ARITHMETIC APPROACH OR GEOMETRICAL ACCURACY? SPONTANEOUS CONCEPTIONS OF TWELVE YEARS OLD STUDENTS TOUCHING IRRATIONALITY

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Published: Oct 8, 2018
DOI: https://doi.org/10.12681/enedim.18837
Keywords:
spontaneous perceptions approximation of square root of a number arithmetisation of magnitudes transparent/non-transparent decimal represen­tation duplicating the square "Meno" irrationality illusion of linearity.
Γιώργος Κόσυβας (Giorgos Kosyvas)
Public Education
Abstract

In this paper, findings of a teaching experiment, carried out on 12-year-old stu­ dents are presented and discussed. Particularly, strategies and arguments con­ cerning the solution of the "doubling the square problem", are analysed, a prob­ lem which was presented for the first time in the platonic dialogue "Meno". This research focuses on the cooperative solution of the problem and the qualitative data used. Among the results the following are included: a) the illusion of linear­ ity:"ifwedoublethesideofαsquare,itsareaisalsodoubled",b)the numerical strategy: approximate estimation of the length of the side of the square followed by its construction and c) the geometric strategy: cutting the initial square, recon­ structing it, representation of a new square that has double its initial area and geometric construction. Geometry, in comparison with arithmetic, reveals spon­ taneous perceptions made by the students that lead to irrationality. Nowdays, geometric culture is on the decline, while excessive standardisation and arith- metisation could hurt the intuition. However, the geometric figure, as in ancient Greece, is a dynamic context, where the exactness of the length could support the comprehension of irrationality

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Author Biography
Γιώργος Κόσυβας (Giorgos Kosyvas), Public Education
School Cancelor
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