Drawings as External Representations of Children’s Fundamental Ideas and the Emotional Atmosphere in Geometry Lessons

Oct 15, 2026

Geometry’s presence in school curricula is often reduced, shifting focus toward computation and procedures rather than students’ competencies and classroom atmosphere. This multiple case study analyzed four students’ conceptions of geometry and their emotional atmosphere during geometry lessons at an individual level. Drawings were used as external representations of students’ geometric ideas and emotions. Results indicate a narrow understanding of geometry and largely frontal teaching with limited communication, while emotional atmosphere was described as positive or ambivalent. Implications address drawings as a research lens and its theoretical and practical value.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages23

Reading Time58 min

AccessFree to download

Introduction

Theoretical Background

Fundamental ideas in geometry

doi: 10.26529/cepsj.299 Drawings as External Representations of Children’s Fundamental Ideas and the Emotional Atmosphere in Geometry Lessons Dubravka Glasnović Gracin*1 and Ana Kuzle2 • The important role that geometry plays in the mathematics curriculum has been extensively documented. However, the reduction of geometry in school mathematics, and the focus on basic computation and procedures, raises the question of the competencies students acquire and the classroom atmosphere in geometry lessons. The goal of this multiple case study was to analyse four students’ conceptions of geometry and the emotional atmosphere in geometry lessons on an individual level. Drawings were used as external representations of the students’geometrical ideas and the emotional atmosphere. The results show that the participants have a narrow understanding of geometry, and that geometry teaching in their classrooms is reduced to frontal teaching with very limited communication. Nevertheless, the emotional atmosphere in these four cases could be described as positive or ambivalent. Based on the data, the results are discussed not only with regard to the utility of drawings as a research method to gain insights into students’ conceptions of geometry and emotional atmosphere in geometry lessons, but also with regard to their theoretical and practical implications. Keywords: drawings, emotional atmosphere, external representations, fundamental ideas, geometry 1 *Corresponding Author. University of Zagreb, Faculty of Teacher Education, Croatia; [dubravka.glasnovic@ufzg.hr](dubravka.glasnovic@ufzg.hr). 2 University of Potsdam, Faculty of Human Sciences, Germany. 32 drawings as external representations of children’s fundamental ideas and the ... Risanje v vlogi reprezentacij učenčevih temeljnih geometrijskih pojmov in prikazovanje doživljanja poukageometrije Dubravka Glasnović Gracin in Ana Kuzle • Poznano je, da ima geometrija v matematičnem kurikulumu pomembno vlogo. Po drugi strani pa je geometriji namenjenih bistveno manj ur v šolski matematiki v primerjavi z aritmetiko, pri kateri je ključno poznavanje postopkov računanja, zato se upravičeno postavlja vprašanje, vkolikšni meri učenci dosežejo cilje pri pouku geometrije in kako pouk doživljajo. Cilj naše študije štirih primerov je bil analizirati, kako učencirazumejo idejo temeljnih pojmov v geometriji in kako reprezentirajodoživljanje pouka geometrije. Učence smo spodbudili, da so oboje prikazali z risanjem oz. z grafično zunanjo reprezentacijo. Rezultati kažejo, da imajo učenci ozko razumevanje ključnih pojmov v geometriji in da je poučevanje razredih učencev, ki smo jih preučevali, omejeno na frontalno obliko z zelo omejeno komunikacijo. Ne glede na to bi lahko pri vseh primerih, ki smo jih preučevali, sklenili, da učenci doživljajo pouk geometrije pozitivno ali ambivalentno. Učenčeve grafične reprezentacijesmo analizirali z vidika vpogleda v učenčevo razumevanje izbranih geometrijskih pojmov ter doživljanja pouka geometrije pa tudi z vidikanjihovih teoretičnih in praktičnih implikacij za pouk matematike. Ključne besede: grafične reprezentacije, doživljanje pouka, zunanje reprezentacije, temeljni pojmi, geometrija Introduction In the past several decades, the overall amount of geometry in many national curricula has been reduced (Mammana & Villani, 1998) due to a desire to increase the coverage of other mathematical disciplines in school mathematics, such as numeracy and statistics (Jones, 2000) . These findings raise certain questions regarding current geometry education: What meanings do students assign to geometry? What geometrical concepts do they learn? What attitudes do they have towards geometry? Or more generally, what do geometry lessons look like today through the eyes of students? Interest in classroom activities and what is happening during lessons has many different components. Apart from mathematical dimensions, it encompasses grasping the social and emotio

FAQs

Why does the study focus on geometry education and classroom emotional atmosphere?

Because geometry instruction in school mathematics is often reduced and shifted toward computation, raising questions about what competencies students develop and how students experience geometry lessons emotionally.

How did the researchers collect data in this multiple case study?

The study used drawings as external representations of each student’s geometric ideas and the emotional atmosphere in geometry lessons.

What did the study find about students’ understanding and classroom communication?

Participants showed a narrow understanding of geometry, and geometry teaching in their classrooms was largely frontal with very limited communication.

Oct 15, 2026

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