@misc{10481/74149,
year = {2022},
month = {3},
url = {http://hdl.handle.net/10481/74149},
abstract = {Proof, a key topic in advanced mathematics, also forms an essential part of the formal
learning experience at all levels of education. The reason is that the argumentation involved calls for
pondering ideas in depth, organizing knowledge, and comparing different points of view. Geometry,
characterized by the interaction between the visual appearance of geometric elements and the
conceptual understanding of their meaning required to generate precise explanations, is one of the
foremost areas for research on proof and argumentation. In this qualitative analysis of the arguments
formulated by participants in an extracurricular mathematics stimulus program, we categorized
students’ replies on the grounds of reasoning styles, representations used, and levels of generality. The
problems were proposed in a lesson on a quotient set based on the similarity among triangles created
with Geogebra and the responses were gathered through a Google form. By means a content analysis,
the results inform about the reasoning style, the scope of the argumentation, and the representation
used. The findings show that neither reasoning styles nor the representations used conditioned the
level of generality, although higher levels of argumentation were favored by harmonic and analytical
reasoning and the use of algebraic representations.},
organization = {Spanish national R + D + I projects	PID2020-117395RB-I00
PID2020-113601GB-I00},
organization = {State Research Agency (SRA) from Spain},
publisher = {MDPI},
keywords = {Argumentation},
keywords = {Mathematical talent},
keywords = {Geogebra},
keywords = {Generalization},
title = {Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students},
doi = {10.3390/math10050789},
author = {Ramírez Uclés, Rafael and Ruiz Hidalgo, Juan Francisco},
}