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**1 - 4**of**4**### WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?

"... This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one o ..."

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This question (what is the philosophy of mathematics education?) provokes a number of reactions, even before one tries to answer it. Is it a philosophy of mathematics education, or is it the philosophy of mathematics education? Use of the preposition ‘a ’ suggests that what is being offered is one of several such perspectives, practices or areas of study. Use of the definite article ‘the ’ suggests to some the arrogation of definitiveness to the account given. 1 In other words, it is the dominant or otherwise unique account of philosophy of mathematics education. However, an alternative reading is that ‘the ’ refers to a definite area of enquiry, a specific domain, within which one account is offered. So the philosophy of mathematics education need not be a dominant interpretation so much as an area of study, an area of investigation, and hence something with this title can be an exploratory assay into this area. This is what I intend here. Moving beyond the first word, there is the more substantive question of the reference of the term ‘philosophy of mathematics education’. There is a narrow sense that can be applied in interpreting the words ‘philosophy ’ and ‘mathematics education’. The philosophy of some area or activity can be understood as its aims or rationale. Mathematics education understood

### Situated Abstraction

"... macrosociological perspectives Activity Theory and Communities of Inquiry Action-Production-Communication approach ..."

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macrosociological perspectives Activity Theory and Communities of Inquiry Action-Production-Communication approach

### DG Discussion

"... Aims and focus The aim of Discussion Group 4 was to explore the nature, role and state of Philosophy of Mathematics Education (PhoME) and particular themes focused on the perspective of PhoME. The group met three times. The initial part of the first session was dedicated to an orientation with an in ..."

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Aims and focus The aim of Discussion Group 4 was to explore the nature, role and state of Philosophy of Mathematics Education (PhoME) and particular themes focused on the perspective of PhoME. The group met three times. The initial part of the first session was dedicated to an orientation with an introductory overview “What is philosophy of mathematics educa tion? ” (see Ernest, 2004, for a written version). The second session, “Strands and issues for discussion within PhoME”, took place in smaller groups addressing different ques tions, followed by a synthesizing session. The prepared questions were: What are the conceptions of mathematics and mathematical knowledge underlying different learning theories? What roles do philosophies of mathematics play in the teaching and learning of mathematics? How do they relate to mathematics curriculum, teaching reforms and classroom practices? Different perspectives – a first metaphoric approach The group agreed on Paul Ernest’s suggestion to consider the PhoME not as one single

### Preface to Chapter 2 Ernest’s Reflections on Theories of Learning

"... Philosophy has always maintained an intricate relationship with mathematics. It was also implicitly accepted that the philosophical positions of a bearer influence his/her view on mathematics and its teaching (Törner & Sriraman, 2007), which leads us into the domain of beliefs theory. However th ..."

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Philosophy has always maintained an intricate relationship with mathematics. It was also implicitly accepted that the philosophical positions of a bearer influence his/her view on mathematics and its teaching (Törner & Sriraman, 2007), which leads us into the domain of beliefs theory. However the centrality of philosophy and its intricate relationship to theory development in mathematics education only came about two decades ago when Paul Ernest and Hans-Georg Steiner (1987) each independently became aware of the importance of epistemological issues that impact the teaching and learning of mathematics. Sierpinska and Lerman (1996) state: Epistemology as a branch of philosophy concerned with scientific knowledge poses fundamental questions such as: 'What are the origins of scientific knowledge?' (Empirical? Rational?); 'What are the criteria of validity of scientific knowledge? ' (Able to predict actual events? Logical consistency?); 'What is the character of the process of development of scientific knowledge? ' (Accumulation and continuity? Periods of normal science, scientific revolutions and discontinuity? Shifts and refinement in scientific programs?). The question of what is mathematics, for teaching and learning considerations brings into relevance the need to develop a philosophy of mathematics compatible with mathematics education. In order to answer this question for mathematics education, several theorists have played a role directly or indirectly. In this preface to chapter 2, we briefly summarize the role that Lakatos, Hersh and Ernest have played. Reuben Hersh began to popularize Lakatos ’ book Proofs and Refutations to the mathematics community in a paper titled, “Introducing Imre Lakatos ” (1978) and called for the community of mathematicians to take an interest in re-