Open AccessFrom Euclid's Elements to the methodology of mathematics. Two ways of viewing mathematical theory
Author(s) -
Piotr Błaszczyk
Publication year - 1970
Publication title -
annales universitates paedagogicae cracoviensis. studia ad didacticam mathematicae pertinentia
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.102
H-Index - 1
eISSN - 2450-341X
pISSN - 2080-9751
DOI - 10.24917/20809751.10.1
Subject(s) - mathematics education , meaning (existential) , focus (optics) , set (abstract data type) , simple (philosophy) , set theory , mathematics , epistemology , mathematical theory , mathematical practice , calculus (dental) , computer science , philosophy , physics , quantum mechanics , optics , programming language , medicine , dentistry
We present two sets of lessons on the history of mathematics designed for prospective teachers: (1) Euclid's Theory of Area, and (2) Euclid's Theory of Similar Figures. They aim to encourage students to think of mathematics by way of analysis of historical texts. Their historical content includes Euclid's Elements, Books I, II, and VI. The mathematical meaning of the discussed propositions is simple enough that we can focus on specific methodological questions, such as (a) what makes a set of propositions a theory, (b) what are the specific objectives of the discussed theories, (c) what are their common features.
In spite of many years' experience in teaching Euclid's geometry combined with methodological investigations, we cannot offer any empirical findings on how these lectures have affected the students' views on what a mathematical theory is. Therefore, we can only speculate on the hypothetical impact of these lectures on students.