## WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?

### BibTeX

@MISC{Ernest_whatis,

author = {Paul Ernest},

title = {WHAT IS THE PHILOSOPHY OF MATHEMATICS EDUCATION?},

year = {}

}

### OpenURL

### Abstract

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

### Citations

184 |
Educational psychology: a cognitive view
- Ausubel
- 1968
(Show Context)
Citation Context ...gical implication, it is theoretically possible to consistently associate a philosophy of mathematics with almost any educational practice or approach. Both a neo-behaviourist or cognitivist (such as =-=Ausubel 1968-=-) and a radical constructivist (such as Glasersfeld 1995) may be concerned to ascertain 11what a child knows before commencing teaching, despite having diametrically opposite epistemologies (absoluti... |

128 |
Proofs and Refutations
- Lakatos
- 1976
(Show Context)
Citation Context ...philosophies of mathematics has been gaining ground, and these propose a different and opposing image of mathematics as human, corrigible, historical and changing (Davis and Hersh 1980, Ernest 1994b, =-=Lakatos 1976-=-, Tymoczko 1986). Fallibilism views mathematics as the outcome of social processes. Mathematical knowledge is understood to be eternally open to revision, both in terms of its proofs and its concepts.... |

121 | a Different Voice - Gilligan - 1982 |

75 |
Radical constructivism: A way of knowing and learning
- Glasersfeld
- 1995
(Show Context)
Citation Context ...onsistently associate a philosophy of mathematics with almost any educational practice or approach. Both a neo-behaviourist or cognitivist (such as Ausubel 1968) and a radical constructivist (such as =-=Glasersfeld 1995-=-) may be concerned to ascertain 11what a child knows before commencing teaching, despite having diametrically opposite epistemologies (absolutist and fallibilist, respectively). Likewise a traditiona... |

56 |
The mathematical experience
- Davis, Hersh
- 1981
(Show Context)
Citation Context ...decades a new wave of ‘fallibilist’ philosophies of mathematics has been gaining ground, and these propose a different and opposing image of mathematics as human, corrigible, historical and changing (=-=Davis and Hersh 1980-=-, Ernest 1994b, Lakatos 1976, Tymoczko 1986). Fallibilism views mathematics as the outcome of social processes. Mathematical knowledge is understood to be eternally open to revision, both in terms of ... |

53 |
Principles and standards for school mathematics
- NCTM
- 2000
(Show Context)
Citation Context ...hat way anywhere. Influential inquiries into the teaching of mathematics have propounded humanised and anti-absolutist (if not wholeheartedly fallibilist) views of school mathematics (Cockcroft 1982, =-=NCTM 2000-=-). The weight of informed educational opinion has likewise supported the progressive reform of mathematics in line with such views, although there has also been a backlash from mathematicians and more... |

35 |
The Philosophy of Mathematics Education
- Ernest
- 1991
(Show Context)
Citation Context ...ng values of the relevant social groups are implicated. This resembles the issues arising from 1 This was a critical response by some to the title of my book, The Philosophy of Mathematics Education (=-=Ernest 1991-=-) 1applying Schwab's (1961) four 'commonplaces of teaching' to the mathematics curriculum. These are the subject (mathematics), the learner of mathematics, the mathematics teacher, and the milieu of ... |

33 |
Learning as a constructive activity
- Glasersfeld
- 1983
(Show Context)
Citation Context ...tructivism, most notably the strong version due to Ernst von Glasersfeld (1995). As he had noted “To introduce epistemological considerations into a discussion of education has always been dynamite” (=-=Glasersfeld 1983-=-: 41). Ironically, the attacks on radical constructivism at that conference, which were intended to expose the weaknesses of the position fatally, served instead as a platform from which it was launch... |

20 | Towards a philosophy of critical mathematics education - Skovsmose - 1994 |

11 |
Fidelity in mathematical discourse: Is one and one really two? American Mathematical Monthly 79(3):252–263
- Davis
- 1972
(Show Context)
Citation Context ... anew, like trees in a forest (Steen 1988). Fallibilism does reject the absolutist image of mathematics as a body of pure and perfect abstract knowledge which exists in a superhuman, objective realm (=-=Davis 1972-=-). Instead mathematics is associated with sets of social practices, each with its history, persons, institutions and social locations, symbolic forms, purposes and power relations. Thus academic resea... |

