Visokolskis, Sandra and Gerván, Héctor Horacio (2021) Applied versus Situated Mathematics in Ancient Egypt: Bridging the Gap between Theory and Practice. [Preprint]

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Abstract

This historiographical study aims at introducing the category of “situated mathematics” to the case of Ancient Egypt. However, unlike Situated Learning Theory (Lave 1988; Greeno, Moore and Smith 1993), which is based on ethnographic relativity, in this paper, the goal is to analyze a mathematical craft knowledge based on concrete particulars and case studies, which is ubiquitous in all human activity, and which even covers, as a specific case, the Hellenistic style, where theoretical constructs do not stand apart from practice, but instead remain grounded in it.
The historiographic interpretation that we will give of situated mathematics is inscribed in a characterization of mathematical styles that focuses on the role of mathematical practice (Visokolskis 2020; Visokolskis et al. 2020). This categorization describes three types of mathematization, where, on the one hand, type I represents the classical and dominant Hellenocentric approach, which seeks to generate a body of principles that could then be applied in other fields. On the other hand, types II and III represent two kinds of situated mathematics, a parametrized and a concrete one. Type II proceeds in the opposite direction from Type I describing an application of a previously obtained theory. That is, given a practice in any domain, it seeks to build a mathematical systematization a posteriori to explain said practice. Finally, type III starts from a concrete practice and develops another similar practice that explains analogically the relationship.
Based on the typology adopted, we seek to describe a case study within ancient Egyptian mathematics, which reveals how it is possible to subsume it in the two types of situated mathematization II and III. The foregoing will allow to bridge the gap between theory and practice.

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Item Type:	Preprint
Creators:	Creators Email ORCID Visokolskis, Sandra sandraviso@gmail.com 0000-0003-4221-902X Gerván, Héctor Horacio hectorg.horacio@gmail.com 0000-0003-3035-1701
Keywords:	Concrete situated mathematics, Parametrized situated mathematics, Ancient Egypt.
Subjects:	General Issues > History of Science Case Studies General Issues > Philosophers of Science General Issues > Science and Society General Issues > Social Epistemology of Science General Issues > Structure of Theories General Issues > Theory Change General Issues > Theory/Observation
Depositing User:	Dr. Sandra Visokolskis
Date Deposited:	03 Oct 2021 03:35
Last Modified:	03 Oct 2021 03:35
Item ID:	19621
Subjects:	General Issues > History of Science Case Studies General Issues > Philosophers of Science General Issues > Science and Society General Issues > Social Epistemology of Science General Issues > Structure of Theories General Issues > Theory Change General Issues > Theory/Observation
Date:	31 July 2021
URI:	https://philsci-archive.pitt.edu/id/eprint/19621

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