Operationalising duval’s geometrical figure apprehension : teacher professional development and assessment of students’ geometric reasoning

Antunović, Branka (author), Manfreda Kolar, Vida (author)

Understanding geometric figures requires the coordination of visualisation, construction, and reasoning processes. While Duval’s framework of geometrical figure apprehension (GFA) has been widely discussed, limited research has examined how it can be operationalised in teacher professional development and systematically assessed in students’ learning. This study investigates the effects of a teacher professional development programme grounded in Duval’s GFA and introduces a newly developed assessment instrument designed to measure students’ coordination of apprehension types. A quasi-experimental design was employed with 88 seventh-grade students and four teachers from Croatian primary schools. Data were collected through pre- and post-testing using an eight-task instrument and analysed with non-parametric statistical methods. Results show statistically significant improvements in the experimental group compared to the control group, particularly in the overall coordination of perceptual, sequential, discursive, and operative apprehensions. The findings indicate that structured teacher support and targeted task design positively influence students’ geometric reasoning. The study contributes by demonstrating how Duval’s theoretical framework can be operationalised in classroom practice and by providing a validated instrument for assessing geometrical figure apprehension in school geometry.

• Language: English
• Keywords: assessment instrument, Duval’s framework, geometrical figure apprehension, geometric reasoning, geometry teacher professional development
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: PEF - Faculty of Education
• Publication status: Published
• Publication version: Version of Record
• Year: 2026
• Number of pages: Str. 871 - 890
• Numbering: Vol. 15, iss. 3
• PID: 20.500.12556/RUL-182212
• UDC: 373.32.016:51
• ISSN on article: 2165-8714
• DOI: 10.12973/eu-jer.15.3.871
• COBISS.SI-ID: 276562435
• Publication date in RUL: 04.05.2026

Record is a part of a journal

• Title: European journal of educational research
• Publisher: R. Ulker
• ISSN: 2165-8714
• COBISS.SI-ID: 19227400

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: Duvaleva teorija, geometrijski liki, geometrija, ocenjevanje znanja, izobraževanje učiteljev, učenci, matematika, osnovnošolsko izobraževanje