarteter Fertigkeiten diskutiert. Wir plädieren dafür, die vorhandene mathematische Bildung der Studienanfängerinnen und -anfänger in den Blick zu nehmen und die Veränderungen aus der Perspektive mathematische...

Die Sprache der Mathematik wurde im Laufe der Jahrtausende lange Entwicklung dieser Disziplin vielen großen Veränderungen unterworfen. Das Ziel dieser Arbeit ist es, die Eigenschaften einer dieser Veränderungen zu beschreiben und ihre Konsequenzen für die Mathematikdidaktik zu untersuchen. Wir glauben, dass viele Konflikte und Missverständnisse in...

In this paper we try to distinguish two different styles of experimental practice—roughly speaking the Galilean and the Newtonian. They differ in the way they intertwine mathematics and experimentation. We offer a theoretical reconstruction of the transition from the Galilean to the Newtonian experimental practice. It seems that this transition was...

There are many interpretations of the birth of modern science. Most of them are, nevertheless, confined to the analysis of certain historical episodes or technical details, while leaving the very notion of mathematization unanalyzed. In my opinion this is due to a lack of a proper philosophical framework which would show the process of mathematizat...

The proponents of analytical philosophy often draw a comparison between mathematics and chess. Their metaphor is to suggest that both the result of mathematical calculation and the content of a mathematical statement are determined by the rules of "mathematical game" of some kind and independent of status quo. The steps made in a given calculation...

The aim of the paper is to draw attention to some possibilities how the methods of formal epistemology can be used in the reflection of social sciences. First of all it is the theory of relativizations and the theory of re-codings and the related methods of the reconstruction of the potentialities and formal aspects of language. In the paper we fur...

The aim of the paper is to clarify Kuhn’s theory of scientific revolutions. We propose to discriminate between a scientific revolution, which is a sociological event of a change of attitude of the scientific community with respect to a particular theory, and an epistemic rupture, which is a linguistic fact consisting of a discontinuity in the lingu...

The aim of the paper is to study the analytical and the expressive boundaries of the language of physics. We try to bring these boundaries into a relation with Kant's theory of antinomies of pure reason. It seems that Kant's theory can be interpreted as the discovery of the expressive boundaries of the language of science. If this interpretation is...

The aim of the present paper is to outline a method of reconstruction of the historical development of the language of physical theories. We will apply the theory presented in Patterns of Change, Linguistic Innovations in the Development of Classical Mathematics to the analysis of linguistic innovations in physics. Our method is based on a reconstr...

Geschichte der Mathematik inspiriert auf vielfältige Weise Gestaltung von Mathematikunterricht. Historische und kulturelle Perspektiven bereichern die gewöhnlich auf logischen Zusammenhängen basierende Entwicklung mathematischer Begriffe und gestatten die Einbeziehung neuer individueller Erfahrungsbereiche, sowie naturwissenschaftlicher und gesells...

Die Algebra hat ihre Wurzeln in der arabischen Mathematik des 8. Jahrhunderts. Bei den Arabern wurde die Algebra in natürlicher Sprache ohne jede Symbolik betrieben. Das Lösen von Gleichungen bestand in der Umformung von Sätzen der arabischen Sprache, die um einige technische Ausdrücke der mathematischen Fachsprache erweitert wurde. Die Existenz ei...

The aim of this article is to sketch a certain method of indirect reconstruction of the process by which mathematics as a deductive discipline emerged in ancienct Greece. We try out this method in a reconstruction of Thaïes' mathematics, but the main aim for which this method has been developed is the work of Pythagoras. We consider the process of...

This book Critical places of primary mathematics through the eyes of teachers presents the results of research that was conducted under a GACR project in the years 2011 to 2013. The aim of the research was to collect and analyze teachers‘ experience with regards to so called critical places in primary and lower secondary school mathematics. These p...

Many of the outstanding discoveries in the history of physics were closely tied to fundamental linguistic innovations, which made them possible. There is an extensive literature discussing the scientific achievements of Galileo, Descartes, and Newton from various perspectives. The aim of the present paper is to contribute to these discussions with...

