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Logic and Foundations of Mathematics Commons™
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Full-Text Articles in Logic and Foundations of Mathematics
Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling
Recognizing Mathematics Students As Creative: Mathematical Creativity As Community-Based And Possibility-Expanding, Meghan Riling
Journal of Humanistic Mathematics
Although much creativity research has suggested that creativity is influenced by cultural and social factors, these have been minimally explored in the context of mathematics and mathematics learning. This problematically limits who is seen as mathematically creative and who can enter the discipline of mathematics. This paper proposes a framework of creativity that is based in what it means to know or do mathematics and accepts that creativity is something that can be nurtured in all students. Prominent mathematical epistemologies held since the beginning of the twentieth century in the Western mathematics tradition have different implications for promoting creativity in …
An Evolutionary Approach To Crowdsourcing Mathematics Education, Spencer Ward
An Evolutionary Approach To Crowdsourcing Mathematics Education, Spencer Ward
Honors College
By combining ideas from evolutionary biology, epistemology, and philosophy of mind, this thesis attempts to derive a new kind of crowdsourcing that could better leverage people’s collective creativity. Following a theory of knowledge presented by David Deutsch, it is argued that knowledge develops through evolutionary competition that organically emerges from a creative dialogue of trial and error. It is also argued that this model of knowledge satisfies the properties of Douglas Hofstadter’s strange loops, implying that self-reflection is a core feature of knowledge evolution. This mix of theories then is used to analyze several existing strategies of crowdsourcing and knowledge …
Wabi-Sabi Mathematics, Jean-Francois Maheux
Wabi-Sabi Mathematics, Jean-Francois Maheux
Journal of Humanistic Mathematics
Mathematics and aesthetics have a long history in common. In this relation however, the aesthetic dimension of mathematics largely refers to concepts such as purity, absoluteness, symmetry, and so on. In stark contrast to such a nexus of ideas, the Japanese aesthetic of wabi-sabi values imperfections, temporality, incompleteness, earthly crudeness, and even contradiction. In this paper, I discuss the possibilities of “wabi-sabi mathematics” by showing (1) how wabi-sabi mathematics is conceivable; (2) how wabi-sabi mathematics is observable; and (3) why we should bother about wabi-sabi mathematics
The Square Of Opposition: Innovations In Teaching Logic, Marc R. Dimartino
The Square Of Opposition: Innovations In Teaching Logic, Marc R. Dimartino
Senior Honors Projects
Teaching classical logic can often be challenging, especially when working with students who lack any prior experience with the more technical aspects of critical thinking. The abstraction of statements into logical symbols and the implementation of various diagramming methods can be enough to frustrate novice logicians, leading to a lack of hope and sometimes failure of mastery. The unique difficulties in teaching classical logic can, in addition, exacerbate tricky pedagogical issues that arise on a day to day basis in the critical thinking classroom. For example, it can be challenging to convey complex information in a meaningful way when dealing …