11 | The concept of the structure of a discipline - Schwab - 1968 |

10 |
The Socialisation of Teachers
- Lacey
- 1977
(Show Context)
Citation Context ...or the various constraints of the social context of schooling to be so powerful that a teacher with connected values and a humanistic view of school mathematics is forced into ‘strategic compliance’ (=-=Lacey 1977-=-), resulting in a separated mathematics classroom practice. This is indicated in Figure 2 by the bold and thin arrows deviating left towards the separated classroom practice following the impact of th... |

8 | The paradigm wars and their aftermath: A "historical" sketch of research on teaching since 1989. Educational Researcher - Gage - 1989 |

6 |
The state of mathematics education: Building a strong foundation for the 21st century
- Riley
- 1998
(Show Context)
Citation Context ...d educational opinion has likewise supported the progressive reform of mathematics in line with such views, although there has also been a backlash from mathematicians and more conservative thinkers (=-=Riley 1998-=-) An important issue for education is the relationship between mathematics and values, especially since the popular image of mathematics is clearly value-laden. The feminist researcher Gilligan (1982)... |

5 | A History of - Howson - 1982 |

4 | Didactics of Mathematics as a Scientific Discipline - Biehler, W, et al. - 2001 |

4 |
Alternative Views of the Nature of Mathematics and their Possible Influence on the Teaching of Mathematics, unpublished
- Lerman
- 1986
(Show Context)
Citation Context ...d that teachers with very distinct personal philosophies of mathematics (absolutist and fallibilist) have been constrained by the social context of schooling to teach in a traditional, separated way (=-=Lerman 1986-=-). I suggest that values as well as beliefs and philosophies play a key role in determining the underlying images and philosophies embodied in mathematics classroom practice. This is not surprising, s... |

2 |
An Ethic of Care
- Larrabee
- 1993
(Show Context)
Citation Context ...e are one species and male/female differences are not as profound as our commonalities, reviews of empirical evidence suggest that there are significant differences by late adolescence and adulthood (=-=Larrabee 1993-=-), and girls are more likely to be empathetic than boys in exhibiting emotional reactions to another’s feelings (Hoffman 1977). Likewise, separated values have come to dominate many institutions and s... |

1 |
Is school mathematics in crisis
- Barnard, Saunders
- 1994
(Show Context)
Citation Context ...s a platform from which it was launched to widespread international acceptance and approbation. This is not without continuing strong critiques of constructivism from mathematicians and others (e.g., =-=Barnard and Saunders 1994-=-). Since then, yet further controversy has erupted between different versions of constructivism, most notably radical constructivism versus social constructivism (Ernest 1994a), as well as powerful cr... |

1 | Philosophy of Mathematics Education: POM(E), PO(ME) OR POE(M)?, Philosophy Of Mathematics Education Newsletter No - Brown - 1995 |

1 |
The Issue of Reform
- Cooney
- 1988
(Show Context)
Citation Context ...proaches in mathematics incorporate assumptions about the nature of mathematics, and that any philosophy of mathematics has classroom consequences (Hersh 1979, Steiner 1987). Empirical research (e.g. =-=Cooney 1988-=-) has confirmed claims that “teachers' views, beliefs and preferences about mathematics do influence their instructional practice” (Thompson 1984: 125). Thus it may be argued that any philosophy of ma... |

1 |
The Contextualising of Mathematics: Towards a Theoretical Map
- Dowling
- 1988
(Show Context)
Citation Context ...tics and school mathematics is a distinct set of such practices. They are intimately bound up together, because the symbolic productions of one practice is recontextualised and reproduced in another (=-=Dowling 1988-=-). However, it is important to distinguish between a fallibilist (or absolutist) epistemology of mathematics, and a fallibilist (or absolutist) account of the nature of mathematics. The former is a st... |

1 |
The Attitudes and Practices of Student Teachers
- Ernest
- 1988
(Show Context)
Citation Context ...teaching. However amongst non-mathematics-specialist future primary school teachers I found a loose correlation between fallibilist conceptions and positive attitudes to mathematics and its teaching (=-=Ernest 1988-=-, 1989b). Thus the connections even just between beliefs and attitudes to mathematics are complex and multifaceted. Research on children’s attitudes towards mathematics in the past two decades shows f... |

