The reflection on the long persistence of unsatisfactory results, has led us to upset the most common idea of fraction: fraction-of-something. To this, we have: (a) corrected the “primitive intuition” of fraction by constructing an “intuitive representation”, (b) set the familiarization of children with fractions as a goal, and (c) practiced the idea of fraction as megaconcept. In our enquiring we have focused on the Pythagorean statement: the comparison is a logos. This latter is like a modern act of mathematisation of the comparison and it is the starting point of our didactic practice. It has the following features: (a) it is imposed, (b) it is a leap, (c) it is elementary, (d) it is an axios, (e) it has the characteristic of resence/absence along the path towards the megaconcept.

Bonissoni, P., Cazzola, M., Longoni, P., Riva, G., Rottoli, E., Sorgato, S. (2019). Philosophical and Didactic Practice in the Universe of Fractions. Trace and Icon. In Proceedings of the Eighth European Summer University on History and Epistemology in Mathematics Education. Oslo.

Philosophical and Didactic Practice in the Universe of Fractions. Trace and Icon

Cazzola, M;Rottoli, E;Sorgato, S
2019

Abstract

The reflection on the long persistence of unsatisfactory results, has led us to upset the most common idea of fraction: fraction-of-something. To this, we have: (a) corrected the “primitive intuition” of fraction by constructing an “intuitive representation”, (b) set the familiarization of children with fractions as a goal, and (c) practiced the idea of fraction as megaconcept. In our enquiring we have focused on the Pythagorean statement: the comparison is a logos. This latter is like a modern act of mathematisation of the comparison and it is the starting point of our didactic practice. It has the following features: (a) it is imposed, (b) it is a leap, (c) it is elementary, (d) it is an axios, (e) it has the characteristic of resence/absence along the path towards the megaconcept.
paper
Familiarization, Megaconcept, Trace, Icon, Plurality of truth
English
Eighth European Summer University on History and Epistemology in Mathematics Education ESU 8
2018
Barbin, E; Jankvist, UT; Hoff Kjeldsen, T; Smestad, B; Tzanakis, C
Proceedings of the Eighth European Summer University on History and Epistemology in Mathematics Education
978-82-8364-211-7
2019
none
Bonissoni, P., Cazzola, M., Longoni, P., Riva, G., Rottoli, E., Sorgato, S. (2019). Philosophical and Didactic Practice in the Universe of Fractions. Trace and Icon. In Proceedings of the Eighth European Summer University on History and Epistemology in Mathematics Education. Oslo.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/251804
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