The Experts below are selected from a list of 20442 Experts worldwide ranked by ideXlab platform

Uffe Thomas Jankvist - One of the best experts on this subject based on the ideXlab platform.

  • history application and Philosophy of Mathematics in Mathematics education accessing and assessing students overview and judgment
    2015
    Co-Authors: Uffe Thomas Jankvist
    Abstract:

    The Regular Lecture addresses the three dimensions of history, application, and Philosophy of Mathematics in the teaching and learning of Mathematics. It is discussed how students’ overview and judgment—interpreted as ‘sets of views’ and beliefs about Mathematics as a discipline—may be developed and/or changed through teaching activities embracing all three dimensions of history, application, and Philosophy. More precisely, an example of such a teaching activity for upper secondary school is described along with a method for both accessing and assessing students’ overview and judgment. Examples of data analysis are given based on a concrete implementation of the teaching activity.

  • a historical teaching module on the unreasonable effectiveness of Mathematics boolean algebra and shannon circuits
    Bshm Bulletin: Journal of The British Society for The History of Mathematics, 2014
    Co-Authors: Uffe Thomas Jankvist
    Abstract:

    This article describes the design and implementation of a historical teaching module, where Danish upper secondary students studied primary source material from the mathematicians R W Hamming, G Boole and C E Shannon. The module is an example of a so-called HAPh-module, which focuses on elements of the history, application and Philosophy of Mathematics. A previous version was presented at the History and Pedagogy of Mathematics (HPM) meeting in Deajeon, Korea in 2012.

  • special issue on history and Philosophy of Mathematics in Mathematics education
    Science Education, 2014
    Co-Authors: Victor J Katz, Uffe Thomas Jankvist, Michael N Fried, Stuart Rowlands
    Abstract:

    Although Science & Education has published papers specifically concerning Mathematics over the years—some quite significant for education—Mathematics has never received the spotlight. Indeed, when the journal was established it bore the subtitle, Contributions from History, Philosophy and Sociology of Science and Mathematics, but so few papers on Mathematics were received in those years that the word ‘‘Mathematics’’ was duly dropped. Yet within the community of science and Mathematics educators, there is no lack of interest at least in the contributions of history and Philosophy of Mathematics to Mathematics education, particularly the history of Mathematics. Besides publications such as those we have listed at the end of this introduction, one can point to the activities of the International Study Group on the Relations between the History and Pedagogy of Mathematics (HPM) which dates back to 1972, and which almost from the start became an affiliated study group of the International Commission on Mathematical Instruction (ICMI), the largest and oldest international organization for Mathematics education. International conferences of HPM have been held in Europe, Canada, Australia, Taiwan, Mexico, and Korea in association with the quadrennial International Congress on Mathematical Education (ICME). The European Summer University on History and Epistemology in Mathematics Education (ESU), now held every 4 years as well, is another regular venue for meetings dealing with history in Mathematics education, as is the working group on History in Mathematics Education at the biennial Congress of European

  • ‘Whys’ and ‘Hows’ of Using Philosophy in Mathematics Education
    Science & Education, 2014
    Co-Authors: Uffe Thomas Jankvist, Steffen Møllegaard Iversen
    Abstract:

    The article elaborates and exemplifies a potential categorization of the reasons for using Philosophy, in particular the Philosophy of Mathematics, in Mathematics education and approaches to doing so—the so-called ‘whys’ and ‘hows’. More precisely, the ‘whys’ are divided into the two categories of ‘Philosophy as a tool’ for teaching and learning Mathematics, and ‘Philosophy as a goal’, referring to a stance of considering it a purpose in itself to teach students certain aspects regarding the Philosophy of Mathematics. A division of the ‘hows’ into three different categories is offered: illumination approaches; modules approaches; and Philosophy-based approaches. A major part of the article is spent on providing illustrative exemplifications of each of these approaches by referring to already implemented uses of Philosophy of Mathematics in Mathematics education as well as by suggesting new ones.

  • history applications and Philosophy in Mathematics education haph a use of primary sources
    Science Education, 2013
    Co-Authors: Uffe Thomas Jankvist
    Abstract:

    The article first investigates the basis for designing teaching activities dealing with aspects of history, applications, and Philosophy of Mathematics in unison by discussing and analyzing the different ‘whys’ and ‘hows’ of including these three dimensions in Mathematics education. Based on the observation that a use of history, applications, and Philosophy as a ‘goal’ is best realized through a modules approach, the article goes on to discuss how to actually design such teaching modules. It is argued that a use of primary original sources through a so-called guided reading along with a use of student essay assignments, which are suitable for bringing out relevant meta-issues of Mathematics, is a sensible way of realizing a design encompassing the three dimensions. Two concrete teaching modules on aspects of the history, applications, and Philosophy of Mathematics—HAPh-modules—are outlined and the mathematical cases of these, graph theory and Boolean algebra, are described. Excerpts of student groups’ essays from actual implementations of these modules are displayed as illustrative examples of the possible effect such HAPh-modules may have on students’ development of an awareness regarding history, applications, and Philosophy in relation to Mathematics as a (scientific) discipline.

Paul Ernest - One of the best experts on this subject based on the ideXlab platform.

  • The Philosophy of Mathematics, Values and Keralese Mathematics
    The Mathematics Enthusiast, 2007
    Co-Authors: Paul Ernest
    Abstract:

    This paper explores the philosophical significance of the Keralese and Indian subcontinent contribution to history of Mathematics. Identifying the most accurate genesis and trajectory of mathematical ideas in history that current knowledge allows should be the goal of every history of Mathematics, and is consistent with any Philosophy of Mathematics. I argue for the need of a broader conceptualization of Philosophy of than the traditional emphasis on scholastic enquiries into epistemology and ontology. For such an emphasis has been associated, though I add need not necessarily be so, with an ideological position that devalues non-European contributions to history of Mathematics. The Philosophy of Mathematics needs to be broad enough to recognise the salient features of the discipline it reflects upon, namely Mathematics.