The paper tries to put the conflict of the natural and the human sciences into its historical context. It describes the changes in classification of scientific disciplines that accompany a scientific revolution, and offers an alternative to Kuhns theory.Instead of a conflict between the proponents and opponents of the new paradigm it interprets the...

Several mathematical theories, as for instance Newton's theory of fluxions and fluents, Frege's theory of the foundations of arithmetic, or Peano's theory of natural numbers were first formulated in a logically inconsistent form. Only after some period of time consistent formulations of these theories were found. The paper analyzes several historic...

The philosophical analysis of the process of idealisation has developed in two independent directions. In the framework of analytical philosophy of science, idealisation is understood as a simplification or deformation of the description of a certain appearance or natural law. In the framework of the phenomenological tradition idealisation is under...

The paper attempts to summarize the debate on Kant’s philosophy of geometry and to offer a restricted area of mathematical
practice for which Kant’s philosophy would be a reasonable account. Geometrical theories can be characterized using Wittgenstein’s
notion of pictorial form. Kant’s philosophy of geometry can be interpreted as a reconstruction o...

Wenn jemand sagt, dass ein Bus um 9 Uhr abfährt – weiß man es dann? Angenommen, man ist darüber unterrichtet, dass die Busse
unter der Woche immer zur vollen Stunde abfahren – von 7 Uhr morgens bis 7 Uhr abends, weiß man es dann mit dem Wissen um
diese allgemeine Regel besser, dass der Bus um 9 Uhr abfährt? Macht es einen Unterschied, ob man den Fa...

The aim of the present paper is to offer a new analysis of the multifarious relations between mathematics and reality. We believe that the relation of mathematics to reality is, just like in the case of the natural sciences, mediated by instruments (such as algebraic symbolism, or ruler and compass). Therefore the kind of realism we aim to develop...

The aim of the present paper is to offer a new analysis of the multifarious relations between mathematics and reality. We believe that the relation of mathematics to reality is, just like in the case of the natural sciences, mediated by instruments (such as algebraic symbolism, or ruler and compass). Therefore the kind of realism we aim to develop...

In a series of papers (Kvasz 1998, 2005 and 2006) I proposed an interpretation of the development of scientific theories as changes of the pictorial form in the sense of the Tractatus. In the development of geometry and of algebra it was possible to identify six different forms, each of which determines the way how linguistic representations are co...

Mathematics is often interpreted as an apriori discipline whose propositions are analytic. The aim of the paper is to support a philosophical position which would view mathematics as a discipline studying its own segment of objective reality and thus contributing to our knowledge of the real world. The author tries to articulate in more details suc...

The aim of the present paper is to show a relevance of several Wittgenstein's insights for the philosophy of mathematics. The paper argues that in both, the early, and the late Wittgenstein, we can find ideas that can be developed into a coherent account of mathematics. This account which is in the paper called "Wittgenstein's unofficial philosophy...

One of the pillars of Sir Karl Popper's philosophy is fallibilism, according to which there is no certain empirical knowledge.
When this position is criticized, it is usually claimed that the scope of fallibilism is restricted, and that there are some
areas where infallible knowledge is possible. In the paper we develop a different line of argument...

Mathematics is traditionally considered being an apriori dis-cipline consisting of purely analytic propositions. The aim of the pre-sent paper is to offer arguments against this entrenched view and to draw attention to the experiential dimension of mathematical knowledge. Following Husserl's interpretation of physical knowledge as knowledge constit...

Mathematics is traditionally considered being an apriori discipline consisting of purely analytic propositions. The aim of the present paper is to offer arguments against this entrenched view and to draw attention to the experiential dimension of mathematical knowledge. Following Husserl's interpretation of physical knowledge as knowledge constitut...

The paper compares Barbour's four ways of relating science and religion with Kuhn's theory of scientific revolutions and Lindbeck's classification of views on the nature of religious doctrine. It turns out that these three theories can be brought into correlation. On the one hand, in the framework of Kuhn's theory, three kinds of scientific revolut...

