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  1. added 2020-03-12
    Crunchy Methods in Practical Mathematics.Michael Wood - 2001 - Philosophy of Mathematics Education Journal 14.
    This paper focuses on the distinction between methods which are mathematically "clever", and those which are simply crude, typically repetitive and computer intensive, approaches for "crunching" out answers to problems. Examples of the latter include simulated probability distributions and resampling methods in statistics, and iterative methods for solving equations or optimisation problems. Most of these methods require software support, but this is easily provided by a PC. The paper argues that the crunchier methods often have substantial advantages from the perspectives (...)
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  2. added 2019-04-26
    Introduction.Andrew Aberdein & Matthew Inglis - 2019 - In Andrew Aberdein & Matthew Inglis (eds.), Advances in Experimental Philosophy of Logic and Mathematics. Bloomsbury Academic. pp. 1-13.
    There has been little overt discussion of the experimental philosophy of logic or mathematics. So it may be tempting to assume that application of the methods of experimental philosophy to these areas is impractical or unavailing. This assumption is undercut by three trends in recent research: a renewed interest in historical antecedents of experimental philosophy in philosophical logic; a “practice turn” in the philosophies of mathematics and logic; and philosophical interest in a substantial body of work in adjacent disciplines, such (...)
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  3. added 2019-03-21
    ¿“Natural” y “Euclidiana”? Reflexiones Sobre la Geometría Práctica y Sus Raíces Cognitivas.Jose Ferreiros & Manuel Garcia - 2018 - Theoria : An International Journal for Theory, History and Fundations of Science 33 (2):325-344.
    We discuss critically some recent theses about geometric cognition, namely claims of universality made by Dehaene et al., and the idea of a “natural geometry” employed by Spelke et al. We offer arguments for the need to distinguish visuo-spatial cognition from basic geometric knowledge, furthermore we claim that the latter cannot be identified with Euclidean geometry. The main aim of the paper is to advance toward a characterization of basic, practical geometry – which in our view requires a combination of (...)
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  4. added 2019-03-18
    Extended Mathematical Cognition: External Representations with Non-Derived Content.Karina Vold & Dirk Schlimm - 2019 - Synthese 1:1-21.
    Vehicle externalism maintains that the vehicles of our mental representations can be located outside of the head, that is, they need not be instantiated by neurons located inside the brain of the cogniser. But some disagree, insisting that ‘non-derived’, or ‘original’, content is the mark of the cognitive and that only biologically instantiated representational vehicles can have non-derived content, while the contents of all extra-neural representational vehicles are derived and thus lie outside the scope of the cognitive. In this paper (...)
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  5. added 2019-03-18
    The Mathematical Facts Of Games Of Chance Between Exposure, Teaching, And Contribution To Cognitive Therapies: Principles Of An Optimal Mathematical Intervention For Responsible Gambling.Catalin Barboianu - 2013 - Romanian Journal of Experimental Applied Psychology 4 (3):25-40.
    On the question of whether gambling behavior can be changed as result of teaching gamblers the mathematics of gambling, past studies have yielded contradictory results, and a clear conclusion has not yet been drawn. In this paper, I bring some criticisms to the empirical studies that tended to answer no to this hypothesis, regarding the sampling and laboratory testing, and I argue that an optimal mathematical scholastic intervention with the objective of preventing problem gambling is possible, by providing the principles (...)
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  6. added 2017-11-22
    Intuição e Conceito: A Transformação do Pensamento Matemático de Kant a Bolzano.Humberto de Assis Clímaco - 2014 - Dissertation, Universidade Federal de Goiás, Brazil
  7. added 2017-09-07
    Learning the Natural Numbers as a Child.Stefan Buijsman - 2019 - Noûs 53 (1):3-22.
    How do we get out knowledge of the natural numbers? Various philosophical accounts exist, but there has been comparatively little attention to psychological data on how the learning process actually takes place. I work through the psychological literature on number acquisition with the aim of characterising the acquisition stages in formal terms. In doing so, I argue that we need a combination of current neologicist accounts and accounts such as that of Parsons. In particular, I argue that we learn the (...)
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  8. added 2017-08-23
    Envisioning Transformations – The Practice of Topology.Silvia De Toffoli & Valeria Giardino - 2016 - In Brendan Larvor (ed.), Mathematical Cultures: The London Meetings 2012--2014. Zurich, Switzerland: Birkhäuser. pp. 25-50.
    The objective of this article is twofold. First, a methodological issue is addressed. It is pointed out that even if philosophers of mathematics have been recently more and more concerned with the practice of mathematics, there is still a need for a sharp definition of what the targets of a philosophy of mathematical practice should be. Three possible objects of inquiry are put forward: (1) the collective dimension of the practice of mathematics; (2) the cognitives capacities requested to the practitioners; (...)
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  9. added 2017-08-23
    An Inquiry Into the Practice of Proving in Low-Dimensional Topology.Silvia De Toffoli & Valeria Giardino - 2015 - In Gabriele Lolli, Giorgio Venturi & Marco Panza (eds.), From Logic to Practice. Zurich, Switzerland: Springer International Publishing. pp. 315-336.
    The aim of this article is to investigate specific aspects connected with visualization in the practice of a mathematical subfield: low-dimensional topology. Through a case study, it will be established that visualization can play an epistemic role. The background assumption is that the consideration of the actual practice of mathematics is relevant to address epistemological issues. It will be shown that in low-dimensional topology, justifications can be based on sequences of pictures. Three theses will be defended. First, the representations used (...)
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  10. added 2017-07-18
    Brain Projective Reality: Novel Clothes for the Emperor.Arturo Tozzi, James F. Peters, Andrew A. Fingelkurts, Alexander A. Fingelkurts & Pedro C. Marijuán - 2017 - Physics of Life Reviews 21:46-55.
    First of all, we would like to gratefully thank all commentators for the attention and effort they have put into reading and responding to our review paper [this issue] and for useful observations that suggest novel applications for our framework. We understand and accept that some of our claims might appear controversial and raise skepticism, because the overall neural framework we have proposed is difficult to frame in established categories, given its strong multidisciplinary character. To make an example, Elsevier is (...)
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  11. added 2017-05-01
    Improving Algebraic Thinking Skill, Beliefs And Attitude For Mathematics Throught Learning Cycle Based On Beliefs.Widodo Winarso & Toheri - 2017 - Munich University Library.
    In the recent years, problem-solving become a central topic that discussed by educators or researchers in mathematics education. it’s not only as the ability or as a method of teaching. but also, it is a little in reviewing about the components of the support to succeed in problem-solving, such as student's belief and attitude towards mathematics, algebraic thinking skills, resources and teaching materials. In this paper, examines the algebraic thinking skills as a foundation for problem-solving, and learning cycle as a (...)
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