Problems with Fallibilism as a Philosophy of Mathematics Education

Rowlands, Stuart; Graham, Ted; Berry, John

doi:10.1007/s11191-010-9234-2

Cited by 7 publications

(8 citation statements)

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“…But then Ernest's relativism would not allow for that. For him, the law of contradiction holds and he often dismisses arguments with one counterexample (such as Koetsier's argument that the weak form of fallibilism can be verified with reference to history; see Rowlands et al 2010). Ernest is quite the absolutist when it comes to the strong form of fallibilism as if any alternative can be refuted by one counterexample.…”

Section: Resultsmentioning

confidence: 99%

“…According to the author initially no, although since the invitation to contribute to the festschrift, yes (he does add, however, that subconsciously it was yes initially). The Paul in the article could be described as a Lakatosian because similar to Lakatos he challenges the mathematicians' certainty regarding proof; whereas the real Paul has interpreted Lakatos to mean that any theorem is subject to refutation as opposed to mere revision (see Rowlands et al 2010). It seems as though van Bendegem has not captured the essential Ernest.…”

Section: The Contentmentioning

confidence: 99%

“…synonymous epistemological issues with equity issues (for a full discussion on what may be described as the essential Ernest see Rowlands et al 2010).…”

mentioning

confidence: 99%

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Bharath Sriraman and Simon Goodchild (eds): Relatively and Philosophically Earnest: Festschrift in Honor of Paul Ernest’s 65th Birthday, A volume in The Montana Mathematics Enthusiast

Rowlands

2010

Sci & Educ

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Section: Resultsmentioning

confidence: 99%

Section: The Contentmentioning

confidence: 99%

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Bharath Sriraman and Simon Goodchild (eds): Relatively and Philosophically Earnest: Festschrift in Honor of Paul Ernest’s 65th Birthday, A volume in The Montana Mathematics Enthusiast

Rowlands

2010

Sci & Educ

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“…History of science, however, shows that there is no guarantee that the scientific community is infallible (cf. Rowlands, Graham, & Berry, 2011). All knowledge develops and forms part of the social, cultural, and local milieu.…”

Section: Social Interactions and The Evolving Nature Of Objectivitymentioning

confidence: 99%

Conclusion: Understanding the Elusive Nature of Objectivity

Níaz¹

2017

Evolving Nature of Objectivity in the History of Science and Its Implications for Science Education

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An evaluation of research in science education reported in this book shows the problematic nature of understanding some of the universal values associated with objectivity such as certainty, value neutral observations, facts, infallibility, scientific method, and truth of scientific theories and laws. Similarly, aspects of Merton's "ethos of science" such as open-mindedness, universalist, disinterested, and communal have also been invoked to understand progress in science. Studies evaluated, however, have pointed out that some of these values are not necessarily essential for understanding objectivity. Philosophy of science itself has explored new territory in this context and Giere (2006a, p. 95) considers that it is presentist hubris to think that we can have an objectively correct or true theories. Daston and Galison (2007) have constructed the evolving nature of scientific judgment (objectivity) through the following phases: truth-to-nature, mechanical objectivity, structural objectivity, and finally trained judgment. Each of these regimes did not supplant the other but they can coexist and supplement each other at the same time. Although objectivity is not synonymous with truth or certainty, it has eclipsed other epistemic virtues and to be objective is often used as a synonym for scientific in both science and science education.Table 7.1 provides an overview of the classification of all the articles evaluated in this book. Following are some of the salient features of the results obtained: (a) S&E was the only journal in which two articles were classified in Level V, which approximates to the evolving nature of objectivity; (b) In all the chapters most of the articles were classified in Levels II and III; (c) Classification of the articles in Level III (62% for JRST, and 44% for S&E) means that the authors recognized the problematic nature of objectivity and hence the need for alternatives; and (d) Very few articles were classified in Level I (none for HPST and ESE), which approximates to the traditional concept of objectivity as found in most science textbooks. These results provide a detailed account (over a period of almost 25 years) of how the science education research community conceptualizes the difficulties involved in accepting objectivity as an unquestioned epistemic virtue of the 179

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“…This is elaborated further in the section after next.  A critique of constructivism's notion of 'absolutism' can be found in Rowlands et al (2010). 2 According to Kneller (1965), creativity can be introduced into education in one of two ways, either by teaching creativity on its own and in its own right, or we draw on the creative potential in all the subject matter we teach.…”

Section: Creativity and The Subject Mattermentioning

confidence: 99%

Discussion Article: Disciplinary Boundaries for Creativity

Rowlands¹

2011

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Creativity is a very topical issue and indeed a political one. For example, the very notion of ‘little c creativity’ seems to be a reflection of the requirements of what could be described as a ‘Post-Fordist’ economy. However, the call to develop creativity in education is largely based on the idea of creativity as the production of novel ideas. The central argument of this article is that creativity cannot be seen purely in terms of novel ideas but that it is intrinsically bound with the teaching of the academic disciplines. It is within the context of creativity in the sense of transforming the disciplines that two paradoxes are discussed. The first paradox is that the truly creative act is not the preserve of the genius but the potential for the whole of humanity. Secondly, creativity involves both thinking within the constraints of the discipline and challenging those constraints. This implies the need for students to engage in meta-discourse, involving the nature and history of the subject-matter taught

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Problems with Fallibilism as a Philosophy of Mathematics Education

Cited by 7 publications

References 20 publications

Bharath Sriraman and Simon Goodchild (eds): Relatively and Philosophically Earnest: Festschrift in Honor of Paul Ernest’s 65th Birthday, A volume in The Montana Mathematics Enthusiast

Bharath Sriraman and Simon Goodchild (eds): Relatively and Philosophically Earnest: Festschrift in Honor of Paul Ernest’s 65th Birthday, A volume in The Montana Mathematics Enthusiast

Conclusion: Understanding the Elusive Nature of Objectivity

Discussion Article: Disciplinary Boundaries for Creativity

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