  • Mathematics education and Philosophy an international perspective
    2003
    Co-Authors: Paul Ernest
    Abstract:

    Reconceptualizing the Philosophy of Mathematics: Fresh Winds in the Philosophy of Mathematics, Reuben Hersh What can the Sociologist of Knowledge Say About 2+2=4?, DavidBloor. Post-Modernist and Post- Structuralist Approaches: Reasoning in a Post-Modern Age, Valerie Walkerdine Mathematical Writing, Thinking, and Virtual Reality, Brian Rotman. The Human Face of Mathematics: Mathematics and Art: Cold Calipers against Warm Flesh?, Philip J. Davis Different Ways of Knowing: Contrasting Styles of Argument in Indian and Greek. The Social Context of Mathematics and Education: The Social Life of Mathematics, Sal Restive.

  • constructivism the psychology of learning and the nature of Mathematics some critical issues
    Science Education, 1993
    Co-Authors: Paul Ernest
    Abstract:

    Constructivism is one of the central philosophies of research in the psychology of Mathematics education. However, there is a danger in the ambiguous and at times uncritical references to it. This paper critically reviews the constructivism of Piaget and Glasersfeld, and attempts to distinguish some of the the psychological, educational and epistemological consequences of their theories, including their implications for the Philosophy of Mathematics. Finally, the notion of ‘cognizing subject’ and its relation to the social context is examined critically.

  • The Philosophy of Mathematics education
    1991
    Co-Authors: Paul Ernest, Jean Paul Van Bendegem, Ole Skovsmose, Maria Aparecida Viggiani Bicudo, Roger Miarka, Ladislav Kvasz, Regina Moeller
    Abstract:

    This survey provides a brief and selective overview of research in the Philosophy of Mathematics education. It asks what makes up the Philosophy of Mathematics education, what it means, what questions it asks and answers, and what is its overall importance and use? It provides overviews of critical Mathematics education, and the most relevant modern movements in the Philosophy of Mathematics. A case study is provided of an emerging research tradition in one country. This is the Hermeneutic strand of research in the Philosophy of Mathematics education in Brazil. This illustrates one orientation towards research inquiry in the Philosophy of Mathematics education. It is part of a broader practice of ‘philosophical archaeology’: the uncovering of hidden assumptions and buried ideologies within the concepts and methods of research and practice in Mathematics education. An extensive bibliography is also included.

Daniel Leivant - One of the best experts on this subject based on the ideXlab platform.

  • finitism imperative programs and primitive recursion
    Foundations of Computer Science, 2021
    Co-Authors: Daniel Leivant
    Abstract:

    The finitistic Philosophy of Mathematics, critical of referencing infinite totalities, has been associated from its inception with primitive recursion. That kinship was not initially substantiated, but is widely assumed, and is supported by Parson’s Theorem, which may be construed as equating finitistic reasoning with finitistic computing.

Stuart Rowlands - One of the best experts on this subject based on the ideXlab platform.

  • special issue on history and Philosophy of Mathematics in Mathematics education
    Science Education, 2014
    Co-Authors: Victor J Katz, Uffe Thomas Jankvist, Michael N Fried, Stuart Rowlands
    Abstract:

    Although Science & Education has published papers specifically concerning Mathematics over the years—some quite significant for education—Mathematics has never received the spotlight. Indeed, when the journal was established it bore the subtitle, Contributions from History, Philosophy and Sociology of Science and Mathematics, but so few papers on Mathematics were received in those years that the word ‘‘Mathematics’’ was duly dropped. Yet within the community of science and Mathematics educators, there is no lack of interest at least in the contributions of history and Philosophy of Mathematics to Mathematics education, particularly the history of Mathematics. Besides publications such as those we have listed at the end of this introduction, one can point to the activities of the International Study Group on the Relations between the History and Pedagogy of Mathematics (HPM) which dates back to 1972, and which almost from the start became an affiliated study group of the International Commission on Mathematical Instruction (ICMI), the largest and oldest international organization for Mathematics education. International conferences of HPM have been held in Europe, Canada, Australia, Taiwan, Mexico, and Korea in association with the quadrennial International Congress on Mathematical Education (ICME). The European Summer University on History and Epistemology in Mathematics Education (ESU), now held every 4 years as well, is another regular venue for meetings dealing with history in Mathematics education, as is the working group on History in Mathematics Education at the biennial Congress of European

Steffen Møllegaard Iversen - One of the best experts on this subject based on the ideXlab platform.

  • ‘Whys’ and ‘Hows’ of Using Philosophy in Mathematics Education
    Science & Education, 2014
    Co-Authors: Uffe Thomas Jankvist, Steffen Møllegaard Iversen
    Abstract:

    The article elaborates and exemplifies a potential categorization of the reasons for using Philosophy, in particular the Philosophy of Mathematics, in Mathematics education and approaches to doing so—the so-called ‘whys’ and ‘hows’. More precisely, the ‘whys’ are divided into the two categories of ‘Philosophy as a tool’ for teaching and learning Mathematics, and ‘Philosophy as a goal’, referring to a stance of considering it a purpose in itself to teach students certain aspects regarding the Philosophy of Mathematics. A division of the ‘hows’ into three different categories is offered: illumination approaches; modules approaches; and Philosophy-based approaches. A major part of the article is spent on providing illustrative exemplifications of each of these approaches by referring to already implemented uses of Philosophy of Mathematics in Mathematics education as well as by suggesting new ones.