Approaching Euclidean proofs through explorations with manipulative and digital artifacts

Abstract

The combined use of origami and dynamic geometry software has recently appeared in mathematics education to enrich students’ geometric thinking. The objective of this research is to study the roles played by the interaction of two artifacts, paper folding and GeoGebra, in a construction-proving problem as well as its generalization in the Euclidean geometry context. For this, we designed and implemented two mathematical tasks with 52 secondary education students (15–16 years old, 10th grade) during the COVID-19 emergency lockdown period in Italy. The tasks involved four phases: constructing, exploring, conjecturing, and proving. This article presents an epistemic analysis of the tasks and a cognitive analysis of the answers given by one of the students. The theoretical tools of the onto-semiotic approach supported these analyses. Cognitive analysis allows us to confront the intended meanings of the task and the meanings actually employed by a student, thus drawing specific conclusions about the roles of such artifacts in written arguments and give an interpretation of their combined use in mathematics education.

KEYWORDS:

• Secondary education
• paper folding
• GeoGebra
• geometric task analysis
• onto-semiotic approach

Acknowledgment

This research is supported by the projects PGC2018-098603-B-I00 (MCIU/AEI/FEDER, UE), PFID-FID-2021-45 and by the group S60_20R-Research in Mathematics Education (Government of Aragón, European Social Fund).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by Ministero dell'Istruzione, dell'Università e della Ricerca (Italy) [grant number Com. study n.6064/Liceo Classico Stabili-Trebbiani].