International Group for the Psychology of Mathematics Education (PME)

Proceedings of the International Group for the Psychology of Mathematics Education · Volume 1

From Manipulation to Construction: the Role of Semiotic Conversions in Bridging the Gap Between the Drawing and the Figure

Eleonora Faggiano, Roberto Capone

University of Bari Aldo Moro

49th Annual Conference of the International Group for the Psychology of Mathematics Education, PME 2026Helsinki27 July 2026 - 1 August 2026pp. 419–426ISSN 2790-36482026Scopus conference code 336559
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Abstract

To address the persistent gap between the drawing (perceptual) and the figure (theoretical) in geometry learning, we examine how a four‑phase sequence, implemented with 20 undergraduates, based on the synergy between manipulative and digital artefacts, supports robust construction in Dynamic Geometry Environments. We integrate Duval’s semiotic registers and the Instrumental Approach to investigate how an intermediate writing instructions task triggers semiotic conversions from perceptual to verbal register and impacted on instrumental genesis: students who identified functional dependencies developed robust schemes of use that withstand the drag-test, while perception-based approaches led to “soft” constructions, confirming the connection and underscoring the teacher’s role.

Keywords

Synergy between artefactssemiotic conversionsinstrumental approachrobust constructionsDynamic Geometry Environment

Recommended citation

Faggiano, E., & Capone, R. (2026). From Manipulation to Construction: the Role of Semiotic Conversions in Bridging the Gap Between the Drawing and the Figure. In Krzywacki H., Hähkiöniemi M., Haataja E., Hannula M.S., Hästö P. (Eds.), Proceedings of the International Group for the Psychology of Mathematics Education, Volume 1 (pp. 419–426). Psychology of Mathematics Education (PME). ISSN 2790-3648.

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