The aim of the paper is to offer a new interpretation of the role of Cartesian physics in the Scientific revolution. The author argues that many components of Newton's theory of motion are of Cartesian origin, an the Cartesian system was an important stage in the development of modern science. If this interpretation is correct, then the philosophic...

The roles of geometry and of arithmetic in contemporary philosophy of mathematics are rather asymmetric. While arithmetic plays a central role in foundational approaches and therefore its logical structure is thoroughly studied and well understood (see Shapiro 2005), geometry is the central topic of the antifoundational approaches (see Boi, Flament...

We based our description of re-codings in the history of mathematics on Frege’ interpretation of the development of arithmetic as a gradual growth of the generality of its language. Frege identified as the fundamental events in the history of mathematics the invention of the constant symbols in arithmetic, the introduction of the variable in algebr...

We have reached the end of our exposition of the patterns of change in the development of mathematics. In the closing chapter I would like to discuss some interpretations of the development of mathematics. I will focus on the approaches based on the works of Kuhn, Lakatos, and Piaget and I will compare them with the approach described in the presen...

The changes that were analyzed in the previous two chapters were of a global nature. Each of them consisted in the rebuilding of the syntactic or semantic structure of wide are as of mathematics. Therefore they happened rarely. They were not the fruit of the work of one mathematician but rather the result of the work of a whole series of them. The...

This book offers a reconstruction of linguistic innovations in the history of mathematics; innovations which changed the ways in which mathematics was done, understood and philosophically interpreted. It argues that there are at least three ways in which the language of mathematics has been changed throughout its history, thus determining the lines...

The aim of the paper is to study the analogies between the development of painting and the history of geometry. It starts with brief comments on geometrical aspects of Renaissance painting, followed by Mannerism, Baroque, and ends with a discussion of Impressionism. The paper represents a sequel to our paper History of Geometry and the development...

If we compare the mathematics of Antiquity with that of the 17-th century, we find differences in a whole range of aspects. For the Ancients notions like infinity, chance, space, or motion fell outside mathematics, while in the 17-th century new mathematical theories about these notions appeared. We believe that this fundamental change can be ascri...

This paper offers an epistemological reconstruction of the historical development of algebra from al-Khwārizmī, Cardano, and
Descartes to Euler, Lagrange, and Galois. In the reconstruction it interprets the algebraic formulas as a symbolic language
and analyzes the changes of this language in the course of history. It turns out that the most fundam...

The aim of this paper is to compare Heidegger's account of the rise of mathematical natural science contained in his Die Frage nach dem Ding with Husserl's conception of mathematisation, the outline of which we find in Die Krisis der europäischen Wissenschaften und die transzendentale Phänomenologie. The paper is made up of two parts. In the first...

The aim of the paper is to describe the main epistemological ruptures in the history of modern physics. Our approach is based on the reconstruction of the formal language of physical theories. We examine how particular aspects of the formal language, such as its analytical, expressive, or explanatory power, as well as its analytical and expressive...

The aim of the paper is to describe the main epistemological ruptures in the history of physics. This description is based on a reconstruction of the formal language of the physical theories. Attention is paid to its various aspects: its analytical, expressive or explanatory power, as well as its analytical and expressive boundaries. Among the main...

The aim of the paper is to discuss some historical circumstances of the constitution of analytic philosphy. The first of them is the birth of modern physics, which led to a new empirical attitude towards reality. The paper tries to underline the important role of scholastic philosophy as well as the philosophy of Descartes in this process. The seco...

Hussserl interpreted idealisation as a process, in which a certain aspect of the natural world is substituted with a mathematical ideality. The aim of this paper is to show how it is possible to interpret the emergence of Newton's physics as the idealisation of the effect wherein the causal effect, as we encounter it in the natural world, is substi...

Coming from a mathematical background, I was always puzzled by Popper’s view, according to which, after the falsification of a scientific theory its degree of corroboration becomes zero. Most of the scientific theories taught in the physics departments have already been falsified, and what is the point of teaching theories, whose degree of corrobor...

