81 research outputs found
Book Review: What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles
This is a review of What is a Mathematical Concept? edited by Elizabeth de Freitas, Nathalie Sinclair, and Alf Coles (Cambridge University Press, 2017). In this collection of sixteen chapters, philosophers, educationalists, historians of mathematics, a cognitive scientist, and a mathematician consider, problematise, historicise, contextualise, and destabilise the terms âmathematicalâ and âconceptâ. The contributors come from many disciplines, but the editors are all in mathematics education, which gives the whole volume a disciplinary centre of gravity. The editors set out to explore and reclaim the canonical question âwhat is a mathematical concept?â from the philosophy of mathematics. This review comments on each paper in the collection
Human-Machine Collaboration in the Teaching of Proof
This paper argues that interactive theorem provers (ITPs) could play an important role in fostering studentsâ appreciation and understanding of proof and of mathematics in general. It shows that the ITP Lean has three features that mitigate existing difficulties in teaching and learning mathematical proof. One is that it requires students to identify a proof strategy at the start. The second is that it gives students instant feedback while allowing them to explore with maximum autonomy. The third is that elementary formal logic finds a natural place in the activity of creating proofs. The challenge in using Lean is that students have to learn its command language, in addition to mathematics course content and elementary logic
Why 'scaffolding' is the wrong metaphor : the cognitive usefulness of mathematical representations.
The metaphor of scaffolding has become current in discussions of the cognitive help we get from artefacts, environmental affordances and each other. Consideration of mathematical tools and representations indicates that in these cases at least (and plausibly for others), scaffolding is the wrong picture, because scaffolding in good order is immobile, temporary and crude. Mathematical representations can be manipulated, are not temporary structures to aid development, and are refined. Reflection on examples from elementary algebra indicates that Menary is on the right track with his âenculturationâ view of mathematical cognition. Moreover, these examples allow us to elaborate his remarks on the uniqueness of mathematical representations and their role in the emergence of new thoughts.Peer reviewe
The Concept of Culture in Critical Mathematics Education
© Springer International Publishing AG, part of Springer Nature 2018. This is a post-peer-review, pre-copyedit version of a chapter published in The Philosophy of Mathematics Education Today. The final authenticated version is available online at: http://dx.doi.org/10.1007/978-3-319-77760-3A well-known critique in the research literature of critical mathematics education suggests that framing educational questions in cultural terms can encourage ethnic-cultural essentialism, obscure conflicts within cultures and promote an ethnographic or anthropological stance towards learners. Nevertheless, we believe that some of the obstacles to learning mathematics are cultural. âStereotype threatâ, for example, has a basis in culture. Consequently, the aims of critical mathematics education cannot be seriously pursued without including a cultural approach in educational research. We argue that an adequate conception of culture is available and should include normative/descriptive and material/ideal dyads as dialectical moments
Une méthode rapide de détermination des matiÚres minérales dans les farines d'origine animale
Ferrando Raymond, Henry N., Froget J., Larvor Pierre. Une méthode rapide de détermination des matiÚres minérales dans les farines d'origine animale. In: Bulletin de l'Académie Vétérinaire de France tome 112 n°3, 1959. pp. 205-207
Mathematical practice, crowdsourcing, and social machines
The highest level of mathematics has traditionally been seen as a solitary
endeavour, to produce a proof for review and acceptance by research peers.
Mathematics is now at a remarkable inflexion point, with new technology
radically extending the power and limits of individuals. Crowdsourcing pulls
together diverse experts to solve problems; symbolic computation tackles huge
routine calculations; and computers check proofs too long and complicated for
humans to comprehend.
Mathematical practice is an emerging interdisciplinary field which draws on
philosophy and social science to understand how mathematics is produced. Online
mathematical activity provides a novel and rich source of data for empirical
investigation of mathematical practice - for example the community question
answering system {\it mathoverflow} contains around 40,000 mathematical
conversations, and {\it polymath} collaborations provide transcripts of the
process of discovering proofs. Our preliminary investigations have demonstrated
the importance of "soft" aspects such as analogy and creativity, alongside
deduction and proof, in the production of mathematics, and have given us new
ways to think about the roles of people and machines in creating new
mathematical knowledge. We discuss further investigation of these resources and
what it might reveal.
Crowdsourced mathematical activity is an example of a "social machine", a new
paradigm, identified by Berners-Lee, for viewing a combination of people and
computers as a single problem-solving entity, and the subject of major
international research endeavours. We outline a future research agenda for
mathematics social machines, a combination of people, computers, and
mathematical archives to create and apply mathematics, with the potential to
change the way people do mathematics, and to transform the reach, pace, and
impact of mathematics research.Comment: To appear, Springer LNCS, Proceedings of Conferences on Intelligent
Computer Mathematics, CICM 2013, July 2013 Bath, U
How to think about informal proofs
This document is the Accepted Manuscript version of the following article: Brendan Larvor, âHow to think about informal proofsâ, Synthese, Vol. 187(2): 715-730, first published online 9 September 2011. The final publication is available at Springer via doi:10.1007/s11229-011-0007-5It is argued in this study that (i) progress in the philosophy of mathematical practice requires a general positive account of informal proof; (ii) the best candidate is to think of informal proofs as arguments that depend on their matter as well as their logical form; (iii) articulating the dependency of informal inferences on their content requires a redefinition of logic as the general study of inferential actions; (iv) it is a decisive advantage of this conception of logic that it accommodates the many mathematical proofs that include actions on objects other than propositions; (v) this conception of logic permits the articulation of project-sized tasks for the philosophy of mathematical practice, thereby supplying a partial characterisation of normal research in the fieldPeer reviewedFinal Accepted Versio
What can the Philosophy of Mathematics Learn from the History of Mathematics?
âThe original publication is available at www.springerlink.comâ. Copyright Springer DOI: 10.1007/s10670-008-9107-0Peer reviewe
EFFET DE L'ADRĂNALINE ET DE LA NORADRĂNALINE SUR LA MAGNĂSIĂMIE ET LA GLYCĂMIE DU RAT INTERFĂRENCE DE LA DIHYDROERGOTAMINE ET DE L'INSULINE
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