1 |
The Impact of Beliefs on the Teaching
- Ernest
- 1989
(Show Context)
Citation Context ... the social context of practice, give rise to the realised theories of learning mathematics, teaching mathematics, and the related use of mathematical texts and curriculum materials in the classroom (=-=Ernest, 1989-=-a). Such a model is partially validated by empirical work. However classroom consequences are not in general strictly logical implications of a philosophy, and additional values, aims and other assump... |

1 |
Mathematics-Related Belief Systems, Poster presented at PME-13
- Ernest
- 1989
(Show Context)
Citation Context ... the social context of practice, give rise to the realised theories of learning mathematics, teaching mathematics, and the related use of mathematical texts and curriculum materials in the classroom (=-=Ernest, 1989-=-a). Such a model is partially validated by empirical work. However classroom consequences are not in general strictly logical implications of a philosophy, and additional values, aims and other assump... |

1 |
The Philosophy of
- Ernest
- 1994
(Show Context)
Citation Context ...hers (e.g., Barnard and Saunders 1994). Since then, yet further controversy has erupted between different versions of constructivism, most notably radical constructivism versus social constructivism (=-=Ernest 1994-=-a), as well as powerful critiques of constructivism learning theory both within science and mathematics education, and from without. 4. Mathematics Teaching The teaching of mathematics is also an area... |

1 | Social Constructivism as a Philosophy of Mathematics - unknown authors - 1998 |

1 |
Some Proposals for Reviving the
- Hersh
- 1979
(Show Context)
Citation Context ...4). Other articulations stress both that teaching approaches in mathematics incorporate assumptions about the nature of mathematics, and that any philosophy of mathematics has classroom consequences (=-=Hersh 1979-=-, Steiner 1987). Empirical research (e.g. Cooney 1988) has confirmed claims that “teachers' views, beliefs and preferences about mathematics do influence their instructional practice” (Thompson 1984: ... |

1 |
Sex-Differences in Empathy and Related
- Hoffman
- 1977
(Show Context)
Citation Context ...that there are significant differences by late adolescence and adulthood (Larrabee 1993), and girls are more likely to be empathetic than boys in exhibiting emotional reactions to another’s feelings (=-=Hoffman 1977-=-). Likewise, separated values have come to dominate many institutions and structures, including mathematics and science, especially in Anglophone and Protestant countries. Many people have come to fee... |

1 | Mathematics Education as a Research Domain - Kilpartrick, Sierpinska, et al. - 1998 |

1 |
Mathematics Teaching: The State of the Art
- Maxwell
- 1989
(Show Context)
Citation Context ...ss an absolutist-like conception of the subject (Buerk 1982). In some cases the outcome is also a strongly negative affective response to mathematics too, sometimes termed ‘mathephobia’ (Buxton 1981, =-=Maxwell 1989-=-). However, in the past few decades a new wave of ‘fallibilist’ philosophies of mathematics has been gaining ground, and these propose a different and opposing image of mathematics as human, corrigibl... |

1 |
The Science of
- Steen
- 1988
(Show Context)
Citation Context ...chical structure. Instead it accepts the view that mathematics is made up of many overlapping structures which, over the course of history, grow, dissolve, and then grow anew, like trees in a forest (=-=Steen 1988-=-). Fallibilism does reject the absolutist image of mathematics as a body of pure and perfect abstract knowledge which exists in a superhuman, objective realm (Davis 1972). Instead mathematics is assoc... |

1 |
Philosophical and Epistemological Aspects of Mathematics and their Interaction with Theory and Practice
- Steiner
- 1987
(Show Context)
Citation Context ...ticulations stress both that teaching approaches in mathematics incorporate assumptions about the nature of mathematics, and that any philosophy of mathematics has classroom consequences (Hersh 1979, =-=Steiner 1987-=-). Empirical research (e.g. Cooney 1988) has confirmed claims that “teachers' views, beliefs and preferences about mathematics do influence their instructional practice” (Thompson 1984: 125). Thus it ... |

1 |
Modern mathematics: does it exist? in Howson
- Thom
- 1973
(Show Context)
Citation Context ...elationship between philosophies of mathematics, values and teaching. A widely accepted position is that “All mathematical pedagogy, even if scarcely coherent, rests on a philosophy of mathematics.” (=-=Thom 1973-=-: 204). Other articulations stress both that teaching approaches in mathematics incorporate assumptions about the nature of mathematics, and that any philosophy of mathematics has classroom consequenc... |

1 | The Relationship Between Teachers - G - 1984 |