The aim of the paper is to present a theoretical framework which would make it possible to embed the conflict between the natural and human sciences into a broader historical context. With the help of categories such as paradigmatic disciplines, mixed discipline of the paradigm, metaphorical realm of the paradigm, and elusive realm of the paradigm...

The aim of this paper is a critical analysis of the methodology of Imre Lakatos. We will try to show that the full potential of Lakatos’ methodological ideas were not allowed manifest itself, because of their being confused with dialectic. By separating the hard core of Lakatosian methodology from the dialectical heritage of his marxist past, we be...

Imre Lakatos’ philosophy of science is rooted in a number of different fields, not all of them purely scientific. During his years of education, he was influenced by mathematics and natural sciences as well as by philosophy, but the role of political ideologies also cannot be denied. His basic philosophical ideas — such as the rationality of scienc...

Imre Lakatos (1922-1974) was one of the protagonists in shaping the "new philosophy of science". More than 25 years after his untimely death, it is time for a critical re-evaluation of his ideas. His main theme of locating rationality within the scientific process appears even more compelling today, after many historical case studies have revealed...

The aim of the paper is to reconstruct the epistemological shifts in the development of algebraic thought during the period reaching from Lagrange to Noether. We believe that, first, it illustrates the usefulness of Wittgenstein's concept of pictorial form (we prefer to call it form of language), because the evolution of algebra can most clearly be...

The nature of changes in mathematics was discussed recently in Revolutions in Mathematics. The discussion was dominated by historical and sociological arguments. An obstacle to a philosophical analysis of this question
lies in a discrepancy between our approach to formulas and to pictures. While formulas are understood as constituents of mathematic...

The aim of the paper is to reconstruct the historical development of classical algebra from Al Khwarizmi to Lagrange and to analyse the fundamental epistemological shifts, which occurred in the understanding of basic algebraic concepts. The paper opens with a general characteristics of algebraic thought as conceptualization of motor schemes. That p...

The aim of the paper is to analyse the geometrical aspects of a series of modern paintings and to show the parallel between them and the development of modern geometry. It starts with El Greco, offering a geometrical explanation of his painting the figures in a prolonged manner. Further the analogy between the impressionist way of creating space (i...

The aim of the paper is to confront Husserl's interpretation of Galileo's physics, from his Crisis, with the content and historical context of Galileo's scientific works. From such an confrontation it turned out, that the basic Husserlian ideas, which Husserl presented in a rather general and loose terms, can be filled with historical content and d...

The question whether Kuhn's theory of scientific revolutions could be applied to mathematics caused many interesting problems
to arise. The aim of this paper is to discuss whether there are different kinds of scientific revolution, and if so, how many.
The basic idea of the paper is to discriminate between the formal and the social aspects of the d...

The aim of this paper is to compare two approaches to semantics, namely the standard Tarskian theory and Wittgenstein’s picture theory of meaning. I will compare them with respect to an unusual subject matter, namely to geometrical pictures. The choice of geometry rather than arithmetic or set theory as the basis, on which this comparison will be m...

The aim of this paper is to introduce Wittgenstein’s concept of the form of a language into geometry and to show how it can
be used to achieve a better understanding of the development of geometry, from Desargues, Lobachevsky and Beltrami to Cayley,
Klein and Poincaré. Thus this essay can be seen as an attempt to rehabilitate the Picture Theory of...

The aim of the article is to provide teachers some ideas about thedevelopment of physical knowledge and to make them more receptive to thedifferences between their and the students thinking. I want to show, thatthese differences lie not only in the richness of experience, but also in thestructure of this experience. I try to point to some of these...

Boundary layers in a nonlinear disk dynamo are considered. The qualitative behavior of the solution and the results of numerical calculations are described.
The steady states of the large-scale magnetic field in a thin-disk galactic dynamo are studied using asymptotic methods. The field is decomposed into a sum of solutions of the degenerate proble...

The solution of the boundary layer problem in a nonlinear galactic dynamo is described.

The solution of the boundary layer problem in a nonlinear galactic dynamo is described.

We discuss the steady states of the -dynamo in a thin disc which arise due to -quenching. Two asymptotic regimes are considered, one for the dynamo numberD near the generation thresholdD0, and the other for |D| >> 1. Asymptotic solutions for |D - D0| 1 the asymptotic solution crucially depends on whether or not the mean helicity alpha, as a functio...

