Special Issue "Philosophy and Education of Mathematics and Computing"

A special issue of Philosophies (ISSN 2409-9287).

Deadline for manuscript submissions: 18 August 2022 | Viewed by 3338

Special Issue Editor

Dr. Attila Egri-Nagy
E-Mail Website
Guest Editor
Mathematics, Akita International University, Akita 010-1211, Japan
Interests: computational semigroup theory; algebraic biology; artificial intelligence; philosophy of mathematics and computation

Special Issue Information

Dear Colleagues,

What is Mathematics? The question is as old as Philosophy itself. Is it a cognitive model, or reality itself? Despite thousands of years of discussion, we still do not know. Not that we have no idea, but we have many partial answers. Can we then stop asking the question? As long as we teach Mathematics, we cannot. What we think about a subject, admittedly or not, influences how we present it, how we teach it. For instance, latent Platonism led to a reader-unfriendly style of mathematical writing that removes any traces of failures or dead ends in the thinking process, only presenting the eternal truth. Therefore, adjusting our philosophical perspective may improve education.

What is computation? What do programmers really do? As if we had not enough trouble with the nature of Mathematics already, the rise of computers further complicated the picture. Computing devices appear to be mathematical engines at a low level, and they can look very different on higher levels. What is a computer then? Since we aim to teach programming to more and more people, the stakes are again high due to the educational considerations.

We invite thinkers who are tackling these issues from different perspectives and with a varied set of methods to contribute this Special Issue. Mathematics and computing keep changing; therefore, it is worth revisiting the fundamental questions.

Dr. Attila Egri-Nagy
Guest Editor

Manuscript Submission Information

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Keywords

  • mathematics
  • computing
  • philosophy
  • education
  • programming

Published Papers (3 papers)

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Research

Article
The Ontological Role of Applied Mathematics in Virtual Worlds
Philosophies 2022, 7(1), 22; https://doi.org/10.3390/philosophies7010022 - 21 Feb 2022
Viewed by 793
Abstract
In this paper, I will argue that with the emergence of digital virtual worlds (in video games, animation movies, etc.) by the animation industry, we need to rethink the role and authority of mathematics, also from an ontological point of view. First I [...] Read more.
In this paper, I will argue that with the emergence of digital virtual worlds (in video games, animation movies, etc.) by the animation industry, we need to rethink the role and authority of mathematics, also from an ontological point of view. First I will demonstrate that the application of mathematics to the creation and description of the digital, virtual worlds behaves in many respects analogously to the application of mathematics to the description of real-world phenomena from the viewpoint of the history of science. However, from other aspects, the application of mathematics significantly differs in this virtual world from the application to real-world fields. The main thesis of my paper is that the role of mathematics in the digital animation industry can be ontologically different from its usual role. In the application of mathematics to digital virtual worlds, mathematical concepts are no longer just modelling tools, forming a subordinated, computational basis, but they can direct and organise, and even create non-mathematical theory, something that we can call, for example, digital physics and biology. I will study this new, creative role of mathematics through some concrete phenomena, specifically through gravity. Our conclusion is that the animation industry opens an entirely new chapter in the relationship between (digital) sciences and mathematics. Full article
(This article belongs to the Special Issue Philosophy and Education of Mathematics and Computing)
Article
A New Model of Mathematics Education: Flat Curriculum with Self-Contained Micro Topics
Philosophies 2021, 6(3), 76; https://doi.org/10.3390/philosophies6030076 - 13 Sep 2021
Viewed by 747
Abstract
The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. [...] Read more.
The traditional way of presenting mathematical knowledge is logical deduction, which implies a monolithic structure with topics in a strict hierarchical relationship. Despite many recent developments and methodical inventions in mathematics education, many curricula are still close in spirit to this hierarchical structure. However, this organisation of mathematical ideas may not be the most conducive way for learning mathematics. In this paper, we suggest that flattening curricula by developing self-contained micro topics and by providing multiple entry points to knowledge by making the dependency graph of notions and subfields as sparse as possible could improve the effectiveness of teaching mathematics. We argue that a less strictly hierarchical schedule in mathematics education can decrease mathematics anxiety and can prevent students from ‘losing the thread’ somewhere in the process. This proposal implies a radical re-evaluation of standard teaching methods. As such, it parallels philosophical deconstruction. We provide two examples of how the micro topics can be implemented and consider some possible criticisms of the method. A full-scale and instantaneous change in curricula is neither feasible nor desirable. Here, we aim to change the prevalent attitude of educators by starting a conversation about the flat curriculum alternative. Full article
(This article belongs to the Special Issue Philosophy and Education of Mathematics and Computing)
Article
Traditional Logic and Computational Thinking
Philosophies 2021, 6(1), 12; https://doi.org/10.3390/philosophies6010012 - 09 Feb 2021
Cited by 1 | Viewed by 1121
Abstract
In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic [...] Read more.
In this contribution, we try to show that traditional Aristotelian logic can be useful (in a non-trivial way) for computational thinking. To achieve this objective, we argue in favor of two statements: (i) that traditional logic is not classical and (ii) that logic programming emanating from traditional logic is not classical logic programming. Full article
(This article belongs to the Special Issue Philosophy and Education of Mathematics and Computing)
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