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

### Abstract

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.

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