Cieľom predkladaného príspevku je na niekoľkých vybraných príkladoch ilustrovať spôsob, akým maliari porušujú geometrické pravidlá zobrazovania priestoru a tým dosahujú zvláštnu pôsobivosť svojich obrazov. Takto vedľa objavovania perspektívy v ranej renesancii a jej tvorivého pouívania v neskorších obdobiach máme tretie miesto dotyku geometrie a m...

How are we to understand and distinguish qualities of mathematical acquirement? The authors show with help of a school relevant example how mathematical awareness can be classified. The classification uses linguistic methods to identify factors important for conceptual understanding of mathematics. The analysis relates historical to activity theore...

What does it mean to have learned mathematics? But how can we make the objectives of mathematics teaching precise? The usual way (like in most national curricula or assessments like PISA or TIMS) is to demand certain competences. The objective of this article is to develop an epistemological concept of mathematical awareness that is embedded in the...

## Projects

Project (1)

I’ve edited a monograph title Philosophy of Mathematics Education Today which was published with Springer in 2018. The book contains state-of-the-art theoretical and philosophical contributions to mathematics education research as well in the philosophy of mathematical practice.
Contact me directly if you would like to see a review copy. Via p.ernest(at)ex.ac.uk.
CONTENTS OF THE BOOK
PREFACE
A Plea for a Critical Transformative Philosophy of Mathematics Education, Luis Radford Pages 1-10
INTRODUCTION TO THE FIELD
The Philosophy of Mathematics Education: An Overview, Paul Ernest Pages 13-35
THE NATURE OF MATHEMATICS
The Who and What of the Philosophy of Mathematical Practices, Jean Paul Van Bendegem, Pages 39-59
The Philosophy of Mathematical Education Between Platonism and the Computer, Michael Otte, Pages 61-79
A Dialogical Conception of Explanation in Mathematical Proofs, Catarina Dutilh Novaes, Pages 81-98
The Amalgam of Faith and Reason: Euclid’s Elements and the Scientific Thinker, Melissa Andrade-Molina, Paola Valero, Ole Ravn, Pages 99-111
CRITICAL MATHEMATICS EDUCATION
Students’ Foregrounds and Politics of Meaning in Mathematics Education, Ole Skovsmose, Pages 115-130
The Struggle Is Pedagogical: Learning to Teach Critical Mathematics, Eric “Rico” Gutstein, Pages 131-143
Some Thoughts on a Mathematics Education for Environmental Sustainability, Richard Barwell, Pages 145-160
Epistemological Questions About School Mathematics, Margaret Walshaw, Pages 161-171
The Concept of Culture in Critical Mathematics Education, Brendan Larvor, Karen François, Pages 173-185
The Ethics of Mathematics: Is Mathematics Harmful?, Paul Ernest, Pages 187-216
PHILOSOPHICAL THEORY IN MATHEMATICS EDUCATION RESEARCH
On the Need for Theory of Mathematics Learning and the Promise of ‘Commognition’, Anna Sfard, Pages 219-228
On the Roles of Language in Mathematics Education, Ladislav Kvasz, Pages 229-240
The Separation of Mathematics from Reality in Scientific and Educational Discourse, Uwe Schürmann, Pages 241-251
Mathematics Education Actualized in the Cyberspace: A Philosophical Essay, Maria Aparecida Viggiani Bicudo, Pages 253-270
PHILOSOPHY OF/IN TEACHING, LEARNING AND DOING MATHEMATICS
Making Distinctions: A Phenomenological Exploration in Mathematics Education, John Mason, Pages 273-296
Using Rules for Elaborating Mathematical Concepts, Michael Meyer, Pages 297-308
Towards a Wider Perspective: Opening a Philosophical Space in the Mathematics Curriculum, Nadia Stoyanova Kennedy, Pages 309-320
Creativity Research in Mathematics Education Simplified: Using the Concept of Bisociation as Ockham’s Razor, Bronislaw Czarnocha, William Baker, Olen Dias, Pages 321-332
Teaching of Velocity in Mathematics Classes—Chances for Philosophical Ideas, Regina Dorothea Möller, Pages 333-342
Time for Work: Finding Worth-While-Ness in Making Mathematics, Hilary Povey, Gill Adams, Colin Jackson, Pages 343-352
Hades—The Invisible Side of Mathematical Thinking, Walther Paravicini, Jörn Schnieder, Ingrid Scharlau, Pages 353-364
Developing Rules Due to the Use of Family Resemblances in Classroom Communication, Jessica Kunsteller, Pages 365-377
The book is an outcome of the successful Topic Study Group (no. 53) on the Philosophy of Mathematics Education at the leading international conference ICME-13, Hamburg July 2016. The papers from that group have already been published in a special issue (no. 31) of the Philosophy of Mathematics Education journal published recently at http://socialsciences.exeter.ac.uk/education/research/centres/stem/publications/pmej/ (link broken - under repair)
and are freely available. See below for the paper titles.
The best of these papers are being extended for inclusion in the book, as well as many further chapters from world class scholars .
Philosophy of Mathematics Education Journal
No. 31 (November 2016) ISSN 1465-2978 (Online)
Editor: Paul Ernest
SPECIAL ISSUE
THE PHILOSOPHY OF MATHEMATICS EDUCATION AT ICME 13
(Papers from Topic Study Group 53 at ICME 13, Hamburg July 2016)
CONTENTS
Paul Ernest An Overview of the Philosophy of Mathematics Education
Jean Paul Van Bendegem Philosophy of Mathematical Practice: What is it All About?
Ole Skovsmose Politics of Meaning in Mathematics Education
Ladislav Kvasz The Language of Mathematics in a Historical, Epistemological, and Educational Perspective
Regina Möller The Teaching of Velocity in Mathematics Classes – Chances for Philosophical Ideas
Maria Aparecida Viggiani Bicudo Developments In Philosophy in/of Mathematical Education
Paul Ernest The Collateral Damage of Learning Mathematics
Iskra Nunez Theoretical Incompleteness: A Driving Mechanism of Evolution in Mathematics Education Research
Jeff Evans & Keiko Yasukawa Researchers as Policy Actors? Examining interactions between mathematics education research and PIAAC
Bronislaw Czarnocha, William Baker & Olen Dias The Ockham Razor of Creativity Research In Mathematics Education
Jessica Kunsteller Using Family Resemblances for Elaborating Mathematical Rules in Classroom Communication
Michael Meyer Concept Formation as a Rule-Based Use of Words
Nadia Stoyanova Kennedy Opening a Philosophical Space in the Mathematics Curriculum
Jörn Schnieder & Ingrid Scharlau Reading Mathematical Texts with Philosophical Methods
Ryan A. Nivens & Samuel Otten Journal Rankings and Representation in Mathematics Education
Uwe Schürmann Mathematical Modelling and the Separation of Mathematics from Reality
Hilary Povey, Gill Adams, Colin Jackson & Emanuela Ughi The Role of Exhibitions by Children in Making Mathematics
Peter Collignon Teaching Applied Mathematics as a Bridge from Philosophy of Science to Philosophy of Mathematics Education
Durga Prasad Dhakal Philosophy of Mathematics and its Relevance In Maths Classroom
Anderson Afonso da Silva & Maria Aparecida Viggiani Bicudo The Production of Knowledge in Mathematics Education Research Groups in Brazil
Filipe Santos Fernandes History of Scientific and Academic Production in Mathematics Education: Representation, Institution and Policy
Fayez M. Mina Complexity and Mathematics Education
Allan Tarp From Essence to Existence in Mathematics Education
Fernanda Aparecida Ferreira & Cintia A. Bento dos Santos Possibilities of the Phenomenological Approach and of Philosophical Hermeneutics in Type Search State of Art
Karla Sepúlveda Obreque & Javier Lezama Andalón Epistemology of Teachers about the Mathematical Knowledge
Taís Barbariz Geometry: Of What it Treats?